**1985**

The abc conjecture was first proposed in

Masser, D. W. (1985), "Open problems", in Chen, W. W. L., *Proceedings of the Symposium on Analytic Number Theory*, London: Imperial College

and states that

For every \(\varepsilon > 0\), there exist only finitely many triples \((a,b,c)\) of positive coprime integers, with \(a + b = c\), such that \(c>{\rm rad}(abc)^{1+\varepsilon}\)

(where the radical of \(n,\ {\rm rad}(n)\) means the product of the distinct prime factors of \(n\)).

It is important because many other results follow from it including Fermat's Last Theorem.

**August 30, 2012 (updated several times in 2013, 2014 and 2015 too)**

A proof was proposed on August 30, 2012 by Shinichi Mochizuki in the papers

http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20I.pdf

http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20II.pdf

http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20III.pdf

http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20IV.pdf

Many newspaper articles followed making it famous but it has not yet been verified and will take a while to do so.

Examples of these are:

**September 10, 2012**

Nature article on Mochizuki's proposed proof of ABC conjecture

**September 12, 2012**

Science magazine article on Mochizuki's proposed proof of ABC conjecture

**September 17, 2012**

New York Times article on Mochizuki's proposed proof of ABC conjecture

**September 19, 2012**

The Telegraph article on Mochizuki's proposed proof of ABC conjecture

**November 4, 2012**

Boston Globe article on Mochizuki's proposed proof of ABC conjecture