Is mathematics a science?

Answer 1

I would say that math is more of an art than an empirical science.

You can of course draw many parallels between math and science, and science most definitely depends upon the logical deductions of mathematics.

But I think science is the process of explaining and, most importantly, accurately predicting the Real World as precisely and simply as possible.

Science can come to a conclusion (ie build a model) of the world merely by observation (ex: I observe an apple fall and then conclude that all objects accelerate towards the earth) without deduction from some underlying truths (ex: objects fall to the earth because objects with mass obey the universal law of gravitation, which causes a force, which according to Newton's law, causes an acceleration)

(Notice that theoretical Physics is becoming more like mathematics as it focuses on a "universal model" that goes beyond a loose group of statistically accurate laws to some fundamental definitions from which the entire universe of physics can be logically deduced (not just explained with statistical relationships derived from empirical evidence) )

So I guess what I am trying to say is that science is generally more similar to inductive reasoning and math is always a deductive process.

But I would say more abstractly that mathematics is fundamentally different because it can take arbitrary definitions and produce logical arguments to find relations and theorems that will always hold true in the imaginary universe of mathematics. The imaginary universe in which mathematical art is drawn is usually inspired by the physical universe around us (ie things like geometry, natural exponential growth, counting and measuring...) but in reality can be completely arbitrary (see non euclidean geometry and cardinality).

For example, Science cannot make conclusions about non euclidean geometry without first observing it in the real world (good luck with that), but Math can come to hundreds of logically consistent and beautiful conclusions about Non Euclidean geometry without being able to draw even one Non Euclidean triangle in the Real World.

Another way of looking at the difference between Science and Math is that Science would have to change the law of gravity if matter started to repel other matter instead of attracting it. The Mathematical logic underlying the law of gravity would still continue on unchanged.

Some people say that mathematics cannot be an art because it is used as a tool in Science. While math is definitely a tool used in science and engineering the way I prefer to see things is this:

All art, whether it is paintings, books of fiction, music, or Math, is at its heart an abstraction whose only connection to reality is the fact that the artists tend to draw their inspirations from the world around them. Though art is just an abstraction in an imaginary universe, all Good art contains fundamental Truths that can be applied to the real world. This is the reason why people pay good money to visit art museums or buy books, the art captivates us because it expresses the same truths that govern the human emotions and relationships and natural events in the world we live in.

And mathematics is no different than other art in that while Math is a complete abstraction from the real world, its real world inspirations have led us to some Mathematical truths that can be used in the real world. (For example euclidean geometry is inspired by the real world and with the truths in the art of Algebra and Calculus, we can deduce truths and make calculations about the relationships between the volume, mass, and acceleration in, say, the Space Shuttle)

So when a scientist uses some mathematical formulas or a mathematical expressions to explain his empirical observations, the scientist has not turned mathematics into a tool; the scientist is merely using the truths expressed in the Art of Mathematics as a way as communicating with those who also argue their ideas with Mathematically inspired truths.

(For example, a scientist who models his observations of radioactive decay with exponential functions does Not deduct from Nor contribute to the beautiful artistic expression of exponentials, rather the mathematics of exponentials is the most convenient way to express the facts that underly the process of radioactive decay)

I guess you could say that Applied mathematics is just a tool for scientists to express their results and more importantly for engineers to manipulate scientific results into cool things like bridges, medicine, and rockets, but in the end Mathematics is a liberal art because it really is a completely abstract Art that is drawn with the tools of logic by the creative expression of the human mind.

Answer 2

Mathematics isn't a science. Mathematics IS science.

All science is based off of math in one way or another, especially the natural sciences.

Answer 3

Mathematics on its own is just a mental game. Using mathematics well in the sciences is very much an art.

Answer 4

No, mathematics is not a science. Science is based on the scientific method. Create a hypothesis, and test your hypothesis through experiment. If most trials of your experiment produce a positive answer to your hypothesis you're probably right, and science accepts the fact.

In math, we create a hypothesis, but we don't care how many times you test it correctly, we won't accept it until you've proven it to be true rigorously, beyond any doubt. Example: The Riemann Hypothesis. It's been conjectured to be true for over one hundred years, and we know it to be true for millions of values, but we don't yet accept it.

The difference is that in mathematics, experiment only helps to form a hypothesis, it does nothing to prove the hypothesis' correctness.

Answer 5

of course, it would depend on how you define science. I would say that science is defined by the scientific method. since math doesn't employ the scientific method, I'd say it's not a science. but in a way it's better, since mathematical statements can be proven. it's possible (though highly unlikely) that the laws of physics could change overnight, but mathematical theorems will always be true, no matter what.

Answer 6

Several, way more than I can list, but I think this is a good one. I'm actually a graduate student in mathematics (so I'm looking to become a professional mathematician), and in particular am studying Number Theory. Probably the biggest open problem in modern mathematics is the Riemann Hypothesis in analytic number theory (the actual statement is kinda difficult to give; basically it says all non-trivial zeros of the Riemann Zeta Function has real part equal to 1/2), and it turns out that this result would have profound impact in string theory in physics (I know nothing about string theory, so I can't really tell you how, but it does give you an idea). Another good one comes from some of my own work in Random Matrix Theory (if you look up "Palindromic Toeplitz Matrices" you'll probably find my paper "Distribution of Eigenvalues of Real Symmetric Palindromic Toeplitz Matrices and Circulant Matrices"). Random Matrix Theory actually began as a problem in physics where they tried to solve Schrodinger's equation for complicated systems in quantum physics (in standard quantum physics, you get the numbers n, l, m, and s to tell you about the location of a specific electron.....basically this comes from finding the eigenvalues for a particular operator called the Hamiltonian....we make the assumption that we're looking at Hydrogen since there's only one proton, but suppose instead we wanted something like Uranium, which has over 200 interacting particles in its nucleus.....Random Matrix Theory allows us to avoid having to work with the Hamiltonian, which becomes prohibitively complex). Turns out that we can use RMT to model the behavior of prime numbers in number theory, and in fact the model works so well that physicists have begun studying prime numbers to get an idea of the behavior of heavy nuclei, since it's less dangerous to work with primes. And that's just the beginning of connections in math and science. But I could probably write a book on this question, so I hope this suffices in sparking your interest.

Answer 7

pure mathematics is science motivated entirely for reasons.

Answer 8

No mathematics is actually a language.

Answer 9

No, in actuality mathematics is a philosophy.

Answer 10

in a way yes...its all linked..especially physics and maths..with all the formulas etc..