The stereotype, outmoded though it is, is that new mathematical discoveries emerge from the minds of dewy young geniuses. But Zhang is over 50. What’s more, he hasn’t published a paper since 2001. Some of the world’s most prominent number theorists have been hammering on the bounded gaps problem for decades now, so the sudden resolution of the problem by a seemingly inactive mathematician far from the action at Harvard, Princeton, and Stanford came as a tremendous surprise.
-I'm no mathematician, but it's nice to read that someone that is OVER 27 achieved this. I'm tired of the "under 30" crap. I'm making more interesting art now than I did when I was younger and I'd imagine that many scientists are doing more interesting work in their later career than their earlier.
The phenomenology of making art and doing math are pretty different, but the lifetime trajectories of our output in these areas might not be. In both fields, when we look in as outsiders to some particular body of work, we tend to see the semi-magical work of geniuses who we don't think we could ever be... but my experience brushing up against artists and mathematicians suggest that they both attain creative productivity through similar processes. Before producing really creative work, they have to get enough experience with their tools that they can say what they mean to without having to think much about it - they just paint, or just shuffle symbols on a page, and it gets them where they want to go. It makes sense that lots of people would only arrive at that kind of fluency later in life.
Zhang's paper. The biggest stumbling block in understanding primes is the persistent ideation of continuums. If we thought in modular form, then we would clearly see that there is nothing "random" about Primes.
Can anyone get this picture to load? Great article.(The left-hand picture on this page is a nice illustration of how this works in the plane; the points are chosen independently and completely randomly, but you see some clumps and clusters all the same.)
Now, I'm confused about the attribution of this article. It says Ed Copeland wrote this, but the linked Slate article is attributed to Jordan Ellenberg, and much of it is verbatim. It looks like Impact Lab copied the image reference without the link. Anyway, here it is the image: https://research.microsoft.com/en-us/um/people/peres/GAF/GAF.html