Which mathematicians were most responsible for formalizing mathematics

[susskind99]

I know that this was done in the late 1500s and early 1600s and even al khwarizmi الخوارمي
in the 9th century did a lot to formalize math. I'm pretty sure fibonacci (not his real name) did not write his famous book using notation. I know Descartes did a lot to formalize math but the other names I'm not aware of.

In any case, I want to know this because I'm trying to formalize philosophy. Of course a lot of philosophical arguments can be formalized but I'm actually working on a periodic table of metaphysical elements. If anyone would like to see my work send me a pm.

 

[SW VandeCarr]

I think you're forgetting Euclid. He was the earliest known person to apply the idea of deducing mathematical theorems from axioms, which is the basic concept involved in virtually all formal systems involving logic and mathematics today. Euclid's axioms applied only to plane geometry and assumed two parallel lines, extended to infinity, never joined or intersected.

Euclid was active in Alexandria, Egypt around 300 BC.

 

[susskind99]

Well, I'm more worried about who translated it from prose into notation. For example, in the 1500s math books were almost entirely written in prose. This began to change slowly I'm pretty sure between circa 1575 and 1625.

 

[SW VandeCarr]

Well, I'm more worried about who translated it from prose into notation. For example, in the 1500s math books were almost entirely written in prose. This began to change slowly I'm pretty sure between circa 1575 and 1625.

OK, but that's not really what's meant by "formal systems" and formalization in mathematics. Leibniz, and particularly Euler contributed most of the notation used in standard analysis (calculus). In 1895 Peano published his Formulario Mathematico which became a standard reference. Five editions were published between 1895 and 1908.

Many others participated in the development of algebraic notation after about 1500. These are easily found on the internet.

http://www.ualr.edu/lasmoller/matrices.html

 

[Jorriss]

What is meant by formalizing ?

 

[SW VandeCarr]

Historically it has meant doing what Euclid did for plane geometry (see above) for other areas of mathematics. In particular it meant placing Set Theory on a firm axiomatic basis. This was accomplished in the early years of the 20th century with ZFC (Zermelo-Freankle + the Axiom of Choice). My understanding is that nearly all mathematical statements can be rendered in or reduced to, at least indirectly, Set Theoretic form and proven in ZFC. ZFC itself can't be proven to be consistent, but is assumed to be so.

EDIT: A complete formal system also defines the "Well Formed Formula" specifying the characters and proper syntax for character strings. In formal logic, rules of inference are also specified laying out the proper elements to be used in the deductive process.

 

[nickbob00]

If you're looking into formal systems, you might want to look into Kurt Godel's incompleteness theorems.