Thursday, June 6, 2013

Keep Thinking: Zhang and Perelman Give Relationship Advice

6 and 7.  42.

The relationship between these three numbers is one of portion--42 is 6 portions of 7 (or 7 portions of six).

Math often makes clear relationships of number (it does other things as well, including confusing the hell out of me).

The mathematical relationships we usually think of are simple, things like addition, subtraction, multiplication.  We use these notions for making change, doing taxes, weighing gear ratios and measuring power output, speed, aerodynamics and gradient.

Most problems remaining for mathematicians are about complex relationships, like Poincare's conjecture, recently proved by Russian recluse Grigori Perelman.  Perelman proved a relationship Poincare suggested, but most of us find the whole thing too complex.  We can't even get what it is that this relationship Poincare conjectured and Perelman proved, explains.
Grigori Perelman

So it was relief that I recently read and mostly understood the twin primes conjecture, a simple theory that relates to these numbers:

1 and 3; 5 and 7; 11 and 13; 17 and 19.  And so on.

What do we see?

Two things:  primes and twins (numbers separated by 2).

Hence, the twin primes conjecture.

This obscure (even in the world of mathematics) middle-aged dude, Yitang Zhang, recently helped us take a huge step forward in understanding the why prime numbers tend to come in twins.
Yitang Zhang
In attaining his success, Zhang simply persisted where the recognized experts failed. Zhang is over 50, an age at which few mathematicians continue to contribute to their field, but he persisted.  "There are a lot of chances in your career," he remarked, "but the important thing is to keep thinking."

Perelman, in contrast, since solving the Poincare, has since abandoned further work in math, despite his youth.  The accolades undid him.  He explained, "As long as I was not conspicuous, I had a choice.  Either to make some ugly thing, or if I didn't do this kind of thing, to be treated as a pet.  Now, when I become a very conspicuous person, I cannot stay a pet and say nothing.  That is why I had to quit."

The world's most brilliant mathematical star abandoned mathematics, refused the $1 million dollar Fields Prize and now lives, unemployed, in his mother's flat in St. Petersburg.  It is unknown if Perelman follows Zhang's advice, to "keep thinking."

But possibly this is a difference not only in the two men, but in the problem they engaged.  Perelman solved the century-old conjecture.  Done. In the drawer.

Zhang's problem remains. His paper explains the twin primes riddle up through 70 million, it does not search through infinity to actually solve the riddle.  The relationship is still unclear.  Work remains.

And maybe that is why Zhang recognizes the value of continuing to think.

We who understand only simple mathematical relationships still must face the challenge other relationships:  between people, between choices and outcomes, and between the past, present and future.  

Last night on the way back from Greenbelt we saw another racer stopped with a flat.  We stopped and helped him out.  It came to me that there was some relationship between our stopping and the fun we'd had earlier, when we'd raced.  Not karma, but some sense of doing good when done good to.

Riding a bike continues to be, for me at least, a way to keep thinking.  I can't claim it leads to proofs; I'm not that brilliant.  It simply has a way of introducing conjectures, which is enough to keep me thinking.  


Chuck Wagon said...

Bike racing has offered several proofs to me, such as that I have no sprint

At it's best, the bike racing community seems composed of individuals who actually are aware that they are a part of something greater than themselves - as you all proved Wednesday. I think that's one of the most foundational awarenesses a person can have, and with the ego'd up type A jackholes we in fancy lycra so often prove ourselves to be, our collective getting that is a source of great joy when I see it.

Kevin Cross said...

Thanks man.

Now attack! Kill the freds!