Category Archives: Number theory

Polymath 8 – a Success!

Yitang Zhang Update (Jan 9, ’14, corrected Jan 10):  Polymath8b have just led to an impressive progress: Goldston, Pintz, and Yıldırım showed that conditioned on the  Elliott-Halberstam conjecture (EHC) there are infinitely many primes of bounded gap below 16. Maynard improved it to 12. … Continue reading

Posted in Mathematics over the Internet, Number theory, Open problems | Tagged , , , , | 7 Comments

Polymath8: Bounded Gaps Between Primes

Yitang Zhang’s very recent shocking paper demonstrated that bounded gaps between primes occur infinitely often, with the explicit upper bound of 70,000,000 given for this gap. Polymath8 was launched for the dual purpose of learning Zhang’s proof and improving the upper bound … Continue reading

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Why is mathematics possible?

Spectacular advances in number theory Last weeks we heard about two spectacular results in number theory.  As announced in Nature, Yitang Zhang proved that there are infinitely many pairs of consecutive primes which are at most 70 million apart! This is a sensational achievement. … Continue reading

Posted in Computer Science and Optimization, Number theory, Open discussion, Philosophy, Updates, What is Mathematics | 15 Comments

Another Forgotten Bet: Is Don Zagier About to Owe Me 1000 Shekels For The Proof of the ABC Conjecture?

      Like everybody else I heard with great interest the news about the attempted solution of the ABC conjecture by Shinichi Mochizuki. (See, e.g.,  here, here, here, and here.) I did not think that this has much to with me … Continue reading

Posted in Number theory, Rationality | Tagged , , | 8 Comments