Comments on: The ABC’s of Arithmetic

By: Steve Landsburg

Steve Landsburg — Tue, 11 May 2010 19:47:19 +0000

Neil: One can. But there are two problems with this.

First, the goal is to find numbers for which C is much bigger than D, for infinitely many different definitions of “much”. So you need not one computer program, but infinitely many.

Second, no matter how long you run one of those programs, it will (after a finite time) have found only a finite number of examples. That throws exactly zero light on whether the total number of examples is finite or infinite.

Nevertheless, it can be extremely useful to compile lists of examples. By studying these lists, mathematicians can begin to guess at the underlying patterns, and there’s a lot to be learned from that.

So what we need is lots of people willing to put their computers to work on this problem. Which is what I’ll talk about tomorrow.

By: Neil

Neil — Tue, 11 May 2010 19:26:00 +0000

I must be missing something. Why cannot a computer program be written that systematically determines and compiles a list of numbers for which C is bigger than D?

By: Steve Landsburg

Steve Landsburg — Tue, 11 May 2010 12:38:33 +0000

Tim Roberts: Thanks for the kind words. It’s an honor to be plagiarized.

By: Tim Roberts

Tim Roberts — Tue, 11 May 2010 10:12:30 +0000

This is the clearest exposition of the ABC conjecture I have come across – so much so that I hope to plagiarise it profusely when I add it to the Unsolved Problems web site at http://unsolvedproblems.org/

Hope this is OK…..

Tim

By: dave

dave — Tue, 11 May 2010 08:18:44 +0000

*rolls his sleeves up*
at first glance i bet that the abc conjecture is false.
its a series problem, right? like the search for primes themselves?