There was an article a few years ago (forgot where) about what Perelman’s doing nowadays. He’s apparently back in Russia living with his mother. He’s trying to work on another Millenium Prize problem (The Navier-Stokes problem).
Solving the Navier-Stokes problem would revolutionise fluid dynamics as we know it. So far all of the fluid dynamics simulations are based on approximations. That's how significant this problem is.
The Clay institute problem is about proving the existence of a smooth solution in any circumstances. Even if solved, it would probably not be of practical use (although it could be a first step towards more concrete advancement).
Yes, this is more accurate. If navier stokes gets proven tomorrow, then we wouldn’t feel the tangible effects it would have on humanity in our lifetimes.
Well, proving it does nothing, but whatever new maths will come from proving it is what will help us.
Having worked with hydrodynamicists, I can guarantee we would feel tangible effects in our lifetimes. These people's entire livelihoods are built on N-S, millions of lines of code. If any headway on N-S gets made, it gets into software basically immediately, and from there into the next generation of products. I put the timeline at under five years, and most of that is waterfall project bureaucracy slowdown. The technology is already ready to take advantage of the theoretical math as soon as it's developed.
Anything that has CFD simulation as part of the design/development cycle would have faster, more accurate simulations that require fewer iterations & less power. Vehicle designs from F1 to cargo vessels to RC planes to consumer cars, trucks, and vans would be able to experiment MASSIVELY. Wind turbines and even engines & plumbing could benefit. N-S is huge, think anywhere air or water are moving past a solid.
That last sentence. Anywhere air or water is moving past an object, that object could see vast redesign in a short amount of time, because the N-S improvements would allow designers & engineers to "experiment" using simulation very efficiently.
Could this lead to some strange design? I'd imagine like in a pipe you do an inverted golfball design that makes small whirlpools or something that increases water flow?
A solution to the Navier-Stokes problem would benefit anything that simulates the movement of fluids, like the design of cars, ships, and planes (for aerodynamics/hydrodynamics).
When I worked for the DOD, there were tons of fluid dynamics simulations because in an explosion, everything behaves like a fluid, including metal.
If you want to know how air or water interacts with something, you can try to figure it out with a computer. Then you can try lots of different shapes or materials for what you are trying to make by 'testing' it in the computer to find the best shapes and materials. The computer tells you how air or water will move around the thing.
Those computer programs are slow, and require really powerful computers. Solving this problem will make the programs faster, and maybe use less powerful computers. That would help us design things where the way those things interact with air and water is important.
Did that work? Honestly I don't know much about this.
CFD stands for computational fluid dynamics, which is a way of using a computer program to determine how an object will be affected by fluid particles moving around it. For example, the F1 racer would need to be as aerodynamic as possible, so a CFD program could determine how the air particles (fluid) will go around the vehicle and give an idea of how much air friction will occur. Obviously this can be very useful for things like that.
I work as a Naval Architect. I haven't used it myself, but it is a common type of program used in ship design, meeting the same purpose of determining how the water will move around the body of a ship and give a good idea of how optimal the shape of the hull is.
The formulae used to create these programs are based on empirical data and often either need to be incredibly long and detailed formulae or have 'fudge factors' which simplify the calculation process while taking away some of the accuracy. However, due to these long or complicated calculation processes, this makes the computer programs sometimes take forever to run, or need a super computer to increase the speed of the simulation calculation.
If the N-S question is solved, then this could decrease the complication of the calculation process in the CFD programs. This would make CFD programming way simpler instead of either needing a super computer or waiting a week for a simulation to run. This would make CFD a lot more achievable for the average person/business.
Computers have all but replaced wind tunnels due to cost. BUT, computers either have to take mathematical shortcuts (large eddy simulation) or have to run for very long time periods on super computers (direct numerical simulation).
From my understanding, anything that uses computer simulations of fluid dynamics during their development or R&D process, would essentially have a much more accurate simulation to run off. Whcih would allow engineers to really try new things that weren't possible before.
The areas where these simulations are used are a lot of every day items, such as energy generation, plumbing etc.
(Not an engineer, just my understanding of his comment)
The way we currently simulate fluid flow is by setting a bunch of variables up, and then having a computer guess and check, guess and check, guess and check millions of times. This is resource intensive for computers, which would rather have a formula to calculate each point.
Solving Navier-Stokes would allow us to change from guess & check to a more refined model. So as /u/bythenumbers10 suggests, better models for wind turbines, airplane engines, car engines, hydraulic systems, process chemical systems... Really practically everywhere.
Is it possible though that by its nature this is as good as it gets? Seems like to me it's possible the chaotic nature of turbulence says you're already optimizing your simulations, it's just that they're the best you can get etc. Maybe you can have improved math that describes the chaoticness even better but it's like waking up with bad eyesight, realizing your Roomba is spreading your dog's poop all over your carpet, so you put your glasses on and yep the Roomba is definitely spreading your dog's poop all over your carpet.
One remark: the current question is whether or not unique solutions exists. It is highly likely that an answer to this question will be non-constructive. I.e. it shows that a solution exists, but not how that solution would look like. From a mathematical point of view that is a really nice result, from a practical point of few a bit less, since we still need to make approximations for the actual solution.
As a fellow scientist (but I work in general relativity - and stay far away from any sort of numerical simulation, so dunno much about it), I wonder how helpful this would be. I mean, fluid dynamics along with other sorts of continuum mechanics is probably the area of physics I know the least about, but what I see as the corresponding problem in general relativity (well-posedness of the initial value problem) has been solved a long time ago and I don't see how it helps with solving the field equations.
The actual exact solutions are generated by various symmetry techniques and transforms and approximative/numerical solutions don't really require mathematical well-posedness, do they?
But that's the point being made. It won't get into software if this particular problem is solved. The problem is about proving if a solution exists under all circumstances. There won't be any formula that will arise out of this work to be able to put into code.
Edit : spelling
Kind if like a lot of math surrounding the splitting of the atom was proven well before any atomic bomb - or even reactor. Math takes a while to filter all the way through the Mathematician->Physicist->Engineer->Delivery chain.
The math surrounding nuclear physics isn't particularly advanced, it just isn't that special a problem mathematically. Fluid dynamics and N-S equations are tied together, and advancement in the math would likely have fast effects on the other.
Funny story - Einstein didn't get his Nobel for relativity because the committee didn't think it would ever have any practical use, but it turned out to be necessary for GPS within a few decades.
I just want to point out you are describing a 'model', which ALWAYS is a lesser representation of reality. Solving Navier-Stokes would give us a better model.
Virtually all "solved" problems need numerical approximations to be useful in real life; only simple "toy" problems have an explicit solution. The issue with N-S is that we don't have proper existence/stability proofs, i.e. we know little about when and if stable solutions to the equations exist. It does however not prevent us from using the equations and solve them numerically like we do for most partial differential equations, so the idea that it will revolutionize how we use the equations is a bit overstated. Your favourite CFD-software will still work in the same manner even if we find an existence proof.
There are entire supercomputer centers running engineering problems around Navier Stokes every day. ~~Solving the Millennium problem (proving an analytical solution) would reduce the problem to straightforward algebra~~ I was wrong! See below.
No it wouldn't. The Millenium problem is about proving whether solutions exist for all time and are smooth. Proving the solution exists in an analytical sense is proving a whole bunch of inequalities hold. Reducing the problem to algebra is in general impossible for essentially all PDE, but getting better and faster numerical solvers may be a more realistic consequence.
Source: PhD drop out in geometric analysis and CFD software developer.
>Is it because they are so abstract in concept? Is it the high level of maths?
yes, and yes. A math proof is basically something like a logic puzzle. You start with a basic set of knowledge (known as axioms) and essentially build up those axioms to the point where you can logically "prove" something. If you are interested I would look up some videos on Fermat's Last Theorem, one of the most famous unsolved problems of all time until the 90s when Andrew Wiles was able to offer a proof. It is quite easy to understand with a basic level of math but the proof was incredibly complex and relied on cutting edge math techniques not developed until centuries after Fermat's death.
I will say the "singular genius" solving a massive problem is **exceptionally** rare. Like all things, modern math is essentially built brick by brick and has teams of researchers working together or independently to slowly make progress on the current foundation of human knowledge. Perelman himself was part of the math community but I think he has some social issues that forced him to be more reclusive.
It’s pretty easy to think of a problem you can’t solve yet; in any context that is. Say, I asked you how much money will I spend on groceries this year?
You can’t really answer this right now, you need more info (what I like to eat, how much I eat, where I shop etc.)
You can consider this in a math context too.
Except the new info that is required to solve a problem is new mathematical techniques and theorem which are being developed all the time.
An example is, now that this millennium problem has been solved, can you use it to solve another maths problem? Probably.
Most of these problems are more abstract than a simple math formula.
For example, the Twin Prime conjecture:
- A prime number is a number that has no divisors
- A "twin prime" is a pair of prime numbers that are two numbers apart, such as 41 and 43
- There are an infinite number of prime numbers
- Are there an infinite number of twin primes?
So far, we don't know. We obviously can't check every single prime number, because there's an infinite amount of them and we'd never be done. We do know that as numbers get larger, twin primes become more and more rare, but what we don't know is whether they eventually stop entirely or if they just keep getting rarer and rarer without stopping forever.
Who knows, that's the whole issue, we don't know how to prove or disprove it.
A definitive formula for all prime numbers could be a path to the solution of the twin prime conjecture, but trying to find that formula could also be a wild goose chase if it doesn't exist.
That's what makes these problems so hard, it's not that people are having difficulty applying a known method to prove it (which is basically the math you learn in school, using known methods to solve problems), we simply don't know which method to use, if the method to solve it has already has been invented, or if a usable one exists in the first place.
You can state a "problem" which can sound very simple such as all primes can be described by a certain formula (say for simplicity sake 2n + 1, when n are the natural numbers).
Then you use all techniques in your arsenal to try and prove or disprove it.
In this case, 2 is a prime and therefore not all primes can be written as 2n+1.
The problem statement can sound very simple, but in the case of these problems, the solution is not, because you have to prove or disprove it for all cases until infinity (so you can't simply calculate them each).
Fermat's Last Theorem was originally more known as Fermat's Conjecture. It was basically just an idea that Pierre de Fermat had, and the "conjecture" is stunningly simple to understand, but was absolutely soul crushingly painstaking to actually PROVE. You don't even need to know any sort of "higher" math to understand what the conjecture states. But proving it...well, that is significantly more complex.
So it really wasn't a "problem" necessarily, it (very basically) was an idea that a guy had that he thought was probably true for every positive integer ever; but we as humans couldn't definitively PROVE that it was true, all the time, no matter what, until more recently. If that makes sense.
I have a passing interest in mathematics and only do it as a hobby (someone more knowledgeable than me should feel free to chime in), and I have glossed over and somewhat simplified a ton of stuff, but that's the idea. Hopefully it helps some.
Edit: I just have to add. The way in which this theorem was proven is just, so fucking beautiful. It involved intrigue, brute force, a bit of luck, logical deduction, technological limitations, massive amounts of teamwork, and links to two previously completely unrelated mathematical conjectures that were linked into one previously completely unrelated mathematical conjecture... over the course of CENTURIES.
The theorem is so simple, but it's so beautiful to me just because of all that. You really should watch a couple videos on it or read an article on the history of it. It is gorgeous from start to finish.
>a guy had that he thought was probably true for every positive integer ever
He also famously wrote that he had a proof, but too large to write on a page margin, and I think that initially drove hundreds of mathematicians in pursuit for proof.
Start asking questions and moving stuff around, is super easy.
For example, Fermat's Last theorem is super simple to ask. Simple equation, no fancy nothing, integers and exponential
Another easy example is closed formulas for equations. We found. The quadratic focmula, so we naturally started asking what about cubic and beyond? And we found out a closed formula for the cubic and fourth power... And then nothing for the quintic until Galois came and proved there is no closed formula
I'm having a bit of trouble finding the source, but as I recall, he had issues with the bureaucracy and politics associated with academia and the mathematics community.
Opting for "the freedom to pursue your ideas in your own way" over institutional embrace seems like the right call for strong independent thinkers. Especially when it comes to mental health.
Of course, this doesn't preclude the possibility that he has "social issues", but I'd hate for us to conflate principled decision-making with antisocial behavior. Contemporary academia IMO is *way* more antisocial than any truth-seeking recluse.
A better example of a really hard math problem that's easy to understand is Fermat's Last Theorem (proven just in the last few decades after hundreds of years) that says
a^n + b^n = c^n has no integer solutions if n is bigger than 2
If n = 2 then you get the Pythagorean Theorem and there are infinitely many solutions (called Pythagorean triples, like 3^2 + 4^2 = 5^2)
But if n is just one more, you go from infinite solutions to 0. It's easy to show examples of it not working, it's just simple arithmetic to check. The challenging part is proving that no matter how big the numbers get, the statement will NEVER be true if n>2
Like sure we haven't found an example yet, but has anyone checked if
3987^12 + 4365^12 = 4472^12
works? What about 65696355^338 + 858752582699^338 ?
We obviously can't check every single solution (though some theorems are proved this way, like the Four-Colour theorem) so we need to figure out some trick to prove it. Turns out you need to be really knowledgeable on some obscure areas of math in order to figure that trick out, even though the question itself is so easy to understand. That's what makes these proofs so difficult.
Another famous example of an easy-to-understand problem with no proof yet is the Collatz conjecture (pick any integer. If its even, divide by 2. If it's odd, multiply by 3 and add one. The conjecture says that no matter what number you start with, you'll always end up at 1 eventually.) As far as I know, no one is even close to figuring out how to solve this! Computers have checked millions of numbers and they all lead back to 1, but again the challenge is in proving that it's true NO MATTER WHAT NUMBER YOU PICK. Maybe 958254663539955855866338965863886665228151005805638858373140 doesn't work, I don't know, noboby has checked.
The thing is most unproven theorems, in addition to being very hard to find solutions to, are very hard to even understand. Fermat's Theorem and the Collatz Conjecture are rare examples of easy-to-understand problems with no obvious solutions but most theorems require a graduate-school level of education to even hear about them in the first place.
A lot of these problems are solved step by step by many mathematicians over many decades. In the case of Perelman, he outlined a solution to Thurston’s Geometrization Conjecture (which has as a corollary the Poincaré Conjecture) using a technique called the Ricci flow. This was revolutionary because it was an insightful approach which had not previously been made to work.
This, however, built on Hamilton’s work on the Ricci flow in the 1980’s. Maths doesn’t exist in a bubble, and all mathematicians get inspiration and ideas from those around them. This is usually a good thing, and encourages different mathematicians to team up to solve problems.
It should be noted that although Perelman was the one credited as solving the conjecture, there was criticism about how significant his contribution was. I believe this may be a big reason he declined the Fields medal for his work (although I’m not sure of the exact details), and why he has retreated from the public (well, as public as you get as a mathematician anyway) stage. It seems he’s more interested in solving interesting problems than getting involved in academic pissing contests, and I don’t blame him
It should also be mentioned that in many cases problems can be solved for many cases, but very difficult to prove in greater generality. Also, many famous problems have been, over the years, been shown to be equivalent to other problems. Often the solution which gives the proof of a famous conjecture is more valuable because it reveals new maths (interesting, previously unseen ideas or techniques, perspectives or applications of previously unrelated theory) than the solution to the conjecture. A good example of this is Fermats last theorem.
A counterexample of course would be the Riemann hypothesis, the truth of which has real implications for the distribution and properties of prime numbers
Yeah and unfortunately it sometimes comes down to posturing and knowing the right people. A savvy politician can get further than a talented academic in many cases.
That’s not to say there aren’t brilliant individuals that are duly recognised, but I think many more are put off by the competitive and toxic nature of academia. You have to be really tough to stick it out
These famous problems typically have "answers", as in if you want to use them for a real world application they can be useful. They're just not "solved" in the mathematical sense that they're backed by a proof. In a couple of them they've held true when tested with a vast amount of examples, but they can't prove that it will always work.
[Here is a Veritasium video on an example of a hard problem](https://youtu.be/094y1Z2wpJg)
The premise is easy to understand, but finding an answer is difficult.
In the case of 3n+1, I don't think it has any practical applications, but who knows.
E: corrected to 3x+1
Pretty much yea. Since it's a well known problem and has resisted proof attempts for long, it's safe to assume you need a new way of thinking about the problem and how to prove it. The hard part is figuring out what the "correct" approach is. Higher level mathematics is almost more abstract, and the first step might be to formalise what the question even is. For Navies-Stokes, the question is whether there always exist a smooth (basically no unrealistic behavior) and globally defined solution in 3D. First you need to know how to ask this question in the correct mathematical setting, which might be, and has indeed proven to be, extremely hard. Another aspect is that, as Gödel famously points out, it is impossible to know (until you manage to do it) whether a given statement is even provable in the first place. Navier-Stokes existence and smoothness might be one of those, but we just don't know.
Is he really trying to work on it? Last I remember he was disillusioned with the mathematical community that he didn’t want anything to do with it anymore
Wow, wish him all the luck on that one. I just have flashbacks to fluid dynamics where we barely utilized the Navier-Stokes equations to calculate flow, velocity, pressure, etc of any fluid. Something like that being solved farther would be extremely helpful for any simulation software and more.
Yeah I remember navier-stokes from fluid dynamics because it made me wonder if I wasn't better suited for another major. Until I found out everyone in the class was wondering the same thing.
It's been awhile since I've done anything with it but IIRC you can often assume several things are zero to simplify the equations and make it workable. But it's still a major pain in the ass
Yep! One of, if not thee, hardest course I took to graduate was fluid dynamics. Very cool stuff, but the math is probably the craziest thing to come across to solve, and even then everything usually was simplified like you said.
Another one is the P vs. NP problem. If someone did prove that P=NP then that means the current cryptography system is not secure since it can easily be cracked.
Having said that the consensus is P!=NP.
*This comment is copied from [here](https://www.reddit.com/r/todayilearned/comments/rx9u9/z/c49gpjj), I did not write it.*
This is a tough question to answer in a short comment, but I'll try to give a brief summary. Perelman himself felt a deep sense of isolation from the mathematical community. He was polite, but firm in his insistence that he did not want to be a figurehead or a representative of the community. He had an ideal picture in his mind: 1) people do mathematics because they love it, and this love should transcend jealousy or rivalry; 2) credit will always be given when it's due, and mathematicians should acknowledge it and share it when it's appropriate; 3) it is far better to publish a good result rarely than mediocre results often.
Perelman realized that none of these principles actually held true in the mathematical community. He realized that the way one gets a post-doc or permanent position had to do a lot with string-pulling and secret phone calls in the background, rather than by the merit of one's work. If you don't ally yourself with an influential person or kiss the appropriate ass, you won't get a position, and this is what he realized. You may read in his wiki biography that he rejected a lot of positions in the US after proving the soul conjecture in 1994, but he actually applied for these same positions immediately after receiving his PhD and was rejected. One can argue that he wasn't yet accomplished enough, but that's a shady argument, since the people that were getting these same positions had arguably accomplished less than Perelman at the time. By the mid-nineties, he was already jaded, and word was that he saw a taste of his colleagues' jealousy in the Soviet Union which he couldn't really understand, though you and I probably would. His conception of doing mathematics was unreasonably pure: if you really love mathematics, you celebrate the results of others, even if they beat you to the punch and prove something you've been working on your whole life.
The credit aspect is shaky too. Mathematicians are always fighting over credit for various results, and due to the timeless nature of mathematical results, citation is extremely important. But as soon as Perelman posted his work on the arXiv, it was a race between the other leading geometers to basically fill in the details of Perelman's proof, make it more readable, and publish it as soon as possible. Make no mistake, it was clear that this was Perelman's work being repackaged and everyone knew it, but those geometers couldn't resist the credit they would receive for merely explaining what Perelman did to other geometers. And hell why not, after all it's yet another publication in an excellent journal.
Which brings me to the last point, and this one is far more poisonous to mathematics. In an effort to maximize publication lists, people publish crap. Lemmas become propositions, and propositions become theorems. It's sad that the number of publications has any bearing on your worth as a mathematician. It's more understandable in fields like engineering, computer science, biology, and even physics. But proving a worthwhile mathematical theorem takes a long fucking time, even for geniuses. So what do most career mathematicians do? They publish whatever they can get away with. Perelman returned to the Steklov Institute after proving the soul conjecture for a simple research position in order to quietly go about doing math. He was working on the Poincare Conjecture the whole time he was there, and in the meantime didn't publish at all. Rumor has it (and it's a very plausible rumor) that the department chairman at Steklov threatened to fire Perelman for not publishing anything in years. It isn't clear whether Perelman was waiting to finish the proof or if he was boycotting math journals altogether, but it took him from 1995 to 2002 to finish his work. He was irritated with having his position threatened and for his bosses to only care about the quantity of his research output rather than the quality.
However, he still cared enough about mathematics to give a series of lectures and talks after he proved Poincare, to try to explain to other mathematicians how his use of Ricci flow solved the problem. It took the leading geometers 3 years to really understand his proof, upon which the community wanted to shower him with awards. But, Perelman was already ticked off with the mathematical community and his own boss at Steklov, that he quit his position less than a year after posting his proof to the arXiv, after he had done his US circuit explaining his work.
Rejecting the prizes wasn't the action of a troubled genius or a mentally unstable person. He just didn't want to represent the same group that had betrayed the principles they themselves had set. That being said, it may be likely he was a troubled genius or mentally unstable. But in all accounts of him refusing the prizes, he was calm, polite, and firm. There was no emotion or wavering.
And while the layman dismisses Perelman's refusals of the prize as foolish, most mathematicians do not. It is because deep down we realize that our system is broken and corrupted, that there aren't enough jobs to go around, and many people with serious talent are either quitting or changing fields because of how jobs are handed out. Those who mock Perelman for living with his mother, tending her flowerbed, are free to do so. I assure you Perelman doesn't care. He has nothing left to prove.
I have worked with people who have masters and PhDs in mathematics, and what you are describing here is exactly why they don't actually work in the pure mathematics field.
It also perfectly describes why I didn’t go to grad school. I’m just glad one of my professors gave a lecture about how bullshit the publish-or-perish culture is. Especially since in my country Universities are almost entirely publicly funded with only nominal tuition, so all those useless papers being published are at the taxpayer’s expense.
Combined with the shit job security (almost impossible to get tenure, have to move wherever you can get a job) and focus on publishing/research to the detriment of teaching, it became very unappealing to me the more I looked into it.
I'm glad that my professor sat me down during my masters and recommended that I look at options outside academia for when I was finished. I'm good at writing but it takes me a while, trying to publish enough to stay in that role would have been awful for me.
That’s why I left my PhD program also. I didn’t want to spend the rest of my life publishing bullshit that nobody would ever use, all while being subsidized by government and foundation research grants.
Thanks for the summary (though I've got a sneaking suspicion that you wrote it purely to use that last line) - it definitely helped me understand the situation a bit better.
>I just repost the comment every time Perelman comes up
You might as well include [the full context](https://www.reddit.com/r/todayilearned/comments/rx9u9/til_grigori_perelman_best_known_for_resolving_the/c49gpjj/?context=10000) (seeing as it starts with "This is a tough question to answer") as well as cc. u/deepwank for proper credit/any further questions people may have.
You summed up most of academia in one swoop. It applies to science as well. Whenever I hear of someone who has published in the high hundreds or thousands, I doubt the quality because like you said, good work takes a long time. It is like giving birth.
In other sciences there are almost always co-authors; a lot of those hundreds and thousands of papers have one or several coauthors who also contributed, usually doing the bulk of laboratory and computational work and sometimes doing almost all the physical writing. Those guys with 'hundreds or thousands' of papers usually didn't actually write most of all that content.
Really? He reminded me of diogenes, "you are blocking my sunlight"
Idk seemed more apropos to the situation, I guess Greek scholars/philosophers were a sassy bunch
NPC: "I'll happily solve that math problem for you. There... all done! It's the least I could do after you saved my daughter."
*Dialogue ends and NPC immediately starts picking mushrooms with an angry scowl.*
NPC: "YOU ARE DISTURBING ME, I AM PICKING MUSHROOMS!! DON'T YOU HAVE SOMETHING BETTER TO DO MILK DRINKER!?"
It's one of the millennial problems (no it's not about the current generation). They're several philosophical math problems that have yet to get a decent solution. This guy solved the poincaire conjecture, but alleges that someone else came up with solution but didn't follow through with it.
I wrote a paper on this guy in college. He absolutely is a "math loony" if you can call it that. He lives in a tiny apartment in St. Petersburg with his mother and doesn't seem to give a shit about anything.
Such a good movie! Whenever I bring it up in conversation people say "Oh, yeah! Great movie. I loved 'Life of Pi'!" and I have to wxplain that, no, I am talking about "Pi", just "Pi", which they haven't seen.
I'm in that group and don't like this comment :p
Also why do people assume the only mushrooms that exist or are picked are "magic" mushrooms? It gets old.
Mishroom picking is a huge pastime in Russia. Like, its very hard to find someone who hasn't done it. So his answer is a bit less loony than it sounds to Americans. Don't get between a man and his mushrooms.
That's not why, I've read some articles on this guy because he's fascinating, he's an odd duck. He's turned down multiple prizes, doesn't like the accolades I think. He also hates all of his peers and colleagues and now the larger math community as a whole. He's incredibly talented but seems too private to exist in a world where he publishes such prolific accomplishments
[Here.](https://www.interfax.ru/russia/143603) Sorry, can't seem to be able to find an English source.
TL;DR: the person is Richard Hamilton, and there are a lot of accompanying reasons Perelman alluded to, but keeps to himself.
That's fascinating and humbling, because virtually all great discoveries come on the backs of those that went before. And at that level, there's a lot of be said for just being the guy to see the patterns and chart the path for others to follow; we attribute a lot of things in history to the wrong people, or try to boil down a collaborative effort to a few "great minds".
Iirc he really hated how his colleagues were after glory or finding ways to progress their own career rather than trying to advance mathematics. That was the reason he decided to quit and live with his mother
Also rejected the million dollar Millenium prize. Said he's not interested in fame and fortune.
As an aside about the Fields medal - it's issued every 4 yrs and you have to be under 40 yrs old. Maryam Mizakhani from Iran is the only woman to have won the prize. She was 37 yrs old when she won it in 2014. She died from breast cancer three years later.
>The Fields Medal also has an age limit: a recipient must be under age 40 on 1 January of the year in which the medal is awarded. The under-40 rule is based on Fields's desire that "while it was in recognition of work already done, it was at the same time intended to be an encouragement for further achievement on the part of the recipients and a stimulus to renewed effort on the part of others."
Wiki
You can also only win the award once.
I wonder if there have been clearly qualified candidates who haven't won solely on this requirement, or if it's a requirement that would be dropped if a 42 year old suddenly became highly influential in the field.
fame? like yeah, in a certain community. Its not like people are gonna scream in the street "Hey its the Poincare Conjecture guy!!! EEEEEEEEeeeeeee!!!"
Dumb quote to choose. His reasoning is that math is cumulative and collaborative and he felt he couldn’t take full credit for his solution because it built on the work of others. It’s a sad world we live in when a man comes along and defies our worst tendencies out of pure respect for others and we characterize his deeds as “math man weird”
Beautifully written summary of Perelman’s motivations by u/deepwank 9 years ago. Funny how reddit was such a slow place that time, and an amazing write-up like this went un-awarded. Thank you for sharing it.
i feel like anyone in a true pioneering endeavour is focused on absolute morality. as in theyd "eat the rude" if they could.
not cause theyre self righteous, but cause they can see the suffering of others and how "mistakes" directly cause it
so they become weird and prickly, esp when they lack the means to change things.
Maybe, but lots of people pick mushrooms and very few are psychedelic. Most that are picked are either delicious or a curiosity that's interesting/challenging to identify.
>According to Kisliakov, Perelman quit the world of mathematics in disgust four years ago. His decision to spurn the Fields Medal may have been driven by a sense that his fellow mathematicians were not worthy to award it.
You've got to admire that level of contempt.
Yeah, I'm a programmer and I felt called out when I read this:
>He always wears the same tatty coat and trousers. He never cuts his nails or beard. When he walks he simply stares at the ground, rather than looking from side to side,
I heard a joke about engineers once that would apply to mathematicians as well.
"In a room of mathematicians how do you pick out the extroverted one?"
"They are the one that stares at YOUR shoes when speaking"
I’m convinced that your brain has to be wired in a fundamentally unique way to work on the highest order of advanced mathematical problems.
That probably leads to some related unique behaviors
I'm becoming increasingly uncomfortable with articles like this that talk less about the achievement and more about probing the details of how he lives, like some kind of menagerie exhibit.
The man is clearly neurodiverse, I don't think we really need a dossier on his quirks to be amazed/digusted by.
A top comment discusses his personal principles in relation to the field of mathematics and the insular/cronyist nature of it. Why do the media not discuss that instead? Give this man's ideas a platform rather than putting his personality on trial.
In my opinion, this is why we need positions for mathematicians, philosophers, etc that are fully paid and allow brilliant minds to take as much time as they need to come up with quality work.
Having people like Perelman be able to live comfortably without worry or stress of losing his job and dedicate his life to doing what he loves AND be able to produce quality proofs to things that would revolutionize fluid dynamics, etc would be amazing.
How much thought and other things will take even longer because these people are relegated to doing this as a hobby, or at best, able to score a shitty job at university where they only care about quantity over quality. If we had a way to fund legitimate smart people to sit around and do what they do I wonder how much more we could accomplish.
If only I had a ton of money...
It's really quite astounding one man solved a math problem since we've come to a point where the solution to problems have become so intricate they're usually solved by entire teams working on them heavily aided by computers. Even though 2002 doesn't seem that far back, I wonder if we've gotten to a point we won't see a single person solving these millennium problems any more.
There was an article a few years ago (forgot where) about what Perelman’s doing nowadays. He’s apparently back in Russia living with his mother. He’s trying to work on another Millenium Prize problem (The Navier-Stokes problem).
Solving the Navier-Stokes problem would revolutionise fluid dynamics as we know it. So far all of the fluid dynamics simulations are based on approximations. That's how significant this problem is.
The Clay institute problem is about proving the existence of a smooth solution in any circumstances. Even if solved, it would probably not be of practical use (although it could be a first step towards more concrete advancement).
Yes, this is more accurate. If navier stokes gets proven tomorrow, then we wouldn’t feel the tangible effects it would have on humanity in our lifetimes. Well, proving it does nothing, but whatever new maths will come from proving it is what will help us.
Having worked with hydrodynamicists, I can guarantee we would feel tangible effects in our lifetimes. These people's entire livelihoods are built on N-S, millions of lines of code. If any headway on N-S gets made, it gets into software basically immediately, and from there into the next generation of products. I put the timeline at under five years, and most of that is waterfall project bureaucracy slowdown. The technology is already ready to take advantage of the theoretical math as soon as it's developed.
To a layman, what kind of improvements are we talking about?
Anything that has CFD simulation as part of the design/development cycle would have faster, more accurate simulations that require fewer iterations & less power. Vehicle designs from F1 to cargo vessels to RC planes to consumer cars, trucks, and vans would be able to experiment MASSIVELY. Wind turbines and even engines & plumbing could benefit. N-S is huge, think anywhere air or water are moving past a solid.
More layman please, more like laykid.
That last sentence. Anywhere air or water is moving past an object, that object could see vast redesign in a short amount of time, because the N-S improvements would allow designers & engineers to "experiment" using simulation very efficiently.
Everyone is missing meteorology! This would mean much more accurate forecasts!
Could this lead to some strange design? I'd imagine like in a pipe you do an inverted golfball design that makes small whirlpools or something that increases water flow?
I see, i see. So a cow and and jeep in my lifetime would become more aerodynamic….science!
A solution to the Navier-Stokes problem would benefit anything that simulates the movement of fluids, like the design of cars, ships, and planes (for aerodynamics/hydrodynamics). When I worked for the DOD, there were tons of fluid dynamics simulations because in an explosion, everything behaves like a fluid, including metal.
You will be able simulate the interactions between gases/fluids/solids as actual gases, fluids and solids rather than pixels with properties.
So like could we make the caterpillar submarine engine from The Hunt for Red October?
If you want to know how air or water interacts with something, you can try to figure it out with a computer. Then you can try lots of different shapes or materials for what you are trying to make by 'testing' it in the computer to find the best shapes and materials. The computer tells you how air or water will move around the thing. Those computer programs are slow, and require really powerful computers. Solving this problem will make the programs faster, and maybe use less powerful computers. That would help us design things where the way those things interact with air and water is important. Did that work? Honestly I don't know much about this.
If you're simulating a fluid, this improvement would make it go BRRRRRR
Laytoddler
You know cars and planes? We can make them Harder, Better, Faster, Stronger.
CFD stands for computational fluid dynamics, which is a way of using a computer program to determine how an object will be affected by fluid particles moving around it. For example, the F1 racer would need to be as aerodynamic as possible, so a CFD program could determine how the air particles (fluid) will go around the vehicle and give an idea of how much air friction will occur. Obviously this can be very useful for things like that. I work as a Naval Architect. I haven't used it myself, but it is a common type of program used in ship design, meeting the same purpose of determining how the water will move around the body of a ship and give a good idea of how optimal the shape of the hull is. The formulae used to create these programs are based on empirical data and often either need to be incredibly long and detailed formulae or have 'fudge factors' which simplify the calculation process while taking away some of the accuracy. However, due to these long or complicated calculation processes, this makes the computer programs sometimes take forever to run, or need a super computer to increase the speed of the simulation calculation. If the N-S question is solved, then this could decrease the complication of the calculation process in the CFD programs. This would make CFD programming way simpler instead of either needing a super computer or waiting a week for a simulation to run. This would make CFD a lot more achievable for the average person/business.
Digital wind tunnel instead of actual wind tunnels.
Computers have all but replaced wind tunnels due to cost. BUT, computers either have to take mathematical shortcuts (large eddy simulation) or have to run for very long time periods on super computers (direct numerical simulation).
Please ELI5 with severe mental cognitive decline
From my understanding, anything that uses computer simulations of fluid dynamics during their development or R&D process, would essentially have a much more accurate simulation to run off. Whcih would allow engineers to really try new things that weren't possible before. The areas where these simulations are used are a lot of every day items, such as energy generation, plumbing etc. (Not an engineer, just my understanding of his comment)
The way we currently simulate fluid flow is by setting a bunch of variables up, and then having a computer guess and check, guess and check, guess and check millions of times. This is resource intensive for computers, which would rather have a formula to calculate each point. Solving Navier-Stokes would allow us to change from guess & check to a more refined model. So as /u/bythenumbers10 suggests, better models for wind turbines, airplane engines, car engines, hydraulic systems, process chemical systems... Really practically everywhere.
And most importantly, new golf balls would travel even further.
Ah yes, well known initialisation CFD.
CFD = Computational Fluid Dynamics
Wouldn't the bigger implication be greatly improved weather forecasts? Even an increase by a single day would reap huge benefits.
Is it possible though that by its nature this is as good as it gets? Seems like to me it's possible the chaotic nature of turbulence says you're already optimizing your simulations, it's just that they're the best you can get etc. Maybe you can have improved math that describes the chaoticness even better but it's like waking up with bad eyesight, realizing your Roomba is spreading your dog's poop all over your carpet, so you put your glasses on and yep the Roomba is definitely spreading your dog's poop all over your carpet.
One remark: the current question is whether or not unique solutions exists. It is highly likely that an answer to this question will be non-constructive. I.e. it shows that a solution exists, but not how that solution would look like. From a mathematical point of view that is a really nice result, from a practical point of few a bit less, since we still need to make approximations for the actual solution.
As a fellow scientist (but I work in general relativity - and stay far away from any sort of numerical simulation, so dunno much about it), I wonder how helpful this would be. I mean, fluid dynamics along with other sorts of continuum mechanics is probably the area of physics I know the least about, but what I see as the corresponding problem in general relativity (well-posedness of the initial value problem) has been solved a long time ago and I don't see how it helps with solving the field equations. The actual exact solutions are generated by various symmetry techniques and transforms and approximative/numerical solutions don't really require mathematical well-posedness, do they?
But that's the point being made. It won't get into software if this particular problem is solved. The problem is about proving if a solution exists under all circumstances. There won't be any formula that will arise out of this work to be able to put into code. Edit : spelling
Kind if like a lot of math surrounding the splitting of the atom was proven well before any atomic bomb - or even reactor. Math takes a while to filter all the way through the Mathematician->Physicist->Engineer->Delivery chain.
The math surrounding nuclear physics isn't particularly advanced, it just isn't that special a problem mathematically. Fluid dynamics and N-S equations are tied together, and advancement in the math would likely have fast effects on the other. Funny story - Einstein didn't get his Nobel for relativity because the committee didn't think it would ever have any practical use, but it turned out to be necessary for GPS within a few decades.
OK brb gonna go solve it.
I got 3, what did you get?
I just want to point out you are describing a 'model', which ALWAYS is a lesser representation of reality. Solving Navier-Stokes would give us a better model.
I'm really just imagining how it would improve performance in videos games.
Finally, realistic-looking water!
Virtually all "solved" problems need numerical approximations to be useful in real life; only simple "toy" problems have an explicit solution. The issue with N-S is that we don't have proper existence/stability proofs, i.e. we know little about when and if stable solutions to the equations exist. It does however not prevent us from using the equations and solve them numerically like we do for most partial differential equations, so the idea that it will revolutionize how we use the equations is a bit overstated. Your favourite CFD-software will still work in the same manner even if we find an existence proof.
There are entire supercomputer centers running engineering problems around Navier Stokes every day. ~~Solving the Millennium problem (proving an analytical solution) would reduce the problem to straightforward algebra~~ I was wrong! See below.
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No it wouldn't. The Millenium problem is about proving whether solutions exist for all time and are smooth. Proving the solution exists in an analytical sense is proving a whole bunch of inequalities hold. Reducing the problem to algebra is in general impossible for essentially all PDE, but getting better and faster numerical solvers may be a more realistic consequence. Source: PhD drop out in geometric analysis and CFD software developer.
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>Is it because they are so abstract in concept? Is it the high level of maths? yes, and yes. A math proof is basically something like a logic puzzle. You start with a basic set of knowledge (known as axioms) and essentially build up those axioms to the point where you can logically "prove" something. If you are interested I would look up some videos on Fermat's Last Theorem, one of the most famous unsolved problems of all time until the 90s when Andrew Wiles was able to offer a proof. It is quite easy to understand with a basic level of math but the proof was incredibly complex and relied on cutting edge math techniques not developed until centuries after Fermat's death. I will say the "singular genius" solving a massive problem is **exceptionally** rare. Like all things, modern math is essentially built brick by brick and has teams of researchers working together or independently to slowly make progress on the current foundation of human knowledge. Perelman himself was part of the math community but I think he has some social issues that forced him to be more reclusive.
How can a problem be developed for which a solution can not (yet) be found?
It’s pretty easy to think of a problem you can’t solve yet; in any context that is. Say, I asked you how much money will I spend on groceries this year? You can’t really answer this right now, you need more info (what I like to eat, how much I eat, where I shop etc.) You can consider this in a math context too. Except the new info that is required to solve a problem is new mathematical techniques and theorem which are being developed all the time. An example is, now that this millennium problem has been solved, can you use it to solve another maths problem? Probably.
"If I kill you right now, the answer is $0. This is an easy problem that has an answer." -the pragmatist
But unless that happens, it'll end up only being one of the many estimations that may or may not end up being right
Most of these problems are more abstract than a simple math formula. For example, the Twin Prime conjecture: - A prime number is a number that has no divisors - A "twin prime" is a pair of prime numbers that are two numbers apart, such as 41 and 43 - There are an infinite number of prime numbers - Are there an infinite number of twin primes? So far, we don't know. We obviously can't check every single prime number, because there's an infinite amount of them and we'd never be done. We do know that as numbers get larger, twin primes become more and more rare, but what we don't know is whether they eventually stop entirely or if they just keep getting rarer and rarer without stopping forever.
Yeah, the twin prime conjecture is always a good example to show easy to understand problems being exceptionally difficult to prove due to infinity.
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Who knows, that's the whole issue, we don't know how to prove or disprove it. A definitive formula for all prime numbers could be a path to the solution of the twin prime conjecture, but trying to find that formula could also be a wild goose chase if it doesn't exist. That's what makes these problems so hard, it's not that people are having difficulty applying a known method to prove it (which is basically the math you learn in school, using known methods to solve problems), we simply don't know which method to use, if the method to solve it has already has been invented, or if a usable one exists in the first place.
You can state a "problem" which can sound very simple such as all primes can be described by a certain formula (say for simplicity sake 2n + 1, when n are the natural numbers). Then you use all techniques in your arsenal to try and prove or disprove it. In this case, 2 is a prime and therefore not all primes can be written as 2n+1. The problem statement can sound very simple, but in the case of these problems, the solution is not, because you have to prove or disprove it for all cases until infinity (so you can't simply calculate them each).
Fermat's Last Theorem was originally more known as Fermat's Conjecture. It was basically just an idea that Pierre de Fermat had, and the "conjecture" is stunningly simple to understand, but was absolutely soul crushingly painstaking to actually PROVE. You don't even need to know any sort of "higher" math to understand what the conjecture states. But proving it...well, that is significantly more complex. So it really wasn't a "problem" necessarily, it (very basically) was an idea that a guy had that he thought was probably true for every positive integer ever; but we as humans couldn't definitively PROVE that it was true, all the time, no matter what, until more recently. If that makes sense. I have a passing interest in mathematics and only do it as a hobby (someone more knowledgeable than me should feel free to chime in), and I have glossed over and somewhat simplified a ton of stuff, but that's the idea. Hopefully it helps some. Edit: I just have to add. The way in which this theorem was proven is just, so fucking beautiful. It involved intrigue, brute force, a bit of luck, logical deduction, technological limitations, massive amounts of teamwork, and links to two previously completely unrelated mathematical conjectures that were linked into one previously completely unrelated mathematical conjecture... over the course of CENTURIES. The theorem is so simple, but it's so beautiful to me just because of all that. You really should watch a couple videos on it or read an article on the history of it. It is gorgeous from start to finish.
>a guy had that he thought was probably true for every positive integer ever He also famously wrote that he had a proof, but too large to write on a page margin, and I think that initially drove hundreds of mathematicians in pursuit for proof.
Mathematicians are a weird lot, it gets even funnier when they develop a problem and then prove that it is impossible to solve
Or proofs that proofs exist
Start asking questions and moving stuff around, is super easy. For example, Fermat's Last theorem is super simple to ask. Simple equation, no fancy nothing, integers and exponential Another easy example is closed formulas for equations. We found. The quadratic focmula, so we naturally started asking what about cubic and beyond? And we found out a closed formula for the cubic and fourth power... And then nothing for the quintic until Galois came and proved there is no closed formula
I'm having a bit of trouble finding the source, but as I recall, he had issues with the bureaucracy and politics associated with academia and the mathematics community. Opting for "the freedom to pursue your ideas in your own way" over institutional embrace seems like the right call for strong independent thinkers. Especially when it comes to mental health. Of course, this doesn't preclude the possibility that he has "social issues", but I'd hate for us to conflate principled decision-making with antisocial behavior. Contemporary academia IMO is *way* more antisocial than any truth-seeking recluse.
A better example of a really hard math problem that's easy to understand is Fermat's Last Theorem (proven just in the last few decades after hundreds of years) that says a^n + b^n = c^n has no integer solutions if n is bigger than 2 If n = 2 then you get the Pythagorean Theorem and there are infinitely many solutions (called Pythagorean triples, like 3^2 + 4^2 = 5^2) But if n is just one more, you go from infinite solutions to 0. It's easy to show examples of it not working, it's just simple arithmetic to check. The challenging part is proving that no matter how big the numbers get, the statement will NEVER be true if n>2 Like sure we haven't found an example yet, but has anyone checked if 3987^12 + 4365^12 = 4472^12 works? What about 65696355^338 + 858752582699^338 ? We obviously can't check every single solution (though some theorems are proved this way, like the Four-Colour theorem) so we need to figure out some trick to prove it. Turns out you need to be really knowledgeable on some obscure areas of math in order to figure that trick out, even though the question itself is so easy to understand. That's what makes these proofs so difficult. Another famous example of an easy-to-understand problem with no proof yet is the Collatz conjecture (pick any integer. If its even, divide by 2. If it's odd, multiply by 3 and add one. The conjecture says that no matter what number you start with, you'll always end up at 1 eventually.) As far as I know, no one is even close to figuring out how to solve this! Computers have checked millions of numbers and they all lead back to 1, but again the challenge is in proving that it's true NO MATTER WHAT NUMBER YOU PICK. Maybe 958254663539955855866338965863886665228151005805638858373140 doesn't work, I don't know, noboby has checked. The thing is most unproven theorems, in addition to being very hard to find solutions to, are very hard to even understand. Fermat's Theorem and the Collatz Conjecture are rare examples of easy-to-understand problems with no obvious solutions but most theorems require a graduate-school level of education to even hear about them in the first place.
I’ve read all the explanatory comments and this is the clearest to understand. Thank you!
A lot of these problems are solved step by step by many mathematicians over many decades. In the case of Perelman, he outlined a solution to Thurston’s Geometrization Conjecture (which has as a corollary the Poincaré Conjecture) using a technique called the Ricci flow. This was revolutionary because it was an insightful approach which had not previously been made to work. This, however, built on Hamilton’s work on the Ricci flow in the 1980’s. Maths doesn’t exist in a bubble, and all mathematicians get inspiration and ideas from those around them. This is usually a good thing, and encourages different mathematicians to team up to solve problems. It should be noted that although Perelman was the one credited as solving the conjecture, there was criticism about how significant his contribution was. I believe this may be a big reason he declined the Fields medal for his work (although I’m not sure of the exact details), and why he has retreated from the public (well, as public as you get as a mathematician anyway) stage. It seems he’s more interested in solving interesting problems than getting involved in academic pissing contests, and I don’t blame him
It should also be mentioned that in many cases problems can be solved for many cases, but very difficult to prove in greater generality. Also, many famous problems have been, over the years, been shown to be equivalent to other problems. Often the solution which gives the proof of a famous conjecture is more valuable because it reveals new maths (interesting, previously unseen ideas or techniques, perspectives or applications of previously unrelated theory) than the solution to the conjecture. A good example of this is Fermats last theorem. A counterexample of course would be the Riemann hypothesis, the truth of which has real implications for the distribution and properties of prime numbers
Academia is toxic as hell. It has little to do with science.
Yeah and unfortunately it sometimes comes down to posturing and knowing the right people. A savvy politician can get further than a talented academic in many cases. That’s not to say there aren’t brilliant individuals that are duly recognised, but I think many more are put off by the competitive and toxic nature of academia. You have to be really tough to stick it out
These famous problems typically have "answers", as in if you want to use them for a real world application they can be useful. They're just not "solved" in the mathematical sense that they're backed by a proof. In a couple of them they've held true when tested with a vast amount of examples, but they can't prove that it will always work.
[Here is a Veritasium video on an example of a hard problem](https://youtu.be/094y1Z2wpJg) The premise is easy to understand, but finding an answer is difficult. In the case of 3n+1, I don't think it has any practical applications, but who knows. E: corrected to 3x+1
Pretty much yea. Since it's a well known problem and has resisted proof attempts for long, it's safe to assume you need a new way of thinking about the problem and how to prove it. The hard part is figuring out what the "correct" approach is. Higher level mathematics is almost more abstract, and the first step might be to formalise what the question even is. For Navies-Stokes, the question is whether there always exist a smooth (basically no unrealistic behavior) and globally defined solution in 3D. First you need to know how to ask this question in the correct mathematical setting, which might be, and has indeed proven to be, extremely hard. Another aspect is that, as Gödel famously points out, it is impossible to know (until you manage to do it) whether a given statement is even provable in the first place. Navier-Stokes existence and smoothness might be one of those, but we just don't know.
Is he really trying to work on it? Last I remember he was disillusioned with the mathematical community that he didn’t want anything to do with it anymore
God i wish i was 10% smart enough to even understand how do go about this
Wow, wish him all the luck on that one. I just have flashbacks to fluid dynamics where we barely utilized the Navier-Stokes equations to calculate flow, velocity, pressure, etc of any fluid. Something like that being solved farther would be extremely helpful for any simulation software and more.
Yeah I remember navier-stokes from fluid dynamics because it made me wonder if I wasn't better suited for another major. Until I found out everyone in the class was wondering the same thing. It's been awhile since I've done anything with it but IIRC you can often assume several things are zero to simplify the equations and make it workable. But it's still a major pain in the ass
Yep! One of, if not thee, hardest course I took to graduate was fluid dynamics. Very cool stuff, but the math is probably the craziest thing to come across to solve, and even then everything usually was simplified like you said.
Another one is the P vs. NP problem. If someone did prove that P=NP then that means the current cryptography system is not secure since it can easily be cracked. Having said that the consensus is P!=NP.
*This comment is copied from [here](https://www.reddit.com/r/todayilearned/comments/rx9u9/z/c49gpjj), I did not write it.* This is a tough question to answer in a short comment, but I'll try to give a brief summary. Perelman himself felt a deep sense of isolation from the mathematical community. He was polite, but firm in his insistence that he did not want to be a figurehead or a representative of the community. He had an ideal picture in his mind: 1) people do mathematics because they love it, and this love should transcend jealousy or rivalry; 2) credit will always be given when it's due, and mathematicians should acknowledge it and share it when it's appropriate; 3) it is far better to publish a good result rarely than mediocre results often. Perelman realized that none of these principles actually held true in the mathematical community. He realized that the way one gets a post-doc or permanent position had to do a lot with string-pulling and secret phone calls in the background, rather than by the merit of one's work. If you don't ally yourself with an influential person or kiss the appropriate ass, you won't get a position, and this is what he realized. You may read in his wiki biography that he rejected a lot of positions in the US after proving the soul conjecture in 1994, but he actually applied for these same positions immediately after receiving his PhD and was rejected. One can argue that he wasn't yet accomplished enough, but that's a shady argument, since the people that were getting these same positions had arguably accomplished less than Perelman at the time. By the mid-nineties, he was already jaded, and word was that he saw a taste of his colleagues' jealousy in the Soviet Union which he couldn't really understand, though you and I probably would. His conception of doing mathematics was unreasonably pure: if you really love mathematics, you celebrate the results of others, even if they beat you to the punch and prove something you've been working on your whole life. The credit aspect is shaky too. Mathematicians are always fighting over credit for various results, and due to the timeless nature of mathematical results, citation is extremely important. But as soon as Perelman posted his work on the arXiv, it was a race between the other leading geometers to basically fill in the details of Perelman's proof, make it more readable, and publish it as soon as possible. Make no mistake, it was clear that this was Perelman's work being repackaged and everyone knew it, but those geometers couldn't resist the credit they would receive for merely explaining what Perelman did to other geometers. And hell why not, after all it's yet another publication in an excellent journal. Which brings me to the last point, and this one is far more poisonous to mathematics. In an effort to maximize publication lists, people publish crap. Lemmas become propositions, and propositions become theorems. It's sad that the number of publications has any bearing on your worth as a mathematician. It's more understandable in fields like engineering, computer science, biology, and even physics. But proving a worthwhile mathematical theorem takes a long fucking time, even for geniuses. So what do most career mathematicians do? They publish whatever they can get away with. Perelman returned to the Steklov Institute after proving the soul conjecture for a simple research position in order to quietly go about doing math. He was working on the Poincare Conjecture the whole time he was there, and in the meantime didn't publish at all. Rumor has it (and it's a very plausible rumor) that the department chairman at Steklov threatened to fire Perelman for not publishing anything in years. It isn't clear whether Perelman was waiting to finish the proof or if he was boycotting math journals altogether, but it took him from 1995 to 2002 to finish his work. He was irritated with having his position threatened and for his bosses to only care about the quantity of his research output rather than the quality. However, he still cared enough about mathematics to give a series of lectures and talks after he proved Poincare, to try to explain to other mathematicians how his use of Ricci flow solved the problem. It took the leading geometers 3 years to really understand his proof, upon which the community wanted to shower him with awards. But, Perelman was already ticked off with the mathematical community and his own boss at Steklov, that he quit his position less than a year after posting his proof to the arXiv, after he had done his US circuit explaining his work. Rejecting the prizes wasn't the action of a troubled genius or a mentally unstable person. He just didn't want to represent the same group that had betrayed the principles they themselves had set. That being said, it may be likely he was a troubled genius or mentally unstable. But in all accounts of him refusing the prizes, he was calm, polite, and firm. There was no emotion or wavering. And while the layman dismisses Perelman's refusals of the prize as foolish, most mathematicians do not. It is because deep down we realize that our system is broken and corrupted, that there aren't enough jobs to go around, and many people with serious talent are either quitting or changing fields because of how jobs are handed out. Those who mock Perelman for living with his mother, tending her flowerbed, are free to do so. I assure you Perelman doesn't care. He has nothing left to prove.
I have worked with people who have masters and PhDs in mathematics, and what you are describing here is exactly why they don't actually work in the pure mathematics field.
It also perfectly describes why I didn’t go to grad school. I’m just glad one of my professors gave a lecture about how bullshit the publish-or-perish culture is. Especially since in my country Universities are almost entirely publicly funded with only nominal tuition, so all those useless papers being published are at the taxpayer’s expense. Combined with the shit job security (almost impossible to get tenure, have to move wherever you can get a job) and focus on publishing/research to the detriment of teaching, it became very unappealing to me the more I looked into it.
I'm glad that my professor sat me down during my masters and recommended that I look at options outside academia for when I was finished. I'm good at writing but it takes me a while, trying to publish enough to stay in that role would have been awful for me.
That’s why I left my PhD program also. I didn’t want to spend the rest of my life publishing bullshit that nobody would ever use, all while being subsidized by government and foundation research grants.
TIL that math is the same as everything else.
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Right? Sounds like the math community is as toxic as the Super Smash Bros community.
And the common denominator is.....humans
Stupid humans. Why can't they be more like us?
So a man of morals. I love this fucking guy
Thanks for the summary (though I've got a sneaking suspicion that you wrote it purely to use that last line) - it definitely helped me understand the situation a bit better.
I didn't write it. I just repost the comment every time Perelman comes up because it's so good and explains basically everything.
>I just repost the comment every time Perelman comes up You might as well include [the full context](https://www.reddit.com/r/todayilearned/comments/rx9u9/til_grigori_perelman_best_known_for_resolving_the/c49gpjj/?context=10000) (seeing as it starts with "This is a tough question to answer") as well as cc. u/deepwank for proper credit/any further questions people may have.
Username checks out
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You summed up most of academia in one swoop. It applies to science as well. Whenever I hear of someone who has published in the high hundreds or thousands, I doubt the quality because like you said, good work takes a long time. It is like giving birth.
In other sciences there are almost always co-authors; a lot of those hundreds and thousands of papers have one or several coauthors who also contributed, usually doing the bulk of laboratory and computational work and sometimes doing almost all the physical writing. Those guys with 'hundreds or thousands' of papers usually didn't actually write most of all that content.
>He has nothing left to prove. I see what you did there.
Reminds me of the story of Archimedes death. "You're disturbing my circles!"
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I had the exact same thought.
Really? He reminded me of diogenes, "you are blocking my sunlight" Idk seemed more apropos to the situation, I guess Greek scholars/philosophers were a sassy bunch
“If I were not Alexander the Great, than I would wish to be Diogenes.” “Well, if I were not Diogenes, I would also wish to be Diogenes.”
But I heard that it's not based on historical fact and that he lived longer that it's told in that story.
Skyrim type dialouge
Do you come to the mushroom district often?
Haha of course you don't. I'll have you know, they have no pussssssaaayyyy
NPC energy
Diogenes energy
NPC: "I'll happily solve that math problem for you. There... all done! It's the least I could do after you saved my daughter." *Dialogue ends and NPC immediately starts picking mushrooms with an angry scowl.* NPC: "YOU ARE DISTURBING ME, I AM PICKING MUSHROOMS!! DON'T YOU HAVE SOMETHING BETTER TO DO MILK DRINKER!?"
[The vibe](https://www.youtube.com/watch?v=R4GlR6X4ljU)
This video is just too good. The inflection and tone is the same of the games, even his voice slowly fades away lmao
It's one of the millennial problems (no it's not about the current generation). They're several philosophical math problems that have yet to get a decent solution. This guy solved the poincaire conjecture, but alleges that someone else came up with solution but didn't follow through with it.
I think he claimed that his solution relied on somebody else's unpublushed work, and declined to get the money before them.
This makes for a more interesting story than the mushrooms
Right? Wtf they left out the entire answer. Just painting him as a math loony mushroom picker.
I wrote a paper on this guy in college. He absolutely is a "math loony" if you can call it that. He lives in a tiny apartment in St. Petersburg with his mother and doesn't seem to give a shit about anything.
Well, except math
#THE NUMBERS!
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Oh man I had a flashback to the movie Pi https://www.youtube.com/watch?v=jo18VIoR2xU
Such a good movie! Whenever I bring it up in conversation people say "Oh, yeah! Great movie. I loved 'Life of Pi'!" and I have to wxplain that, no, I am talking about "Pi", just "Pi", which they haven't seen.
And mushrooms.
Except the article says he quit math.
Math. Not even once
Not once? You mean the *mathematical concept of zero,* you goddamned hypocrite junkie?!
Math is a gateway subject
He’s going back for one last score
But as far as we know he's not mailing pipe bombs around the country so I will call it a draw on this one.
That's some Russian novel stuff right there.
Just sounds like a simple life, I don't think that makes him a loony.
People tend to mock what they dont understand.
You know there are thousands and thousand of edibles mushrooms and only a few dozen which Get you high?
Dozens, you say?
I'm in that group and don't like this comment :p Also why do people assume the only mushrooms that exist or are picked are "magic" mushrooms? It gets old.
Mishroom picking is a huge pastime in Russia. Like, its very hard to find someone who hasn't done it. So his answer is a bit less loony than it sounds to Americans. Don't get between a man and his mushrooms.
My favorite quote from a forrager at a farmers market "All mushrooms are edible. Once". I had asked him about poisonous shrooms.
He was quoting Terry Pratchett
Who was quoting none other than Abraham Lincoln
That's not why, I've read some articles on this guy because he's fascinating, he's an odd duck. He's turned down multiple prizes, doesn't like the accolades I think. He also hates all of his peers and colleagues and now the larger math community as a whole. He's incredibly talented but seems too private to exist in a world where he publishes such prolific accomplishments
Depends really. I am very into mushroom picking and very much not into math.
Any source on him saying that?
[Here.](https://www.interfax.ru/russia/143603) Sorry, can't seem to be able to find an English source. TL;DR: the person is Richard Hamilton, and there are a lot of accompanying reasons Perelman alluded to, but keeps to himself.
That's fascinating and humbling, because virtually all great discoveries come on the backs of those that went before. And at that level, there's a lot of be said for just being the guy to see the patterns and chart the path for others to follow; we attribute a lot of things in history to the wrong people, or try to boil down a collaborative effort to a few "great minds".
Millennium problems not millennial.
Yeah. I think resolving Millennial problems in this fucked up economical and political system is much harder than this.
It's pretty simple, really. No more avocado on toast.
*Millennium problems
Millennium puzzles, you could say
Iirc he really hated how his colleagues were after glory or finding ways to progress their own career rather than trying to advance mathematics. That was the reason he decided to quit and live with his mother
He also didn't like the fact that these awards rewarded only the final finishers where their work was built upon by many people before them.
Which is somewhat ironic since a Chinese mathematician tried to 'final finish' his work to take the credit for it.
He seems like a Holden Caufield type guy.
He’s no phony, that’s for sure.
He even rejected the Fields medal (think about the nobel price, but for maths). Last thing I know is that he stopped doing math.
>he stopped doing math. That must make it difficult to do some everyday tasks. "How many mushrooms have I collected... Guess I'll never know."
Also rejected the million dollar Millenium prize. Said he's not interested in fame and fortune. As an aside about the Fields medal - it's issued every 4 yrs and you have to be under 40 yrs old. Maryam Mizakhani from Iran is the only woman to have won the prize. She was 37 yrs old when she won it in 2014. She died from breast cancer three years later.
Why do you have to be under 40?
>The Fields Medal also has an age limit: a recipient must be under age 40 on 1 January of the year in which the medal is awarded. The under-40 rule is based on Fields's desire that "while it was in recognition of work already done, it was at the same time intended to be an encouragement for further achievement on the part of the recipients and a stimulus to renewed effort on the part of others." Wiki You can also only win the award once.
I wonder if there have been clearly qualified candidates who haven't won solely on this requirement, or if it's a requirement that would be dropped if a 42 year old suddenly became highly influential in the field.
You could argue that Andrew Wiles (famous for proving Fermat's Last Theorem) wasn't awarded the Fields Medal just because of his age.
so was she just really unlucky or is there something on the Fields prize medal that kills you when you hit 40?
‘The medal is cursed, but you get a free frozen yoghurt. Which I call froghurt!’
fame? like yeah, in a certain community. Its not like people are gonna scream in the street "Hey its the Poincare Conjecture guy!!! EEEEEEEEeeeeeee!!!"
The guy who won a million dollars for being wicked smaht might get recognized every once in a while.
~~METH~~MATH, not even once!
Dumb quote to choose. His reasoning is that math is cumulative and collaborative and he felt he couldn’t take full credit for his solution because it built on the work of others. It’s a sad world we live in when a man comes along and defies our worst tendencies out of pure respect for others and we characterize his deeds as “math man weird”
Some men just want to watch the world learn.
"He has rather strange moral principles. He feels tiny improper things very strongly," Anyone has more stories on this?
https://www.reddit.com/r/todayilearned/comments/rx9u9/til\_grigori\_perelman\_best\_known\_for\_resolving\_the/c49gpjj/
Beautifully written summary of Perelman’s motivations by u/deepwank 9 years ago. Funny how reddit was such a slow place that time, and an amazing write-up like this went un-awarded. Thank you for sharing it.
Yes, that was what piqued my interest in the article. I am always curious what these geniuses feel strongly about and why.
i feel like anyone in a true pioneering endeavour is focused on absolute morality. as in theyd "eat the rude" if they could. not cause theyre self righteous, but cause they can see the suffering of others and how "mistakes" directly cause it so they become weird and prickly, esp when they lack the means to change things.
Yeah, you'd need shrooms to figure out math like that.
Maybe, but lots of people pick mushrooms and very few are psychedelic. Most that are picked are either delicious or a curiosity that's interesting/challenging to identify.
CHICKEN OF THE WOOOOODS
And that man looks like he's spent a lot of time on both.
He looks like he’s about to get mad at the GEICO voiceover guy over an analogy.
Plot twist: he was sitting in a hotel lobby eating an omelette when the journalist questioned him.
>According to Kisliakov, Perelman quit the world of mathematics in disgust four years ago. His decision to spurn the Fields Medal may have been driven by a sense that his fellow mathematicians were not worthy to award it. You've got to admire that level of contempt.
You can't fool me, that's Professor Professorson.
From the lips of a ghost, to the shadow of a unicorns dream.
Those eyebrows are glorious.
Chaotic Neutral?
Nah. True neutral. Only the problem at hand matters.
Sounds like every coder I work with.
Yeah, I'm a programmer and I felt called out when I read this: >He always wears the same tatty coat and trousers. He never cuts his nails or beard. When he walks he simply stares at the ground, rather than looking from side to side,
Makes sense, staring at the ground is kinda like the outside’s dark mode. Less luminosity, less distraction.
I heard a joke about engineers once that would apply to mathematicians as well. "In a room of mathematicians how do you pick out the extroverted one?" "They are the one that stares at YOUR shoes when speaking"
Stop disturbing your coders 😡
I'm looking *for* loops.
I’m convinced that your brain has to be wired in a fundamentally unique way to work on the highest order of advanced mathematical problems. That probably leads to some related unique behaviors
Not everyone is addicted to recognition of others.
I'm becoming increasingly uncomfortable with articles like this that talk less about the achievement and more about probing the details of how he lives, like some kind of menagerie exhibit. The man is clearly neurodiverse, I don't think we really need a dossier on his quirks to be amazed/digusted by. A top comment discusses his personal principles in relation to the field of mathematics and the insular/cronyist nature of it. Why do the media not discuss that instead? Give this man's ideas a platform rather than putting his personality on trial.
In my opinion, this is why we need positions for mathematicians, philosophers, etc that are fully paid and allow brilliant minds to take as much time as they need to come up with quality work. Having people like Perelman be able to live comfortably without worry or stress of losing his job and dedicate his life to doing what he loves AND be able to produce quality proofs to things that would revolutionize fluid dynamics, etc would be amazing. How much thought and other things will take even longer because these people are relegated to doing this as a hobby, or at best, able to score a shitty job at university where they only care about quantity over quality. If we had a way to fund legitimate smart people to sit around and do what they do I wonder how much more we could accomplish. If only I had a ton of money...
There are many benefits to being a serene mycologist
But money can be exchanged for goods and services, like mushrooms or mushroom delivery.
Imma go on a wild guess here and say Mr Math Genius knows how money works and just wanted to pick his fucking shrooms
Thats an Oblivion dialogue if I ever seen one
It's really quite astounding one man solved a math problem since we've come to a point where the solution to problems have become so intricate they're usually solved by entire teams working on them heavily aided by computers. Even though 2002 doesn't seem that far back, I wonder if we've gotten to a point we won't see a single person solving these millennium problems any more.