Does the proof of Fermat’s Last Theorem (FLT) go beyond Zermelo Fraenkel set theory (ZFC)?
Or does it merely use Peano Arithme Page 1 The Bulletin of Symbolic Logic Volume 16, Number …

In 1931, the young Kurt Gödel published his First Incompleteness Theorem, which tells us
that, for any sufficiently rich theory of arithmetic, there are some arithmetical truths the theory …

The philosophy of mathematics has experienced a renewal in recent years due to a more
open and interdisciplinary way of asking and answering questions. Traditional philosophical …

Of all the demands that mathematics imposes on its practitioners, one of the most
fundamental is that proofs ought to be correct. It has been common since the turn of the …

Publisher Summary This chapter provides an overview of the Hilbert's program. Hilbert's
program is, in the first instance, a proposal and a research program in the philosophy and …

The prime number theorem, established by Hadamard and de la Vallée Poussin
independently in 1896, asserts that the density of primes in the positive integers is …

Roads to Infinity Page 1 Roads to Infinity The Mathematics of Truth and Proof John Stillwell
While man advances in the set the completene such books set theory the whole, and both (the …

The metamathematical tradition, tracing back to Hilbert, employs syntactic modeling to study
the methods of contemporary mathematics. A central goal has been, in particular, to explore …

An account of mathematical understanding should account for the differences between
theorems whose proofs are “easy” to discover, and those whose proofs are difficult to …

Roughly, a proof of a theorem, is “pure” if it draws only on what is “close” or “intrinsic” to that
theorem. Mathematicians employ a variety of terms to identify pure proofs, saying that a pure …