Relationship between Mathematics and Science?

Question

Relationship between Mathematics and Science?

Answer 1

They are fundamentally different.

Mathematics is non-empirical, and doesn't need to match up to the real world to be "true" (valid). It proceeds from ideas assumed to be true, and works by rules to conclusions. For example, there are many different "Geometries" each based on different sets of fundamental assumptions. All are valid as mathematics, whether they correspond to the real-world or not.

Science is empirical, and must constantly test its ideas against the real world. If a scientific theory does not correspond to the real world, it is invalid.

Within science, mathematics is a useful and powerful tool. If fundamental mathematical assumptions are supported by empirical evidence, then mathematics provides powerful methods for coming to new conclusions about the natural world.

For an interesting essay on the subject, see below...

Answer 2

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 3

Without mathmatics, physics and chemistry will have a hard time trying to define quantities precisely.
At postgraduate level, mathematics, physics, chemistry and even biology become interdisciplinary. mathematics can be considered the foundation to the sciences.

Mathematics is used extensively in computational biology, computational chemistry, computational physics, almost all chapters in phyics, physical chemistry, analytical chemistry.

Answer 4

Mathematics is a science. It is a study of numbers, numeric expressions, and numeric equations. When you say the science of architecture, you are basically saying the study of buildings. Get it? Science is a slight synonym for study. Sorta.

Answer 5

mathematics is the mother of all sciences.it is the most scientific of all sciences.it helps to quantify and compute qualitative variables of other sciences

Answer 6

mathematics is actually a branch of science.

Answer 7

measurement is essential to science without math we can't conduct experiments

Answer 8

god created numbers and rest is done by human on this earth.

Answer 9

Same as man and mother-in-law...