Mathematics · History & Philosophy of Mathematics
A topic within History & Philosophy of Mathematics, itself one of 10 topics in that field and part of Mathematics.
2 works
Richard Dedekind
Defines the real numbers as cuts in the rationals and the natural numbers by their order-generating properties alone, arguing that continuity and number themselves need logical construction rather than geometric intuition.
link checked 17 Sept 2026Richard Zach (Stanford Encyclopedia of Philosophy)
Explains Hilbert's proposal to secure all of mathematics by proving the consistency of formal systems using only finitary methods, and traces how Godel's incompleteness theorems undercut the program's original strong form.
link checked 17 Sept 2026