Is math a science?
>>7723039
No.
>>7723039
no. science is inductive and empirical. math is deductive and axiomatic.
If science was a car, math would be the transmission. Math on its own, is not a science, but if you remove the transmission from the car it would no longer function.
No.
All mathematicians agree upon this as well. Math isn't even trying to be a science. There are no experiments to be done, you just do things.
t. Mathematician
>>7723050
>science is inductive
wrong
>math is axiomatic
even more wrong
Can uneducated philosotards like you please stop talking about things they don't understand?
>>7723039
maths
>>7723039
Sure. You often have an idea about how something will work, you try to concoct circumstances where things will hold, then you see what happens. Things can go fully, partially, or not at all right, and then you say "Ok well why did things go that way" then you try to come up with a new explanation and go again.
>>7723050
math doesn't come up with itself. Thought experiment: that would be the same as saying that if the world were deterministic then physics is not a science, because you "axiomatically" put in some conditions, and there was only one way it could go, deductively. But that's obviously not the right notion. Just like in the real world, rarely do mathematicians have the "whole picture" when they set out to prove something. They make some assumptions about the (mathematical) universe they are working in, true, but so do most physicists. If things aren't going as planned, the axioms (i.e. assumptions) might have to be changed.
Often many "experiments" have to be done along the way, and sometimes theorems have to be broken down into a bunch of cases, just as with empirical science, before progress is made, or it is obvious how to proceed "experimentally".
It's a tool
>>7723100
Math is not the activity and practice of doing math. Math is not science, the practice of doing math is what you're describing, and it's very similar to the practice of doing science.
It's a formal science, now can we please stop getting this thread every week
>>7723039
Oh yeah its definitely not a science its not like there was ever a mathematician who was also a scientist who deduced mathematical truths through the scientific method
>Gauss
>Newton
>Fibonacci
>Euler
>>7723132
i might agree, but I also think that's a philosophical point that not all mathematicians agree on. certain strong forms of intuitionism might say that math is exactly doing it and building it, and there isn't any other thing out there. Mac lane seemed to have a somewhat more utilitarian view of math - that is, the "right" mathematics is the math that, for you, shows up the most often and is applicable in the widest range of circumstances, but it doesn't exist outside of usage or particular forms (or abstractions of them). but I see your point.
>>7723132
this is also especially tricky if you define science in terms of a particular procedural schema, which math does follow fairly closely
>>7723569
They also shat in the toilet. Poo in loo is now a science.
>>7723039
You definitely hypothesis test in math, it just doesn't take large sums of money.
>>7723050
hilbert pls
"the veracity of mathematical statements is determined by continuously checking every observation and known examples and see if the statement still holds true"
said no one ever
>>7723039
Applied math is.
suppose you were contracted to make a certain number of product over a planning period. there's a cost for holding the product in storage. what is the optimal way of manufacturing this product over a planning period?
theres your question.
background research: has anyone done this? what do you know there's calculus of variations
construct a hypothesis: assume a form for the rate of production (ex: y' = ay)
test with an experiment: make model and solve it
procedure working: analyze model
>>7723652
Topkek
1. Mathematics is the language of nature.
2. Everything around us can be represented and understood through numbers.
3. If you graph these numbers, patterns emerge.
Therefore: There are patterns everywhere in nature.
>>7724037
1. Language is the language of nature.
2. Everything around us can be represented and understood through language, even things that do not exist.
3. If you compile all of language's uses and applicability, patterns emerge.
Therefore: There are patterns everywhere relative to human perception.
>>7723039
>>math is axiomatic
>even more wrong
do you even know what mathematics is ?
you make axioms and see what logically true statements arise from those axioms .
>>7723039
science-
the intellectual and practical activity encompassing the systematic study of the structure and behavior of the physical and natural world through observation and experiment.
mathematics-
the abstract science of number, quantity, and space.
it is a science by definition ,
>>7724057
You're a dick baller by definition.
>>7724037
>1. Mathematics is the language of nature.
meme statement ,language is defined as a a means of communication which is defined as the transfer of information ,and information in nature is basically all the properties of everything so 'communication' would be physical interaction between different physical entities .
>2. Everything around us can be represented and understood through numbers.
there is not a single thing in the universe that can be represented or understood using numbers . you can maybe make models and approximations of things using numbers but not understand or represent anything .
>3. If you graph these numbers, patterns emerge.
yes but that that dosnt tell you anything for certain since the numbers you graph dosnt represent anything other then models and approximations .
>Therefore: There are patterns everywhere in nature.
prove it ,there is no way of knowing if there exists a single pattern in all of nature .
also only a subset of mathematics deals with numbers .
>>7724063
this , you need it to fit the definition of a science to be called a science . math doesn't "study of the structure and behavior of the physical and natural world". it studies logical statements about things , be it numbers or any other mathematical entity .
>>7724040
>>7724040
When I was a little kid my mother told me not to stare into the sun. So once when I was six I did. The doctors didn't know if my eyes would ever heal. I was terrified, alone in that darkness. Slowly, daylight crept in through the bandages, and I could see. But something else had changed inside of me. That day I had my first headache.
>>7724057
>do you even know what mathematics is ?
I'm a math PhD student.
>you make axioms and see what logically true statements arise from those axioms .
This is not how math is done. This is only what fedora'd highschoolers falsely believe how math is done. Outside of formal logic itself, almost no mathematician ever deals with axioms or formal inference from axioms.
>>7724077
>there is no way of knowing if there exists a single pattern in all of nature
i mean you can graph a lot of natural phenomena with sin/cos/exponential functions so i would disagree
unless of course you disagree with my definition of pattern
which you probably do because this is /sci/
Sure. But what is love?
>>7723100
>math doesn't come up with itself.
Mathematicians come up with math by themselves. There is no input from empirical data, just deduction from the set of axioms chosen and whatever constructs are made. Now, deduction might be made by guessing a solution and then bridging the gap with a proof, but that is still deduction. It's the proof we care about most, not the guessed solution.
>Thought experiment: that would be the same as saying that if the world were deterministic then physics is not a science, because you "axiomatically" put in some conditions, and there was only one way it could go, deductively.
That's nonsense. We wouldn't know *how* the world is deterministic without looking at it. We then choose from mathematics which deterministic construct matches what we see the best. This is an empirical, inductive process that completely separates physics from math.
>>7723451
whats the difference between formal and empirical science?
>>7724399
we've known how to state Diophantine equations for thousands of years but that doesn't mean we know *how* the deductive system is going to produce results about them, or even whether the elementary constructions will have anything to say about them. that is, without looking at examples and coming up with new systems that analyze them.
I'll admit it's a loose analogy, but the overlap is far from nil.
of course, there are many differences, like even if your mathematics is using the "wrong" axioms, you can still prove true facts about that model.
