A high school senior from China, Nishang Dang, announced today a proof of the the Goldbach conjecture: every even number greater than 2 is the sum of 2 primes.
“I just combined two interesting methods,” he said, “I had no idea it would work.” The proof is synthesis of the methods behind Vinodograv’s Theorem (every sufficiently large integer is the sum of three primes, using the Hardy-Littlewood Circle Method) and the Green-Tao Theorem (on arithmetic progressions of prime numbers, using graph-theoretic methods, in particular Szemeredi’s Lemma). Nishang had been previously spent his high school years training for the China Mathematics National Olympiad in hopes of being chosen for the prestigious Chinese IMO team, but narrowly missed the cutoff each time, including this year. “I thought, screw that, let’s go do an impossibly hard problem instead. Turned out it wasn’t so impossible.”
“Nishang has proof himself worthy,” the Chinese IMO team leader has purported to have said, and said he was considering putting Nishang on the team, despite his olympiad record.
The paper is available on arXiv here.