What is the difference between meta mathematics and mathematics?

Answer 1

I am not skilled at stating meta-mathematics, but meta-mathematics is the study of mathematics by using mathematical methods. By generating "metatheorems" proved theories that have used mathematics to explain the fundamentals of mathematics). Meta-mathematics usually uses set logic, philosophical logic, and proof theory to explain mathematics. These usually try to prove the inner philosophy or fundamentals of numbers and operations. A good example of a problem relating to meta-mathematics is the "Entscheidungsproblem", which inputs an algorithm and outputs a language, whether that algorithm is true or false, like the Riemann Hypothesis or the Cayley-Hamilton theorem of linear algebra, both being true. This was to prove the fact that it is impossible to have an unsolvable equation. This was cracked when the Diophantine Equation was analyzed. Although it seems that it's possible to take a non-linear varying number, and produce a valid result through a constant number. However, most problems have an infinite amount of valid solutions. Others have no solutions, as the divisor is always invalid, or must be divided by zero or furthermore terminating the use of the variables, or even going in circles, when its multiple (especially the least common) of the sums of the 2 polynomials' is its least common divisor.