Who proved the ABC conjecture?

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Who proved the ABC conjecture?

Shinichi Mochizuki
In 2012, Shinichi Mochizuki at Kyoto University in Japan produced a massive proof claiming to have solved a long-standing problem called the ABC conjecture. Spanning 500 pages across four papers, Mochizuki’s proof was written in an impenetrable style, and number theorists struggled to understand its underlying ideas.

Is a conjecture proved?

A conjecture is considered proven only when it has been shown that it is logically impossible for it to be false. There are various methods of doing so; see methods of mathematical proof for more details.

Has the Goldbach conjecture been proven?

It has been confirmed for numbers up to more than a million million million. But there is an infinite number of possibilities, so this approach can never prove the conjecture. Many brilliant mathematicians have tried and failed to prove it.

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What’s the world’s hardest math problem?

These Are the 10 Toughest Math Problems Ever Solved

  • The Collatz Conjecture. Dave Linkletter.
  • Goldbach’s Conjecture Creative Commons.
  • The Twin Prime Conjecture.
  • The Riemann Hypothesis.
  • The Birch and Swinnerton-Dyer Conjecture.
  • The Kissing Number Problem.
  • The Unknotting Problem.
  • The Large Cardinal Project.

Is a conjecture always true?

a statement you believe to be true based on inductive reasoning. The case of which to show that a conjecture is always true, you must prove it. To show that a conjecture is false, you have to find only one example in which the conjecture is not true. It can be a drawing, a statement, or a number.

What are the consequences of the abc conjecture?

The abc conjecture has a large number of consequences. These include both known results (some of which have been proven separately since the conjecture has been stated) and conjectures for which it gives a conditional proof.

What is the abc conjecture in number theory?

abc conjecture. The abc conjecture (also known as the Oesterlé–Masser conjecture) is a conjecture in number theory, first proposed by Joseph Oesterlé (1988) and David Masser (1985).

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Will Mochizuki ever prove the abc conjecture?

I’m not saying Mochizuki will never prove the ABC Conjecture. But he hasn’t yet, even if the stuff in his manuscript is correct. In order for it to be a proof, someone, preferably the entire community of experts who try, should understand it, and he should be the one explaining it.

What is the difference between abc conjecture and Szpiro’s conjecture?

The abc conjecture originated as the outcome of attempts by Oesterlé and Masser to understand the Szpiro conjecture about elliptic curves, which involves more geometric structures in its statement than the abc conjecture. The abc conjecture was shown to be equivalent to the modified Szpiro’s conjecture.