I saw this article here, which talk about a Japanese mathematician that claims to have solved one of the most important problems in his field: the abc conjecture.
Please, could someone explain to me, in simple words, what is this problem and why it is so important? Thank you!
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In the article, have you read the section that start with "Primal importance The abc conjecture refers to numerical expressions of [...]"? If so, what sort of explanation would you like -- more in depth, at which level? (e.g., compared to Wikipedia) – Clement C. Oct 17 '15 at 12:13
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You might find helpful the MathOverflow Question from 2013, Philosophy behind Mochizuki's work on the ABC conjecture. As for the ABC conjecture, which is a specific conjecture that would be confirmed by that work, you will find several previous posts under the Related section to the right (on the desktop version of the site). E.g. Can someone explain the ABC conjecture to me?. – hardmath Oct 17 '15 at 12:31
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To be fair to the OP, the article cited doesn't actually state the conjecture; merely a description that if a and b tend to be divisible by large powers of primes a + b = c won't be. Which is a very concise "feel" of the conjecture but one can hardly blame the OP for thinking it is vague. The wikipedia article is good though. – fleablood Dec 15 '15 at 18:32