*(Quanta Magazine)*

Two mathematicians have found what they say is a hole at the heart of a proof that has convulsed the mathematics community for nearly six years.

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# Tag: Shinichi Mochizuki

## 👓 Titans of Mathematics Clash Over Epic Proof of ABC Conjecture | Quanta Magazine

Read Titans of Mathematics Clash Over Epic Proof of ABC Conjecture by Erica Klarreich *(Quanta Magazine)*
## Shinichi Mochizuki and the impenetrable proof of the abc conjecture

Read The biggest mystery in mathematics: Shinichi Mochizuki and the impenetrable proof of the ABC Conjecture *(Nature News & Comment)*

Two mathematicians have found what they say is a hole at the heart of a proof that has convulsed the mathematics community for nearly six years.

This break in the story of the ABC conjecture is sure to make that portion of Mike Miller’s upcoming math class on Gems And Astonishments of Mathematics: Past and Present at UCLA much more interesting.

A Japanese mathematician claims to have solved one of the most important problems in his field. The trouble is, hardly anyone can work out whether he's right.

The biggest mystery in mathematics

This article in Nature is just wonderful. Everyone will find it interesting, but those in the Algebraic Number Theory class this fall will be particularly interested in the topic – by the way, it’s not too late to join the class. After spending some time over the summer looking at Category Theory, I’m tempted to tackle Mochizuki’s proof as I’m intrigued at new methods in mathematical thinking (and explaining.)

The

abcconjecture refers to numerical expressions of the typea + b = c. The statement, which comes in several slightly different versions, concerns the prime numbers that divide each of the quantitiesa,bandc. Every whole number, or integer, can be expressed in an essentially unique way as a product of prime numbers — those that cannot be further factored out into smaller whole numbers: for example,15 = 3 × 5or84 = 2 × 2 × 3 × 7. In principle, the prime factors ofaandbhave no connection to those of their sum,c. But theabcconjecture links them together. It presumes, roughly, that if a lot of small primes divideaandbthen only a few, large ones dividec.

Thanks to Rama for bringing this to my attention!