Wiki-style co-operative mathematics can work for even the highest levels of maths research, reports (subscribers only) the New Scientist (subscription offer) – challenging the idea that maths advances can only come from tortured geniuses working alone.
The system, called Polymath (there is a blog about it here) was tested out on the “density Hales-Jewett theorem” (DHJ) – an issue in combinatorics. I don’t pretend to understand the DHJ theorem, so here’s the New Scientist’s take:
“Imagine colouring in squares in a grid. What percentage can you colour before you are forced to make a straight line along a row, column or diagonal? The DHJ theorem says the percentage increases in cubic grids, and in higher-dimensional grids you are able to colour almost all the squares…”
A proof of the theorem existed but it was written (it says here) in the language of “ergodic theory“: the aim of the project, which has been named “Polymath1”, was to find a simpler proof based on combinatorics.
It took just six weeks and contributions from 39 people for the task to be successfully completed and the proof has now been submitted for publication.
Perhaps most interestingly, for people like me, at least, is that some of the useful contributions came from what might be described as “amateur” mathematicians (the New Scientist have interviewed a Phoenix maths teacher, Jason Dyer, about his role). The graph here
– probably too small to read – shows that some of the most important contributions in general came from those with low professional seniority.
Mathematics is generally not taken seriously enough in my view – and I just don’t mean we don’t teach our kids maths properly – I have already discussed the societal impact of the proof or disproof of : something that ought to make it a global policy priority (in truth it may well be inside GCHQ or the NSA, but we don’t know).
So anything that helps maths research in this way ought to be treated as big, and good, news.
- Welcome to WikiMaths – home of hard sums (guardian.co.uk)
- A Possible Polymath Project? (rjlipton.wordpress.com)
- The beauty of Incompleteness Theorem of Kurt Gödel (bvkm.wordpress.com)
- Foil the Fool: The Vertical on Polynomial Multiplication (shawnurban.wordpress.com)
- The Proof Path (jhlchan.wordpress.com)
- What is 0^0? And is math true, or just useful? (3quarksdaily.com)
- Math Genius Solves 100 Year Old Problem – Techland.com (techland.time.com)