The Obviously True Theorem No One Can Prove

About this Video

• Video Title: The Obviously True Theorem No One Can Prove
• Channel: Veritasium
• Speakers: Derek Muller, Casper, Elmer, Professor Strogatz (likely)
• Duration: 42:34

Introduction

This Veritasium video explores Goldbach's conjecture, a seemingly simple yet unproven mathematical statement: every even number greater than 2 is the sum of two prime numbers. The video traces the history of the conjecture, from its origins with Christian Goldbach and Leonhard Euler to modern attempts at proof using methods like the circle method and sieve methods. It highlights the contributions of mathematicians like Ramanujan and Chen Jingrun, illustrating the challenges and breakthroughs in tackling this enduring problem.

Key Takeaways

1. Goldbach's Conjecture: Every even number greater than 2 can be expressed as the sum of two prime numbers (strong conjecture); every odd number greater than 5 can be expressed as the sum of three prime numbers (weak conjecture).
2. Historical Context: The conjecture originated in a letter exchange between Goldbach and Euler in the 1700s and has remained unproven for centuries.
3. Mathematical Approaches: The video details attempts to prove the conjecture using the circle method (Hardy & Littlewood), sieve methods (Chen Jingrun), and computational verification.
4. Weak Goldbach Conjecture Proven: The weak Goldbach conjecture was proven by Harald Helfgott in 2013, using a combination of computational and analytical methods.
5. Strong Goldbach Conjecture Remains Open: The strong Goldbach conjecture remains unproven, requiring potentially new mathematical approaches.
6. Chen Jingrun's Contribution: Chen significantly advanced the understanding of the strong conjecture by proving that every sufficiently large even number is the sum of a prime and a semiprime (a number that is either prime or the product of two primes).