What are the 4 fundamental laws in mathematics?

Answer 1

I don't know why there should be 4 laws (=axioms) specifically.

In mathematics you can choose whatever system of axioms and laws and work your way with those. Even "logic" (propositional calculus) can be redefined in meaningful ways.

the most commonly used system is Zermolo-Fraenkel+choice:

http://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory#Axioms

It has 9 axioms though, not 4.

One might want to take into consideration the rules of "logic" as basic laws:

http://en.wikipedia.org/wiki/Propositional_calculus

Another common set of axioms that can be created inside the ZFC system is peano arithmetic:

http://en.wikipedia.org/wiki/Peano_arithmetic

I hope I understood your question.

The short answer is "there is no such thing".

I think the questioner may have meant the 5 fundmental laws in mathematics, also known as the axioms of arithmetic, these are as follows:

A1 - for any such real numbers a and b, a+b=b+a, the commutative law

A2 - for any such real numbers a,b and c, a+(b+c) = (a+b)+c, the associative law

A3 - for any real number a there exists an identity, 0, such that, a+0 = a, the identity law

A4 - for any real number a there exists a number -a such that a+(-a)=0, the inverse law

A5 - for any real numbers a and b, there exists a real number c, such that a+b=c, the closure property.

These 5 axioms, when combined with the axioms of multiplication and a bit of logic/analytical thinking, can build up every number field, and from there extend into differentiation, complex functions, statistics, finance, mechanics and virtually every area of mathematics.