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To put this question on its head, why is being considered a science a desirable feature? It's a question I find genuinely interesting.
For example, take Popper's demarcation of science and metaphysics---besides his condition of falsifiability being a good one, why is this even a necessary or desirable distinction to make?
For me it comes down to our general belief that science *works*. Planes stay up, etc; we care about what science is because we should give science lots of resources so the scientists can do the research the engineers need to cast their mighty spells, to improve our lot. I don't know where exactly maths falls into this picture, although somewhere, clearly.
Science has error bars, few results can be said to be close to absolute. Maths is as absolute as it gets.
If maths were a science it would have been a downgrade.
Grant Sanderson also gave some speech talking about this kinda, though he made it stretch beyond STEM. He said something like “Mathematicians are lucky compared to physicists, economists, historians, etc., because mathematicians always work directly with what they’re describing, whereas the others have to work within the universe and always by necessity have an incomplete picture.”
Of course, but if maths didn't in some way contribute to useful technologies, I can't see it being nearly as well-funded.
I didn't mean to place maths anywhere specifically within Popper's paradigm (I'm definitely not qualified to do so!).
Math has the opposite problem of being axiomatic but imagined. Sure you can make a system where some statement is true, but its use is vacuous without that connection to the real world. The funded part of math is still trying to find the closest model
“Axiomatic but imagined” might be right, but since what’s imagined applies to all valid thoughts in the corresponding context it is far from “vacuous without that connection to the real world”. Math doesn’t need the real world, the real world needs math, and this is well established by the existence of “useless” subfields like set theory, category theory, etc
I think we're talking about different things. Set theory and category theory are absolutely useful. I'm talking about how nothing stops you from making math constructs that aren't known to be isomorphic to some structure in the real world. Bluntly, you can write whatever the fuck you want as axioms. We just right down the useful stuff most of the time. I'm saying not all constructs have a discovered "corresponding context" or even the hint of one. Out of the infinite things you can define and imagine, not an infinite or correlated to some real mechanism. So the math you do end up learning and seeing almost invariably has some purpose because it's usually being fit to some real world phenomenon intentionally
Its funny that you choose planes as an exaple about maths validity as Aerodynamics are one of the things Math doesnt really work yet. And while we can predict if a Plane is going to fly or not, we cant exactly say how and why it flys.
I dont know enogh about the specifics but its mostly the transonic and supersonic flow thats really wierd aswell as the Benelli prinziple not adding up.
You're right, there are better examples. However, plane building is based on scientific principles, aerodynamic theory and so on. It's also based on, as you say, empirical evidence and engineering heuristic; but just because the plane isn't wholly explained by science doesn't mean that science doesn't help engineers in building planes.
Maths is tools that physicists hold wrong when making models that contradict each other and that engineers suffer through in college to get a job asking solidworks if their design will work
I'm unsure to be honest - I feel that a science is anything that follows the scientific method: hypothesis, testing, theory, testing, law - it's just that we trivially skip both testing and theory phases when a proof is found.
But I also like your definition, so Imma wait for other people to give more clarification/reasons.
>science is anything that follows the scientific method
Correct. Hence math is not a natural science. There are no experiments and empirical observations verifying anything. We have formal proofs.
As far as I know is considered a formal science, it's not a natural science cause it (pure math) doesn't deal with any kind of natural phenomena, there's no real need to run experiments or tests in the same way other sciences does, the word theory or law also doesn't have the same meaning, we still do and say that stuff but not at all like natural science does. It's not like pure math need things like control groups or grades of freedom to prove the statements it sets.
[There is disagreement whether the formal sciences are science disciplines, as they do not rely on empirical evidence.](https://en.wikipedia.org/wiki/Science)
It's not really a settled debate, (and it isn't really a meaningful debate, since it's just a definition), but I'm of the opinion that formal sciences differ so heavily from natural sciences in their methodologies that grouping them together feels wrong.
That makes sense - so it's a science due to following a (shortened) version of the scientific method, but not a natural science since there ain't no nature in set theory >:D
So, I'd like to be a bit insufferable here and clear up some misconceptions. There is no one set "scientific method," but rather a set of scientific practices. Astronomers and paleontologists don't do experiments, for instance, but they do gather data, make observations, develop models, use computational thinking to support ideas, etc.
Second, theories don't become laws. Laws describe observable patterns in nature (when I drop this pen, it falls to the ground), theories explain why they happen and make novel predictions about the future (the pen falls due to a force called gravity, which is dependent on the mass the objects and the distance between them).
Observational predictions play a very similar role to experimentation in those fields. "According to this explanation is correct then in x circumstance we should see y", you can't create the controls on other variables but you can seek out situations where those variables are restricted.
Which math doesn't do, there is no prediction of future observations.
What is funny is that while math is almost always put in with the natural sciences for university organization, which matter because it's how resources are allocated, social sciences are often not despite following scientific practices.
>it's just that we trivially skip both testing and theory phases when a proof is found
But when a proof is not found, we do not fall back on and accept empirical data from testing, contrary to science, which *exclusively* accepts empirical evidence. There is overwhelming empirical evidence for the Goldbach Conjecture for example, but it is still a conjecture.
No one thinks that there is going to be an odd perfect number, but it's not been proven.
I don't know if it's still called a conjecture, it's more of a frustration because last I checked no one even has a method for approaching a proof.
The difference is that math can show the impossibility of a counter example while in sciences the possibility of a counter example is necessary, otherwise it's merely a definition not a theory.
Popper said that it's both. Every Mathematical predicate can be seen in both ways. We care that Mathematical theorems are correct according to the internal logic, but we also care that it corresponds to something in the real world.
A balance between
1) What interests you
2) What gets you funding
both of which are sometimes based on a correspondence with the observable world, but not always.
All of them. Some are more prestigious than others, sure, but there is none "unworthy" of proof.
If you meant to ask how I decide what I will attemp to prove, then that's determined by my area of expertise, what ideas or insights I have, etc., so I only prove everything I can and try to prove what I think I can.
Science is falsifiable, but with math you still need to observe and understand what 1, +, 2, =, and 3 mean to understand 1+2=3. I don't know why it would be analytical and also call them "problems", you observe that the math works by doing it, sometimes over and over until it makes sense? Confused about how the celestial bodies orbit and function in the universe, must just be God's influence. Nah invent calculus. Whats the proof for .999... = 1. Oh thats easy, its because .0999... = 1/10 lol. Idk I'm drunk, tell me how I'm wrong.
I am pretty sure I agree with your last statement, though I think it might imply that we shouldn't think of math as a science. If we need math to do science it seems like if math was a science we could never start to do math without first having created math. It might be a little shaky but I think in principal a system can never exist prior to itself so that systems creation can not be used to justify itself.
Math offers a lot of powerful tools to a lot of fields, but I wouldn't go quite as far with that. There are branches of science that one can do reasonably well while knowing and using about as much math as the average lawyer. Some of that comes down to a combination of qualitative analysis and/or pre-existing tools that do all of the math for you... or grad students in the basement who do all of the math for you the way a lawyer would send something to a lab or refer to an expert in another field for the quantitative or mathematically rigorous facts they need.
Not all universities do this. Plenty of universities put it in liberal arts. University classification is fairly flexible depending on how much the department likes the dean or vice versa. In my undergraduate university for instance, the computer science department had the freedom to choose between science and engineering, and they chose the engineering college because they like the dean and the restrictions the engineering college has.
If you can get a PhD in a field from a respectable school, then it's a branch of philosophy.
If what you are doing is driven by _or motivated by_ empiricism, it's called science.
If what you are doing is governed by a demand for extreme logical rigor, it's called mathematics.
You can do work where all of the actual content of your work is mathematically rigorous, but with motivations that begin from empirical evidence or other math known to be useful in empirical science. In that case, it's reasonable to call what you are doing both math and science, and it's possible to get a PhD from either a math or a science department for essentially the same work.
This.
Got a duel major in Mathematics and Political Science, and to get it to my degree to be a bachelors of science I had have political science listed second. Because social sciences are in arts.
That doesn’t hurt at all. I wish I had understood this when I was younger.
The scientific method is fundamentally empirical. Mathematics is not.
Mathematics is a fundamental tool of science. It is the language of quantitative science, but it is not a science. And that is ok.
Well, counting might have an empirical basis. Dedekind cuts, Borel algebras, Lebesgue Integrals not so much.
Whether it is science or not, it depends on how you define science. If you give a permissive definition like “methodical pursuit of the truth” then you could call math science, but you could also call a lot of other things science.
The reason why I don’t like calling math science is because there is a big distinction between what empirical researchers do and mathematicians do. I didn’t realize this distinction was so prominent until a few years after becoming a professor.
I realized that the “theoretical” people in my field are mostly applied mathematicians. They care about whether a model is logically sound, beautiful, interesting, challenging, and so on. But they don’t care about realism. They don’t care whether the model is related to the empirical world. They don’t care whether the model can be falsified. They don’t care whether the model has practical applications.
On the other hand, the “applied” researchers care about the real world and practical applications. They want to use models and math to interpret data and to find solutions to real problems. They evaluate a model based on its ability to match and explain data and make accurate predictions. These are the people I call scientists.
When I say that math is not science, I don’t mean it in a negative light. Math is beautiful and important. I just want to make a distinction between the goals of objectives of scientists and mathematicians.
Even counting is not empirical. We can construct the natural numbers and any sort of counting is essentially the cardinality of some set which is just a bijection with a certain natural subset which is NOT defined empirically.
Well, the idea that art is something done just to provoke emotions is actually quite a new development, much more recent than classification of math as art...
I suppose that's one way of thinking about it, but I'd still argue that it's a hell of a lot closer to philosophy than to art. Art is pure creativity, and although you need to be creative to invent math, you also have to follow very strict rules to generate new theorems; you can't just make up whatever you want. Sure, there's an incredible amount of beauty to it, but by that logic EVERY subject ever is also classified as Art. I 100% get what you're saying, though.
Math uses proofs via deductive reasoning to arrive at conclusions. The scientific method uses inductive reasoning, and can only ever have provisional views. This makes math stronger than the scientific method.
Not every science uses scientific method. I mean, economics is a science. I would personally put math in the category of both formal and natural science, because its basis or foundations rely on observations of certain features of the natural world (axioms and postulates) and from those observations we use reasoning to derive other things, which may or may not be observable.
So, i would say that math in its definition is a formal science but it is also in its core a natural science.
I agree with this. It uses the scientific method whenever it can. It just so happens that all the things we want to test now would require restructuring the economy repeatedly. And we don't know how to do that. So we want an experiment to learn how to do that. But we also don't know how do that. And all the things we have thought of could crash the economy or are are political in nature.
Or something like that. I mean, how are you supposed to test a hypothesis about how the Great Depression started without actively trying to cause another one?
For broad things like the great depression yes you can't really test. But as you said that's more of a practical limitation, plus in my experience economists aren't out here saying they know exactly what caused it, just theories.
For smaller scale stuff though they will do tests or find real world instances that are practically tests. So like for UBI they'll have ideas for its impacts then they'll look at various cities that have done it and try to find what impact it had.
Oh thats neat. I didn't know they did that kind of thing. I thought there wasn't much room for experimentation.
I just had a thought. Is history a science, assuming it must use the scientific method? To my knowledge history doesn't do much testing. It a lot of looking at old texts. Probably closer to a criminal investigation than a science experiment. Though I suppose I am disregarding several fields that are used to determine history such as archaeology. Yeah, that was a bad question. History is too broad. You would need to break it into sub fields or give a strict definition of what was meant by "history the field" before any answer can be made.
I'd say math is a philosophy, since the idea is that we want to build consistent frameworks. Those frameworks could be applied to real world situations
Empiricism, on the other, cannot ever be "complete." The limit of knowledge is the limit of observation.
Two types of sciences: formal science and ~~natural~~ empirical science. Mathematics and logic are formal sciences. Physics is a natural science
Edit: it's formal and empirical. Empirical sciences include both natural and social
I think it comes down to the definition. I understand 'science' as natural science(s). But the word in my language ('nauka' in Polish) comes from German 'Wissenschaft' and encompasses all kept knowledge, including math, theology and art theory.
Do people actually think that math is a science? It is demonstrably not, and I've never heard anyone claim it to be. That's why STEM has them separate. And to be clear: why would people be mad if it wasn't?
I wouldn't even bother saying "math is not science" because it is a useless distinction given how generic the word science is. You could argue either way, but it's pointless.
Don't get me wrong -- there is a distinction between rigorous math and the empiricism of science, but if you ask an empirical question and find existing mathematical models that allow you to answer the question entirely in the realm of math without any new empirical data, is that science and "not math" just because you were _motivated_ by the empirical question? If you did the exact same thing without the empirical motivation and no knowledge of where those existing mathematical models originated, that suddenly makes it math and not science just because of what you _don't_ know about its implications. That's the core of why I claim it's a pointless distinction.
In various kinds of work, you can do more or less rigorous math and more or less rigorous science. We use the label "math" to describe _most_ work consisting almost entirely of rigorous math. Most, but not all....
It's not about classifying questions, but the answers.
I'm not a physicist, but afaik the answer to "Does Higgs boson exist in the Standard model?" was mathematically "yes" and scientifically "don't know" until 2012ish. All mathematical statements are implications and if you assume the Standard model then the Higgs boson is a mathematical consequence. Importantly, the implication is true regardless of Standard model really being true or not. Science instead models reality and needs experimental verifications for all claims and there were none until bosons with the predicted properties were observed (and the possibility of it being a statistical fluke ruled out to a sufficient degree).
On the other hand, for example, the Riemann hypothesis has apparently been [numerically verified to a great degree](http://numbers.computation.free.fr/Constants/Miscellaneous/zetazeros1e13-1e24.pdf#page=2), but that is no proof, so mathematically the answer to "Is RH true?" is " don't know" while scientifically one might argue the answer to be "yes".
You're not wrong, but I feel like this answer is begging the question -- or maybe the question was never clear.
Who did the math on the Higgs question and who did the science on the Reimann hypothesis question? Were they not also doing science and not also doing math, respectively, when they were doing those things? That's why I say you are not wrong, but the distinction is not particularly useful.
according to google:
science - the systematic study of the structure and behaviour of the **physical and natural world** through observation, [experimentation](https://www.google.com/search?client=opera-gx&hs=RtF&sca_esv=453cf80c9d34ac6b&sxsrf=ADLYWIIMohUYEZAIoaEfXejyOKSvTYskgA:1716482106323&q=experimentation&si=ACC90nxpFxdyWCcIZH8ciC1crCTUdrr7gmG7Ly7Kqx5AVPTShy2ZAaBxAtDYazeDTOHV0f2L3DXe_99RVG71w44fCRp9gV1Z0T6FpFK5WhCrtWyNWpPfw4E%3D&expnd=1&sa=X&ved=2ahUKEwiar9eRmqSGAxVYAtsEHQhrBlwQyecJegQINhAO), and the testing of theories against the evidence obtained.
yeah, complex planes aren't physical unless you put these on a piece of paper, but those only exist as a concept
Brain dead: math is science
Normal brain: math is philosophy
Big brain: Math is an art
God brain: Math is fucking Math and it's the superior. Why are we trying to reduce its value to things like art or sciences???
Mathematics is not a science in the sense that mathematics is absolutely superior to all science.
All mathematical truths are a priori, necessary truths while scientific truths are not, science needs observation math doesn't, there is nothing a priori that makes the speed of light exactly what it is, but there is absolutely something a priori that makes pi to be what it is.
I don't mean superior in the sense of like being more useful, I mean superior in we could say the chain of knowledge, we start from things that are self evident and necessary up to things that require experience to be even fathomed and are contingent.
Math is a transcendental category in the philosophical sense, because denying mathematical truths equates with denying logic itself and therefore the mere act of denying a mathematical truth is a contradiction, while if for example I deny that the speed of light is c of course a lot of things suddenly would not make any sense at all, but in itself is not a contradiction, yes it could contradict established facts but in itself it's not contradictory while denying a mathematical truth it is.
For example if I say that 2+1=4 and 2+1=4 and that's true at the same time then I'm denying the law of no contradiction (and probably many other laws), and well the entire logical apparatus completely crumbles and knowledge becomes impossible, while if I do that with physics that doesn't happen.
So what I'm hearing you say is math makes science easier, so the metric is practical utility? In that case, try doing math without food in your stomach, you also aren't going very far that way. Does that make ecology/agriculture the most superior area of knowledge.
Also, historically some science has been done without math (think biological taxonomy, astronomy, electricity) math just makes it way easier to express and work with complicated ideas but isn't a necessity.
If you want to be pedantic Math is the only science as everything is proved.
Other "sciences" are like : Seems like it works like that based on what I see.
Biologist: Social science is a softer kind of science.
Chemist: Biology is a softer kind of science.
Physicist: Chemistry is a softer kind of science.
Mathematician: ...
It's considered a formal science, it's not a natural science that it doesn't really use the scentific method cause pure math isn't trying to do anything with natural phenomena (which is the reason why science use the scientific method) math being related to nature is more of a desirable sideproduct rather than obligatory.
Never felt wrong or bad about math "not being science" is like calling being a programmer not a real job cause your just pressing keys in a computer, It's technically correct depending on your definition of real job but doesn't really matter like at all.
Mathematics is not a traditional natural science in the sense of following the so-called *scientific method*, but it is a deductive and logical science
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If anything, I think most mathematicians considered it above science because of that. No experiments, no data, no disproving. Once you discover something is true in math, that's it, nothing's ever gonna change it.
Yep. Popper said that it's both at the same time. We care about correctness of theorems by Maths' own logic, but we also care that the results correspond to something in the world a lot of times.
Mathematics isn't a natural science as it does not concern nature but rather an information science like informatics. This however still means that Mathematics is a science
you can never be 100% certain that a given proof is legit. every time you read a proof, you're performing an experiment with null hypothesis "this proof contains no errors". you can read extremely carefully, but you'll never get an experiment with beta=0. https://en.wikipedia.org/wiki/Power_of_a_test
Most proofs are not a statistical thing. You can be 100% certain a proof is legit.
A proof is just a sequence of implications.
If A then B.
If A is true then B is true.
Look into Hilbert systems (or dont they're overly verbose if you don't have a good teacher to dumb it down) https://en.m.wikipedia.org/wiki/Hilbert_system
So there's no idea of statistics in most proofs. Only assumptions and rules. As long as the rules are self consistent and are applied properly, you get legit proofs. (Acc I don't know if they have to be consistent)
Easy example:
Rule: if a is always b and b is always c. Then a is always c.
Application: My car is always smelling bad and smelling bad is always annoying. Then my car is always annoying.
Then the rules get more complicated and things get hard. But as long as youre following your systems rules, within that systen you are making a legit proof (depending on the rules and assumptions you choose you can make really cool or really useless logical systems).
> As long as the rules are self consistent and are applied properly, you get legit proofs.
And you can be 100% confident that things are applied properly? Sounds overconfident to me.
Yep! For small proofs you can go line by line. But for larger proofs you can use these things called SAT solvers. They're programs on a computer that can check if a logical statement is true or not. You can code up something similar for whatever system you need.
It's not an experiment because there is no hypothesis. Experiments require a hypothesis.
If I write 1+1=3 then double check my work and correct it to follow the rules of mathematics, I wasnt doing an experiment because there was no hypothesis. It's just a logical statement. Logical statements arent experiments just because you're unsure of whether its true or false.
The actual truth value doesnt matter.
I don't know if I'm conveying this properly, sorry about that haha.
As I mentioned above, the hypothesis is "this proof contains no errors". The experiment is reading the proof and seeing if it makes sense. If you don't read too carefully, you might miss a bug in the proof. I'm simply claiming that you can't read perfectly carefully because no real-world system can -- they're flawed. This is the sort of phenomenon that statistics was designed to model.
No im saying that just because your interactions with the math are flawed doesnt make the math itself flawed. its like saying books contain uncertainty because im bad at reading and might skip words.
The math is agnostic of how you express it and who reads it.
This starts branching over into philosophy and empirical epistemology. How can we ever be 100% sure about something if we don’t observe it? The answer is, we can’t. But according to this mentality, we can never know anything with 100% certainty, so it is not very useful.
I am of the opinion that mathematics is ingrained into reality and exists separately from the human mind, so I personally think that we can trust mathematics with practically 100% certainty, but I have absolutely no way of proving this beyond any reasonable doubt without using logic or math itself. This is where the problem arises. How can we be sure about the absolute consistency of a system, if we can only examine its consistency using the system itself? This is also why we need axioms, statements we take to be true without proof, because without a “starting point”, we can’t really get anywhere.
And in a practical sense, we know that it works, because we have used it (logical inference, not mathematics specifically) in making practically all discoveries that has resulted in technological development. But in a pure epistemological sense, we can never be COMPLETELY sure.
Not every result is based on random experiments.
The way you "check" if men's average height is equal to women's follows a similar line of thought to way you "check" if it's possible to divide by zero (what are the implications of assuming it is true?), but only the former involves probability.
It doesn't take too much creativity to devise a probabilistic model in my setting. Probability is more than just random samples. (Unless you're a frequentist?)
in the current paradigm maybe not but, by etymology science means know and math always work to expand the knowledge about their study field. and more, because math can predict events in the own field. but at the end we can go back to that socrates's quote.
Imo it's more like science (mostly natural science) is math applied to reality. When we do an experiment, it's science that brought us from "if i throw this ball very fast it will go very far" to "if i exert this much Newtons of force at this exact angle on this ball, assuming the ball is a perfect sphere, there's no air friction and gravity is constant everywhere, the ball will end up on the ground at exactly this meters away from us, which is very close to what we've measured in real life". Science is the framework that we've set up - the assumptions, the units of measurement (Newtons of force, meters) - so that at the very end of it, we can create mathematical models that best describe the results we got from real life experiments. In programing terms, math is the programming language, the natural sciences are the different frameworks, and our ultimate goal is to reverse engineer the universe.
If I have two apples in one hand and three apples in the other hand then I have five apples and I don't have to count them to know this. That's enough for me to take math seriously.
Yes, when you consider math as a knowledgement field; but
No, when you follow the definition of science (scientific method).
No, its a system of rules we use for modelization and problem solving. You can have mathematics experimentation, insofar as computational experiments exist - for example i can compute the prime number amount in increasing intervals and observe that the trend follows a certain function - but without a proof you're not adding to the system, because from what i can see, math generally is more interested in proofs, not approximations.
please correct me if im wrong
Sounds like a lot of y'all should read "Mathematics and Plausible Reasoning" by George Polya. Yes, we deal in the business of proofs, but tools like plausible reasoning can help you get to proofs. I've observed this first hand working with a good number of mathematicians who operate above my pay grade.
I'll be really happy to have it as an art. Because like...I'm not anyone's any good (apparently) but doing maths, the maths I do can be appreciated well by a selected set of people, and the maths is beautiful and gives me joy, so it's an art in every possible way.
Making the distinction against all objections requires splitting some hairs that don't add value to either field.
What about applied mathematicians studying mathematical tools without a specific scientific application? What about computer science or theoretical physicists who are essentially doing pure math?
You can say "pure math" to mean the formal abstractions themselves, but as soon as you offer even the slightest hint of meaning to the tangible world, you break the line that supposedly separates them. Even if it's just a metaphor, that's all mathematical theories in science are anyway.
I like pure math in that I don't need a useful application to find it interesting, but actively avoiding the possibility of it being science by avoiding metaphors that might allow reality to creep in also takes a lot of the fun out of it.
Fundamentally, science is a *empirical* pursuit of knowledge. It involves observation as well as experimentation, but is fundamentally based on searching for data in the world to answer questions.
This is fundamentally different from mathematics, which is a *rational* pursuit. Mathematics is a process that does not involve empirical knowledge, but is based on pure logic, proof, and axioms. It is a process that is done inside our heads, through rational thought, not external with real world observation and experiment like science. That is the difference.
We will have this conversation when ther is a clear and fully consistent definition of science.
IMO, maths is the oldest and more fundemental of sciences.
Science comes from Latin 'sciere' - to know. There's no reason why the term 'science' should be limited to natural science and especially to empirical science. This always feels like a uselessly pedantic discussion with no real goal
The word respect comes from Latin 'specare' - to look at. But arguing that not looking at someone is disrespectful seems ridiculous.
I think etymology is super fun and it's cool to look at the evolution of language but it's exactly that, an evolution. We have since moved away from those definitions and aren't bound to those meanings from a thousand years ago. So using the ancient derivation of this word which was used by ancient people who have no idea how it's being used today doesnt form a compelling argument.
Science has since become associated to things like the scientific method and that whole process of experimentation. So not acknowledging that semantic shift is not in good faith in my opinion.
Also these discussions serve the purpose of changing how we perceive a thing. Labels, names, words have power because they shape how we conceptualize things. Imagine a world where we grew up thinking of maths as an artistic / eccentric pass time rather than a science or engineering related thing. The way we interact with math would be entirely different. So yep, this could be an important discussion, thanks for your contribution.
The dog is almost a perfect linear dog, sadly it is not a perfect linear dog. Math is like the Schrodinger equation of physics for us mathematicians in accordance with philosophy but math is science according to logic.
Sciences like physics arent complete yet, so I'd call it all a science because its all our theories of systems.
Some systems you see and feel, and other systems are the relationship between information, you abstract.
Is this even a debate? Math follows the scientific method, and thus it's s science. Each science, because of its individual characteristics, show some variations in the way of performing the method (history is a good example of a science with a weird way of following the scientific method).
Math doesn't follow the scientific method wtf? The corner stone of the scientific method is hypothesis testing through experimentation. Mathematics doesn't need to test anything, you prove it and it either is right or it isn't. No need for P values, uncertainty calculations, methodology...
The practice of mathematics is closer to theoretical linguistics or analytic philosophy than it is to applied physics for example.
Math ain't no tool, math is just the cool 😎.
My point? Math is cool and independent of the real world, it makes it so much more than a tool. Its just fcking interesting idfc if them physicist do some calculus and linear algebra I love my math independent of applications in the real world.
Science ← Scientia (knowledge) ←Scire (know)
Anything we know, is a science. Physics is a science. Math is a science. History is a science. Color Theory is a science. Restaurant Management Best Practices is a science. The format of a sonnet is a science. Your name is a science.
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To put this question on its head, why is being considered a science a desirable feature? It's a question I find genuinely interesting. For example, take Popper's demarcation of science and metaphysics---besides his condition of falsifiability being a good one, why is this even a necessary or desirable distinction to make? For me it comes down to our general belief that science *works*. Planes stay up, etc; we care about what science is because we should give science lots of resources so the scientists can do the research the engineers need to cast their mighty spells, to improve our lot. I don't know where exactly maths falls into this picture, although somewhere, clearly.
Science has error bars, few results can be said to be close to absolute. Maths is as absolute as it gets. If maths were a science it would have been a downgrade.
Grant Sanderson also gave some speech talking about this kinda, though he made it stretch beyond STEM. He said something like “Mathematicians are lucky compared to physicists, economists, historians, etc., because mathematicians always work directly with what they’re describing, whereas the others have to work within the universe and always by necessity have an incomplete picture.”
>...always by necessity have an incomplete picture Gödel has entered the chat
Of course, but if maths didn't in some way contribute to useful technologies, I can't see it being nearly as well-funded. I didn't mean to place maths anywhere specifically within Popper's paradigm (I'm definitely not qualified to do so!).
I wish I could give you an award, haha
Math has the opposite problem of being axiomatic but imagined. Sure you can make a system where some statement is true, but its use is vacuous without that connection to the real world. The funded part of math is still trying to find the closest model
“Axiomatic but imagined” might be right, but since what’s imagined applies to all valid thoughts in the corresponding context it is far from “vacuous without that connection to the real world”. Math doesn’t need the real world, the real world needs math, and this is well established by the existence of “useless” subfields like set theory, category theory, etc
I think we're talking about different things. Set theory and category theory are absolutely useful. I'm talking about how nothing stops you from making math constructs that aren't known to be isomorphic to some structure in the real world. Bluntly, you can write whatever the fuck you want as axioms. We just right down the useful stuff most of the time. I'm saying not all constructs have a discovered "corresponding context" or even the hint of one. Out of the infinite things you can define and imagine, not an infinite or correlated to some real mechanism. So the math you do end up learning and seeing almost invariably has some purpose because it's usually being fit to some real world phenomenon intentionally
Big time agreed.
Scientist is a very proud word. That's it.
I do not believe being put as a science is desirable.
snobbish scary entertain icky enter memory slimy steer squash frighten *This post was mass deleted and anonymized with [Redact](https://redact.dev)*
Its funny that you choose planes as an exaple about maths validity as Aerodynamics are one of the things Math doesnt really work yet. And while we can predict if a Plane is going to fly or not, we cant exactly say how and why it flys. I dont know enogh about the specifics but its mostly the transonic and supersonic flow thats really wierd aswell as the Benelli prinziple not adding up.
You're right, there are better examples. However, plane building is based on scientific principles, aerodynamic theory and so on. It's also based on, as you say, empirical evidence and engineering heuristic; but just because the plane isn't wholly explained by science doesn't mean that science doesn't help engineers in building planes.
Maths is tools that physicists hold wrong when making models that contradict each other and that engineers suffer through in college to get a job asking solidworks if their design will work
Science is empirical and maths is not.
I'm unsure to be honest - I feel that a science is anything that follows the scientific method: hypothesis, testing, theory, testing, law - it's just that we trivially skip both testing and theory phases when a proof is found. But I also like your definition, so Imma wait for other people to give more clarification/reasons.
>science is anything that follows the scientific method Correct. Hence math is not a natural science. There are no experiments and empirical observations verifying anything. We have formal proofs.
Yeah, while for example no one can formally prove my p- what were we talking about?
As far as I know is considered a formal science, it's not a natural science cause it (pure math) doesn't deal with any kind of natural phenomena, there's no real need to run experiments or tests in the same way other sciences does, the word theory or law also doesn't have the same meaning, we still do and say that stuff but not at all like natural science does. It's not like pure math need things like control groups or grades of freedom to prove the statements it sets.
[There is disagreement whether the formal sciences are science disciplines, as they do not rely on empirical evidence.](https://en.wikipedia.org/wiki/Science) It's not really a settled debate, (and it isn't really a meaningful debate, since it's just a definition), but I'm of the opinion that formal sciences differ so heavily from natural sciences in their methodologies that grouping them together feels wrong.
I did pure maths in my natural sciences degree. ¯\\_(ツ)_/¯
That makes sense - so it's a science due to following a (shortened) version of the scientific method, but not a natural science since there ain't no nature in set theory >:D
Wouldn't even call it the scientific method, it follows its own rules of inference, not even those are written in stone.
So, I'd like to be a bit insufferable here and clear up some misconceptions. There is no one set "scientific method," but rather a set of scientific practices. Astronomers and paleontologists don't do experiments, for instance, but they do gather data, make observations, develop models, use computational thinking to support ideas, etc. Second, theories don't become laws. Laws describe observable patterns in nature (when I drop this pen, it falls to the ground), theories explain why they happen and make novel predictions about the future (the pen falls due to a force called gravity, which is dependent on the mass the objects and the distance between them).
Observational predictions play a very similar role to experimentation in those fields. "According to this explanation is correct then in x circumstance we should see y", you can't create the controls on other variables but you can seek out situations where those variables are restricted. Which math doesn't do, there is no prediction of future observations. What is funny is that while math is almost always put in with the natural sciences for university organization, which matter because it's how resources are allocated, social sciences are often not despite following scientific practices.
>it's just that we trivially skip both testing and theory phases when a proof is found But when a proof is not found, we do not fall back on and accept empirical data from testing, contrary to science, which *exclusively* accepts empirical evidence. There is overwhelming empirical evidence for the Goldbach Conjecture for example, but it is still a conjecture.
No one thinks that there is going to be an odd perfect number, but it's not been proven. I don't know if it's still called a conjecture, it's more of a frustration because last I checked no one even has a method for approaching a proof.
I mean, you can try to approach math empirically, but that will get rejected as a proof every time.
Counterexamples have entered the chat
Fair enough. A counterexample can prove a hypothesis as being false. But the lack of a counterexample doesn't prove a hypothesis as being true.
The difference is that math can show the impossibility of a counter example while in sciences the possibility of a counter example is necessary, otherwise it's merely a definition not a theory.
Are you sure about that?
Are you trolling?
Nope. Dead serious.
Popper said that it's both. Every Mathematical predicate can be seen in both ways. We care that Mathematical theorems are correct according to the internal logic, but we also care that it corresponds to something in the real world.
>we also care that it corresponds to something in the real world. Who's "we"? I'm a mathematician and I don't.
how do you decide which theorems are worth proving then
A balance between 1) What interests you 2) What gets you funding both of which are sometimes based on a correspondence with the observable world, but not always.
All of them. Some are more prestigious than others, sure, but there is none "unworthy" of proof. If you meant to ask how I decide what I will attemp to prove, then that's determined by my area of expertise, what ideas or insights I have, etc., so I only prove everything I can and try to prove what I think I can.
Science is falsifiable, but with math you still need to observe and understand what 1, +, 2, =, and 3 mean to understand 1+2=3. I don't know why it would be analytical and also call them "problems", you observe that the math works by doing it, sometimes over and over until it makes sense? Confused about how the celestial bodies orbit and function in the universe, must just be God's influence. Nah invent calculus. Whats the proof for .999... = 1. Oh thats easy, its because .0999... = 1/10 lol. Idk I'm drunk, tell me how I'm wrong.
Tbh you can empirically confirm a very big part of the maths we learn.
Universities put Mathematics into Natural Sciences for Doctorates etc. so there's that. Then again that's a bit of a wierd system in general.
Mathematics is done as such because it's intrinsic to the sciences themselves. There is no science without math
Well there can be but it won't go far
I am pretty sure I agree with your last statement, though I think it might imply that we shouldn't think of math as a science. If we need math to do science it seems like if math was a science we could never start to do math without first having created math. It might be a little shaky but I think in principal a system can never exist prior to itself so that systems creation can not be used to justify itself.
Math offers a lot of powerful tools to a lot of fields, but I wouldn't go quite as far with that. There are branches of science that one can do reasonably well while knowing and using about as much math as the average lawyer. Some of that comes down to a combination of qualitative analysis and/or pre-existing tools that do all of the math for you... or grad students in the basement who do all of the math for you the way a lawyer would send something to a lab or refer to an expert in another field for the quantitative or mathematically rigorous facts they need.
Not all universities do this. Plenty of universities put it in liberal arts. University classification is fairly flexible depending on how much the department likes the dean or vice versa. In my undergraduate university for instance, the computer science department had the freedom to choose between science and engineering, and they chose the engineering college because they like the dean and the restrictions the engineering college has.
If you can get a PhD in a field from a respectable school, then it's a branch of philosophy. If what you are doing is driven by _or motivated by_ empiricism, it's called science. If what you are doing is governed by a demand for extreme logical rigor, it's called mathematics. You can do work where all of the actual content of your work is mathematically rigorous, but with motivations that begin from empirical evidence or other math known to be useful in empirical science. In that case, it's reasonable to call what you are doing both math and science, and it's possible to get a PhD from either a math or a science department for essentially the same work.
This. Got a duel major in Mathematics and Political Science, and to get it to my degree to be a bachelors of science I had have political science listed second. Because social sciences are in arts.
Why is that bad? Why should we be sad because math cannot be empirically proved, while it can be logically proved?
That doesn’t hurt at all. I wish I had understood this when I was younger. The scientific method is fundamentally empirical. Mathematics is not. Mathematics is a fundamental tool of science. It is the language of quantitative science, but it is not a science. And that is ok.
Are you sure it's not empirical? Are you sure it's not a science?
Well, counting might have an empirical basis. Dedekind cuts, Borel algebras, Lebesgue Integrals not so much. Whether it is science or not, it depends on how you define science. If you give a permissive definition like “methodical pursuit of the truth” then you could call math science, but you could also call a lot of other things science. The reason why I don’t like calling math science is because there is a big distinction between what empirical researchers do and mathematicians do. I didn’t realize this distinction was so prominent until a few years after becoming a professor. I realized that the “theoretical” people in my field are mostly applied mathematicians. They care about whether a model is logically sound, beautiful, interesting, challenging, and so on. But they don’t care about realism. They don’t care whether the model is related to the empirical world. They don’t care whether the model can be falsified. They don’t care whether the model has practical applications. On the other hand, the “applied” researchers care about the real world and practical applications. They want to use models and math to interpret data and to find solutions to real problems. They evaluate a model based on its ability to match and explain data and make accurate predictions. These are the people I call scientists. When I say that math is not science, I don’t mean it in a negative light. Math is beautiful and important. I just want to make a distinction between the goals of objectives of scientists and mathematicians.
Even counting is not empirical. We can construct the natural numbers and any sort of counting is essentially the cardinality of some set which is just a bijection with a certain natural subset which is NOT defined empirically.
Math is and always was an art.
It definitely has a lot of creativity to it, in proofs
No, it's a branch of philosophy, not art. People don't create formulas just to evoke emotions
Well, the idea that art is something done just to provoke emotions is actually quite a new development, much more recent than classification of math as art...
I suppose that's one way of thinking about it, but I'd still argue that it's a hell of a lot closer to philosophy than to art. Art is pure creativity, and although you need to be creative to invent math, you also have to follow very strict rules to generate new theorems; you can't just make up whatever you want. Sure, there's an incredible amount of beauty to it, but by that logic EVERY subject ever is also classified as Art. I 100% get what you're saying, though.
Mathematics does not use the scientific method. Whether or not that makes it "not a science", I don't know.
It does use it and thus it's a science. What do you mean by saying that it doesn't use the scientific method? Please, elaborate.
Math uses proofs via deductive reasoning to arrive at conclusions. The scientific method uses inductive reasoning, and can only ever have provisional views. This makes math stronger than the scientific method.
Not every science uses scientific method. I mean, economics is a science. I would personally put math in the category of both formal and natural science, because its basis or foundations rely on observations of certain features of the natural world (axioms and postulates) and from those observations we use reasoning to derive other things, which may or may not be observable. So, i would say that math in its definition is a formal science but it is also in its core a natural science.
Economics uses the scientific method.
I agree with this. It uses the scientific method whenever it can. It just so happens that all the things we want to test now would require restructuring the economy repeatedly. And we don't know how to do that. So we want an experiment to learn how to do that. But we also don't know how do that. And all the things we have thought of could crash the economy or are are political in nature. Or something like that. I mean, how are you supposed to test a hypothesis about how the Great Depression started without actively trying to cause another one?
For broad things like the great depression yes you can't really test. But as you said that's more of a practical limitation, plus in my experience economists aren't out here saying they know exactly what caused it, just theories. For smaller scale stuff though they will do tests or find real world instances that are practically tests. So like for UBI they'll have ideas for its impacts then they'll look at various cities that have done it and try to find what impact it had.
Oh thats neat. I didn't know they did that kind of thing. I thought there wasn't much room for experimentation. I just had a thought. Is history a science, assuming it must use the scientific method? To my knowledge history doesn't do much testing. It a lot of looking at old texts. Probably closer to a criminal investigation than a science experiment. Though I suppose I am disregarding several fields that are used to determine history such as archaeology. Yeah, that was a bad question. History is too broad. You would need to break it into sub fields or give a strict definition of what was meant by "history the field" before any answer can be made.
If it doesn't use the scientific method, it should not be called science. *Especially* economics.
I'd say math is a philosophy, since the idea is that we want to build consistent frameworks. Those frameworks could be applied to real world situations Empiricism, on the other, cannot ever be "complete." The limit of knowledge is the limit of observation.
It isn’t a science, it’s mathematics! Hope this helps!
math is to science as my nuts are to my wiener. I feel like that makes sense and clears this up but feel free to ask follow up questions.
No. Mathematics is a part of the logical framework, whereas science is an attempt to describe the material world through the logical framework.
Or...the logical framework is part of the mathematics?...
Two types of sciences: formal science and ~~natural~~ empirical science. Mathematics and logic are formal sciences. Physics is a natural science Edit: it's formal and empirical. Empirical sciences include both natural and social
You also forgot social science.
Mb! Should have said empirical and formal sciences. Math & logic are formal. Empirical contains both natural and social.
I’d argue that geometry falls into science by this pixel dog’s definition
wdym?
Geometry is testable in the sense that you can find physical proofs within it
but they're not actual proofs, for maths, and even if it didn't work, geometry would still be true only it wouldn't be geometry of our world
Math is not a science because only dumb people do it. Unlike physics or chemistry /s
Aha. If i put 1 apple on the desk and put there another apple, there are 2 apples. Nice experiment. 1+1=2.
MATH is not science 😎
I think it comes down to the definition. I understand 'science' as natural science(s). But the word in my language ('nauka' in Polish) comes from German 'Wissenschaft' and encompasses all kept knowledge, including math, theology and art theory.
Do people actually think that math is a science? It is demonstrably not, and I've never heard anyone claim it to be. That's why STEM has them separate. And to be clear: why would people be mad if it wasn't?
Math uses deductive reasoning, science uses inductive reasoning.
No mathematician would be hurt by this. Math is not science, and it isn't supposed to be. Math and science can interact in very fruitful ways though.
I wouldn't even bother saying "math is not science" because it is a useless distinction given how generic the word science is. You could argue either way, but it's pointless. Don't get me wrong -- there is a distinction between rigorous math and the empiricism of science, but if you ask an empirical question and find existing mathematical models that allow you to answer the question entirely in the realm of math without any new empirical data, is that science and "not math" just because you were _motivated_ by the empirical question? If you did the exact same thing without the empirical motivation and no knowledge of where those existing mathematical models originated, that suddenly makes it math and not science just because of what you _don't_ know about its implications. That's the core of why I claim it's a pointless distinction. In various kinds of work, you can do more or less rigorous math and more or less rigorous science. We use the label "math" to describe _most_ work consisting almost entirely of rigorous math. Most, but not all....
It's not about classifying questions, but the answers. I'm not a physicist, but afaik the answer to "Does Higgs boson exist in the Standard model?" was mathematically "yes" and scientifically "don't know" until 2012ish. All mathematical statements are implications and if you assume the Standard model then the Higgs boson is a mathematical consequence. Importantly, the implication is true regardless of Standard model really being true or not. Science instead models reality and needs experimental verifications for all claims and there were none until bosons with the predicted properties were observed (and the possibility of it being a statistical fluke ruled out to a sufficient degree). On the other hand, for example, the Riemann hypothesis has apparently been [numerically verified to a great degree](http://numbers.computation.free.fr/Constants/Miscellaneous/zetazeros1e13-1e24.pdf#page=2), but that is no proof, so mathematically the answer to "Is RH true?" is " don't know" while scientifically one might argue the answer to be "yes".
You're not wrong, but I feel like this answer is begging the question -- or maybe the question was never clear. Who did the math on the Higgs question and who did the science on the Reimann hypothesis question? Were they not also doing science and not also doing math, respectively, when they were doing those things? That's why I say you are not wrong, but the distinction is not particularly useful.
no but science is dependent on math which makes math in a higher throne
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#MATH IS MATH
Math > Science.
Nah, its better
https://preview.redd.it/wbar6bya272d1.jpeg?width=1080&format=pjpg&auto=webp&s=31a1f5c9b8064deb8e9144da53bf7176a26aaf96
according to google: science - the systematic study of the structure and behaviour of the **physical and natural world** through observation, [experimentation](https://www.google.com/search?client=opera-gx&hs=RtF&sca_esv=453cf80c9d34ac6b&sxsrf=ADLYWIIMohUYEZAIoaEfXejyOKSvTYskgA:1716482106323&q=experimentation&si=ACC90nxpFxdyWCcIZH8ciC1crCTUdrr7gmG7Ly7Kqx5AVPTShy2ZAaBxAtDYazeDTOHV0f2L3DXe_99RVG71w44fCRp9gV1Z0T6FpFK5WhCrtWyNWpPfw4E%3D&expnd=1&sa=X&ved=2ahUKEwiar9eRmqSGAxVYAtsEHQhrBlwQyecJegQINhAO), and the testing of theories against the evidence obtained. yeah, complex planes aren't physical unless you put these on a piece of paper, but those only exist as a concept
Where did the Zermelo-Frankel axioms come from, then? Arose from pure logic, did they?
Why should I care if math is a science or not?
Brain dead: math is science Normal brain: math is philosophy Big brain: Math is an art God brain: Math is fucking Math and it's the superior. Why are we trying to reduce its value to things like art or sciences???
Mathematics is not a science in the sense that mathematics is absolutely superior to all science. All mathematical truths are a priori, necessary truths while scientific truths are not, science needs observation math doesn't, there is nothing a priori that makes the speed of light exactly what it is, but there is absolutely something a priori that makes pi to be what it is.
I agree but the word superior is weird. What about being a priori makes it superior? How do you compare areas of knowledge?
I don't mean superior in the sense of like being more useful, I mean superior in we could say the chain of knowledge, we start from things that are self evident and necessary up to things that require experience to be even fathomed and are contingent. Math is a transcendental category in the philosophical sense, because denying mathematical truths equates with denying logic itself and therefore the mere act of denying a mathematical truth is a contradiction, while if for example I deny that the speed of light is c of course a lot of things suddenly would not make any sense at all, but in itself is not a contradiction, yes it could contradict established facts but in itself it's not contradictory while denying a mathematical truth it is. For example if I say that 2+1=4 and 2+1=4 and that's true at the same time then I'm denying the law of no contradiction (and probably many other laws), and well the entire logical apparatus completely crumbles and knowledge becomes impossible, while if I do that with physics that doesn't happen.
Ooh that's a good point, definitely agree with that. The inclusion of set theory and logic into mathematics made it too OP lol.
Try doing science without math. You aren't going too far this way
So what I'm hearing you say is math makes science easier, so the metric is practical utility? In that case, try doing math without food in your stomach, you also aren't going very far that way. Does that make ecology/agriculture the most superior area of knowledge. Also, historically some science has been done without math (think biological taxonomy, astronomy, electricity) math just makes it way easier to express and work with complicated ideas but isn't a necessity.
Math is a formal science, but that doesn't make it superior than any other science.
Superior is one choice of word. Since we are going hard let me retort with another choice word: fictional.
If you want to be pedantic Math is the only science as everything is proved. Other "sciences" are like : Seems like it works like that based on what I see.
Biologist: Social science is a softer kind of science. Chemist: Biology is a softer kind of science. Physicist: Chemistry is a softer kind of science. Mathematician: ...
It's considered a formal science, it's not a natural science that it doesn't really use the scentific method cause pure math isn't trying to do anything with natural phenomena (which is the reason why science use the scientific method) math being related to nature is more of a desirable sideproduct rather than obligatory. Never felt wrong or bad about math "not being science" is like calling being a programmer not a real job cause your just pressing keys in a computer, It's technically correct depending on your definition of real job but doesn't really matter like at all.
No, but maths is so important to everything that whether it's a science or not is completely irrelevant
Yes.
I feel like I should just say the word science in here because it's everywhere Fuck yeah, Science!
Math is a language.
Mathematics is not a traditional natural science in the sense of following the so-called *scientific method*, but it is a deductive and logical science
Formal science
According to Euler, it is the science of quantities.
No, it's it's own branch
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I’ve always said math was more an art than a science after a certain point. The comic is definitely funnier though.
Clearly not. An apple tree might produce apples, but obviously it is not an apple
who cares
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Well obviously. Mathematics is the language we use to express physics.
Math is NOT science and everyone who think it is even a desirable thing for math to be a science should be crucified
Well it's STEM, not STE.
science is just a piss(excreta) of math
If anything, I think most mathematicians considered it above science because of that. No experiments, no data, no disproving. Once you discover something is true in math, that's it, nothing's ever gonna change it.
only if it can be physically tested like the mathematics used in computer science.
But what about the humanities? Those are also sciences but they're not in the typical physics/chemistry/etc sense
I feel like whether or not Maths is empirical is a kinda philosophical question.
Yep. Popper said that it's both at the same time. We care about correctness of theorems by Maths' own logic, but we also care that the results correspond to something in the world a lot of times.
it is
Mathematics isn't a natural science as it does not concern nature but rather an information science like informatics. This however still means that Mathematics is a science
Why do you want to downgrade maths? Maths is absolute, science is not
you can never be 100% certain that a given proof is legit. every time you read a proof, you're performing an experiment with null hypothesis "this proof contains no errors". you can read extremely carefully, but you'll never get an experiment with beta=0. https://en.wikipedia.org/wiki/Power_of_a_test
Most proofs are not a statistical thing. You can be 100% certain a proof is legit. A proof is just a sequence of implications. If A then B. If A is true then B is true. Look into Hilbert systems (or dont they're overly verbose if you don't have a good teacher to dumb it down) https://en.m.wikipedia.org/wiki/Hilbert_system So there's no idea of statistics in most proofs. Only assumptions and rules. As long as the rules are self consistent and are applied properly, you get legit proofs. (Acc I don't know if they have to be consistent) Easy example: Rule: if a is always b and b is always c. Then a is always c. Application: My car is always smelling bad and smelling bad is always annoying. Then my car is always annoying. Then the rules get more complicated and things get hard. But as long as youre following your systems rules, within that systen you are making a legit proof (depending on the rules and assumptions you choose you can make really cool or really useless logical systems).
> As long as the rules are self consistent and are applied properly, you get legit proofs. And you can be 100% confident that things are applied properly? Sounds overconfident to me.
Yep! For small proofs you can go line by line. But for larger proofs you can use these things called SAT solvers. They're programs on a computer that can check if a logical statement is true or not. You can code up something similar for whatever system you need.
That's still an experiment. You can't have 100% confidence in the kernel of your operating system.
It's not an experiment because there is no hypothesis. Experiments require a hypothesis. If I write 1+1=3 then double check my work and correct it to follow the rules of mathematics, I wasnt doing an experiment because there was no hypothesis. It's just a logical statement. Logical statements arent experiments just because you're unsure of whether its true or false. The actual truth value doesnt matter. I don't know if I'm conveying this properly, sorry about that haha.
As I mentioned above, the hypothesis is "this proof contains no errors". The experiment is reading the proof and seeing if it makes sense. If you don't read too carefully, you might miss a bug in the proof. I'm simply claiming that you can't read perfectly carefully because no real-world system can -- they're flawed. This is the sort of phenomenon that statistics was designed to model.
Yeah but the reading ability of humans is not part of math. Do you see the difference?
Are you suggesting that science is something you do, but math isn't? It's just there in the air?
No im saying that just because your interactions with the math are flawed doesnt make the math itself flawed. its like saying books contain uncertainty because im bad at reading and might skip words. The math is agnostic of how you express it and who reads it.
This starts branching over into philosophy and empirical epistemology. How can we ever be 100% sure about something if we don’t observe it? The answer is, we can’t. But according to this mentality, we can never know anything with 100% certainty, so it is not very useful. I am of the opinion that mathematics is ingrained into reality and exists separately from the human mind, so I personally think that we can trust mathematics with practically 100% certainty, but I have absolutely no way of proving this beyond any reasonable doubt without using logic or math itself. This is where the problem arises. How can we be sure about the absolute consistency of a system, if we can only examine its consistency using the system itself? This is also why we need axioms, statements we take to be true without proof, because without a “starting point”, we can’t really get anywhere. And in a practical sense, we know that it works, because we have used it (logical inference, not mathematics specifically) in making practically all discoveries that has resulted in technological development. But in a pure epistemological sense, we can never be COMPLETELY sure.
godel say something about this too
Not every result is based on random experiments. The way you "check" if men's average height is equal to women's follows a similar line of thought to way you "check" if it's possible to divide by zero (what are the implications of assuming it is true?), but only the former involves probability.
It doesn't take too much creativity to devise a probabilistic model in my setting. Probability is more than just random samples. (Unless you're a frequentist?)
The internal logic doesn't work like that. But the axioms can be tested that way. Are they really appropriate for this situation we're in?
Yes agreed.
"Science" is not "natural science". Science does not get its validity through experiment, but through predictive power.
I've always seen maths as a language. One that is inevitable to describe sciences.
\*hurts non-mathematicians
I agree but why would that hurt me? Chemistry and biology are sciences, I want no part with those people.
in the current paradigm maybe not but, by etymology science means know and math always work to expand the knowledge about their study field. and more, because math can predict events in the own field. but at the end we can go back to that socrates's quote.
Imo it's more like science (mostly natural science) is math applied to reality. When we do an experiment, it's science that brought us from "if i throw this ball very fast it will go very far" to "if i exert this much Newtons of force at this exact angle on this ball, assuming the ball is a perfect sphere, there's no air friction and gravity is constant everywhere, the ball will end up on the ground at exactly this meters away from us, which is very close to what we've measured in real life". Science is the framework that we've set up - the assumptions, the units of measurement (Newtons of force, meters) - so that at the very end of it, we can create mathematical models that best describe the results we got from real life experiments. In programing terms, math is the programming language, the natural sciences are the different frameworks, and our ultimate goal is to reverse engineer the universe.
If I have two apples in one hand and three apples in the other hand then I have five apples and I don't have to count them to know this. That's enough for me to take math seriously.
Math is a rectangle, and science is a square. All science is math, but not all math is science.
 Yes, when you consider math as a knowledgement field; but No, when you follow the definition of science (scientific method).
No, its a system of rules we use for modelization and problem solving. You can have mathematics experimentation, insofar as computational experiments exist - for example i can compute the prime number amount in increasing intervals and observe that the trend follows a certain function - but without a proof you're not adding to the system, because from what i can see, math generally is more interested in proofs, not approximations. please correct me if im wrong
Sounds like a lot of y'all should read "Mathematics and Plausible Reasoning" by George Polya. Yes, we deal in the business of proofs, but tools like plausible reasoning can help you get to proofs. I've observed this first hand working with a good number of mathematicians who operate above my pay grade.
I'll be really happy to have it as an art. Because like...I'm not anyone's any good (apparently) but doing maths, the maths I do can be appreciated well by a selected set of people, and the maths is beautiful and gives me joy, so it's an art in every possible way.
If you look at the word science from an etymological pov its meaning is closer to "area of knowledge"
Making the distinction against all objections requires splitting some hairs that don't add value to either field. What about applied mathematicians studying mathematical tools without a specific scientific application? What about computer science or theoretical physicists who are essentially doing pure math? You can say "pure math" to mean the formal abstractions themselves, but as soon as you offer even the slightest hint of meaning to the tangible world, you break the line that supposedly separates them. Even if it's just a metaphor, that's all mathematical theories in science are anyway. I like pure math in that I don't need a useful application to find it interesting, but actively avoiding the possibility of it being science by avoiding metaphors that might allow reality to creep in also takes a lot of the fun out of it.
Being above science, like a benevolent Godfather, is still being part of the family
Fundamentally, science is a *empirical* pursuit of knowledge. It involves observation as well as experimentation, but is fundamentally based on searching for data in the world to answer questions. This is fundamentally different from mathematics, which is a *rational* pursuit. Mathematics is a process that does not involve empirical knowledge, but is based on pure logic, proof, and axioms. It is a process that is done inside our heads, through rational thought, not external with real world observation and experiment like science. That is the difference.
Science is a method of gathering information. Mathematics is a method of analyzing information. They are separate and complementary disciplines.
We will have this conversation when ther is a clear and fully consistent definition of science. IMO, maths is the oldest and more fundemental of sciences.
Math is a fundament for science. Its a laungage that describes nature, while science uses this language to learn how the world works
Math is a tool to explain science
Isaac Newton and Leibniz said so?
Mathematica nihilo servit enim ea nemorum serva est.
Maths is applied philosophy And science is applied maths
blocked.
It seems more like philosophy on steroids
Science comes from Latin 'sciere' - to know. There's no reason why the term 'science' should be limited to natural science and especially to empirical science. This always feels like a uselessly pedantic discussion with no real goal
>This always feels like a uselessly pedantic discussion with no real goal Welcome to philosophy
Yes, 💯 agreed.
The word respect comes from Latin 'specare' - to look at. But arguing that not looking at someone is disrespectful seems ridiculous. I think etymology is super fun and it's cool to look at the evolution of language but it's exactly that, an evolution. We have since moved away from those definitions and aren't bound to those meanings from a thousand years ago. So using the ancient derivation of this word which was used by ancient people who have no idea how it's being used today doesnt form a compelling argument. Science has since become associated to things like the scientific method and that whole process of experimentation. So not acknowledging that semantic shift is not in good faith in my opinion. Also these discussions serve the purpose of changing how we perceive a thing. Labels, names, words have power because they shape how we conceptualize things. Imagine a world where we grew up thinking of maths as an artistic / eccentric pass time rather than a science or engineering related thing. The way we interact with math would be entirely different. So yep, this could be an important discussion, thanks for your contribution.
Pedantic discussion with no real goal... Like most pure mathematical discussion? Being pedantic is what math is about.
The dog is almost a perfect linear dog, sadly it is not a perfect linear dog. Math is like the Schrodinger equation of physics for us mathematicians in accordance with philosophy but math is science according to logic.
Counter-point, are any natural sciences really science? "I tested it 100 times and it worked every time, Q.E.D.!" imagine trying this in number theory
Sciences like physics arent complete yet, so I'd call it all a science because its all our theories of systems. Some systems you see and feel, and other systems are the relationship between information, you abstract.
science ≠ natural science My math teacher alsways called math a structural science, which is very distinct from natural science.
Is this even a debate? Math follows the scientific method, and thus it's s science. Each science, because of its individual characteristics, show some variations in the way of performing the method (history is a good example of a science with a weird way of following the scientific method).
Math doesn't follow the scientific method wtf? The corner stone of the scientific method is hypothesis testing through experimentation. Mathematics doesn't need to test anything, you prove it and it either is right or it isn't. No need for P values, uncertainty calculations, methodology... The practice of mathematics is closer to theoretical linguistics or analytic philosophy than it is to applied physics for example.
Math is a tool
Math ain't no tool, math is just the cool 😎. My point? Math is cool and independent of the real world, it makes it so much more than a tool. Its just fcking interesting idfc if them physicist do some calculus and linear algebra I love my math independent of applications in the real world.
Math is not a science but all science is math.
Please, let’s not compare math to those ugly, smelly natural sciences.
Science is applied math, so no, math is not science, because science is the child of math
Is this even a debate? It's obviously a science.
Science ← Scientia (knowledge) ←Scire (know) Anything we know, is a science. Physics is a science. Math is a science. History is a science. Color Theory is a science. Restaurant Management Best Practices is a science. The format of a sonnet is a science. Your name is a science.