# Mathematics being the only pure science

## Main Question or Discussion Point

Mathematics being the only "pure science"

Today, in Astronomy, being an entry level science class, the professor goes over basic concepts of science. Such as that we seek to falsify, because it is much easier than verifying. In fact, verifying is impossible because we cannot have an infinite amount of tests and data.

Of course, all of that is 100% correct as far as I know, but then he said:

"..except in Mathematics. We can verify things in Mathematics, Mathematics is the only pure science."

Agree?

This contradicts some quotes I've seen such as "all of math is theory."

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I agree with your professor when he said that all in math can be verified. That's the beauty of it, you can actually show something to be correct ALWAYS. In science, we can only say that something agrees with our experiments within an error of 5%. But mathematics gives us absolute certainty!

However, I disagree when your professor says that mathematics is a science. Science works with experiments and tries to approximate the real world. Mathematics does not try to work with the real world. The real world doesn't really matter.

Remember that in mathematics you are not proving that the hypotheses are true, nor are you proving that the conclusion is true. What you are proving is that the conclusion is implied by the hypotheses.

You also need to remember that in math, you only "prove" something within the context of the set of axioms (which are inherently unprovable), so, in the end, even math is not "100% verifiable" - it's only verifiable if the axioms are also true.

However, I disagree when your professor says that mathematics is a science. Science works with experiments and tries to approximate the real world. Mathematics does not try to work with the real world. The real world doesn't really matter.
Why would you say that math doesn't try to deal with the real world? If not, then how else did we come up with the basic laws of multiplication, division addition and subtraction... As far as I know they didn't just drop from math land... but rather from observations (however simple) of the physical world. When I put two rocks together they make two rocks... and when I have three of these (two rock groups) I get six rocks... This is probably how the first mathematical laws were created, then Euclid and others took this simplified Science and created more complex theorems surrounding the basic conjectures.

But Like any Science, mathematics is subject to uncertainty, for example, could we build a computer that "thinks" 1+1=3? I would say yes, so what is to say we are not a product of a world that works upon entirely different mathematical laws? Of course this view is not worth worrying about, like solipsism, but I think it is worth pointing out that Mathematics has arisen from our physical world, simply because there is no where else it could have come from... enlighten me if there is.

I suppose you could say complex numbers or non-real/abstract numbers and the space/functions created from them don't obey our physical world, however they do help to describe it.

G01
Homework Helper
Gold Member

However, I disagree when your professor says that mathematics is a science. Science works with experiments and tries to approximate the real world. Mathematics does not try to work with the real world. The real world doesn't really matter.
I disagree with the professor as well. Mathematics does not utilize the scientific method, so it can't really be called a science. There is no reason it should, of course, and in many cases it would be of no help.

I get confused with the term computer science. The theoretical part of the computer "science" (like the automata theory, turing machines, algorithms) are part of logic, hence it should be part of mathematics. There is no science in computer science.

but I think it is worth pointing out that Mathematics has arisen from our physical world, simply because there is no where else it could have come from... enlighten me if there is.
It is a language which has arisen as a matter of humans attempting to understand and communicate their perceptions of the world around them. The only thing special about math is that it appears far better suited to describing the world around us than normal language. Its not better at this because the physical world made it that way, it is better because we have made it that way. From notches in sticks to calculus the former is obviously less capable of accurately describing the world.

However, I disagree when your professor says that mathematics is a science. Science works with experiments and tries to approximate the real world. Mathematics does not try to work with the real world. The real world doesn't really matter.
Yes I agree, when I saw the title I was thinking mathematics is definitely pure but not a science. I could be wrong of course, but I really do not think of it as a science.

Mathematics is the language of logic.

Pythagorean
Gold Member

natural (as opposed to moral) philosophy is the "pure" science, but good philosophy would lead one to physics, chemistry, biology, psychology, sociology, geology, etc...

Mathematics is a semantic-free language. That makes it 100% accurate and 100% useless. We have to dilute mathematics with semantics to explain our observations, and that inevitably leads to ambiguities and contradictions.

MarcoD

I agree with your professor when he said that all in math can be verified.
He wasn't totally correct there. You can prove that you can't prove everything in math. Some people found that quite upsetting a century ago.