Why Mathematicians Re-Prove What They Already Know | Quanta Magazine

Abstraction: Mathematicians repeatedly re-proving infinitude of prime numbers

Key points:

• Romeo Meštrović compiled nearly 200 proofs of Euclid's theorem on infinite primes in a 2018 survey
• Leonhard Euler's 1737 proof originated analytic number theory by linking divergence of harmonic series to prime infinitude
• New proofs use Fermat's Last Theorem (itself an extremely hard result) to derive this simple conclusion, revealing cross-domain connections
• Gasarch's 2023 proof chains Schur's theorem (1916) and Euler's cube sum impossibility to derive infinite primes
• Andrew Granville used van der Waerden's theorem (1927) and Fermat's result on evenly-spaced perfect squares
• New proofs may illuminate connections between prime infinitude and hardness of integer factorization underlying public-key cryptography

Connections: Leonhard Euler · Number Theory · Mathematical Proof · Analytic Number Theory

Source: https://www.quantamagazine.org/why-mathematicians-re-prove-what-they-already-know-20230426/