When you start thinking deeply about a mathematics problem you may enter the "zone", a period of intense focus where you think solely about the problem and potential solutions, and more importantly block out all other thoughts and even lose track of time. Mathematicians don't own the zone, actors, musicians, athletes and many others have their own version of the zone. But for math, when working on an open problem, you have no idea how difficult a solution may be, or if a solution exists at all. Most of the time you will fail (if not you need to try harder problems). Failure is not wasted time. You may find a counterexample, a partial solution and always you will come out with a better understanding of the problem. Then days, months or years later, some new proof idea comes from a paper, a talk or just the back of your head, and back in the zone you go. And when you do succeed you get a feeling not unlike scoring a goal in a soccer game. You should see my proof dance.
With AI generated and assisted proofs, we may think of outsourcing the zone to ChatGPT and Claude. We may prove more and stronger theorems, but you'll understand the results just a little bit less and mathematics will become a little less fun.
This https://binaryigor.com/the-joy-and-power-of-understanding.html blog post is tangentially related to yours.
ReplyDeletewe are on the same page.
ReplyDeletei recall another blogpost that dealt with what settings induce you to enter different types of zones, but don't know whether the term zone was mentioned in the post but it definitely dealt with that very topic.
You most likely are referring to PrePublish or Perish post here:
Deletehttps://blog.computationalcomplexity.org/2020/02/pre-publish-and-perish.html?m=1
The most interesting connection I see is that training LLMs and their temperature setting is analogous to the environment setting and output mode for humans that this post is dealing with.
Ahh -- this was the guest post by Evangelos Georgiadis. Incidentally, a while back there was a podcast on that very blogpost by another computer scientist who went through it and commented on it.
Delete"..and back in the zone you go" how? easily said than actually done no? to get the same mindset any tricks?
ReplyDeleteThe key is to find a place with no distractions. Sometimes I've been in the zone while I was jogging or taking a shower.
DeleteDoes it work after you have struggled and figured the answer after a long time period? I feel like what is the point to write it down and not getting the same 'zone'. Any tips?
DeleteIt's good to write down the ideas you get. Every now and then you can go back to it. And when I see a new technique I like to see if will help on any of my old problems.
DeleteLook, it's a work our routine; your mind to work out, rather than be exposed to atrophy by outsourcing everything to someone/something else. Think of being in the zone as the time your body starts to sweat and feel actually good about things ... workout (the process) , sweat (being in the zone - the attempted progress) , result (growth).
ReplyDeleteThere is no royal AI road to mathematics!
This is very much connected with the school of art criticism which says that you have to understand the act of creating go really understand the art. Also this: https://en.wikipedia.org/wiki/The_Act_of_Creation
ReplyDelete