ICTS

The ABC conjecture of Masser-Oesterle is a fundamental problem in number theory, which states that three positive integers which share a close additive relationship (namely that A + B = C) cannot simultaneously have a close multiplicative relationship (namely that all three have "too few" distinct primes in their factorizations). I will describe a number of classical examples in number theory that motivate the conjecture; formulate the conjecture itself; describe an analogy between integers and polynomials that leads to a simpler (but much easier) statement; and report on the uncertainty surrounding the status of the conjecture.