60-Year-Old Maths Problem Partly Solved By Amateur (theguardian.com)

An amateur mathematician has made the first breakthrough in more than 60 years towards solving a well-known maths problem. From a report: Aubrey de Grey, who is more widely known as a maverick biologist intent on extending the human lifespan, has taken the academic world by surprise after announcing a new solution to the so-called Hadwiger-Nelson problem. The problem sounds deceptively simple, but despite some professionals spending years trying to crack it, progress has stalled since shortly after the puzzle was first posed in 1950. "Literally, this is the first progress in more than 60 years," said Gil Kalai, a mathematician at Hebrew University of Jerusalem.

The problem is as follows. Imagine a collection of dots connected by lines. The dots can be arranged any way at all, the only rule is that all the connecting lines must be of equal length. For instance, in a square the diagonal would not be joined up, but the outer edges would be. Now, colour in all the dots so that no two connected points have the same colour. How many colours are required. For a square, the answer would be two. But the Hadwiger-Nelson problem asks what the minimum would be for any configuration -- even one that extends across a plane of infinite size.

Comments

Jesus

[Anonymous Coward]

I almost fell asleep reading that summary. Is this of any practical use what so ever? What is that â" in the last sentence supposed to be?

Re:Jesus

[jellomizer]

It could, the geometric shape can be abstracted into other things. Such as time, and process, I could see this being used to help optimize a parallel programming process where a particular code takes so long to run, but to avoid collisions the different elements in time, will need to hit different process points at different time, then you need to span it up, so how many unique process points will you need. Say with a massively parallel system, such as an advanced quantum computer.

Re:Jesus

[gtall]

Hmmm...lemme guess, when Evariste Galois was inventing group theory, you'd be in the peanut gallery claiming you couldn't see any use for it (hint, he did it in the early 1800s). And when those wild and crazy guys were screwing up developing the math for quantum mechanics, you'd be asking them for a practical use (hint, they did it in the early 1900s).

In short, if someone cannot point to a use of something, it shouldn't be done. How enlightened of you? Have you explained your theory to scientists? I'm sure they'd listen to you.

Professional just means you get paid...

[Kenja]

it does not mean you're any good at what you do.