Dear Jaques,

I think you describe very well what many or most mathematicians have felt at some point and of course I do not have any easy solution. But here is one thing that has helped me several times: Instead of learning a new technique and try to apply it to your problem, take a known result (that you like) and try to find your own proof of it. You may say that this is not very heroic but it can actually be quite useful, for yourself and others. At any rate it helps you to understand the theorem better, and if you find a nice proof it can be of interest to others as well, and it can even lead to generalizations of the theorem you started with.

]]>Consider participation in Algebraic General Topology research https://mathematics21.org/algebraic-general-topology-and-math-synthesis/ – This is a breakthrough but very simple research: It is based on a set of simple axioms that were missed by decades by mathematicians. You could laugh if you see how much simple axiom sets were missed. Therefore, this is both easy and research productive. Yes, both easy and breakthrough.

]]>After reading you career advices I feel like I am not able to find the right problems on which to work on, even if I own PhD (currently a postdoc). Most of the problems I encountered or asked myself eventually fell into two distinct categories: trivial problems (easy adaptation of known results, not even connecting two ideas from two distinct papers) and too hard problems (on which I have no way to start, or where the problems rapidly starts to be unsolvable). This is a serious problem as it gives the feeling that I am constantly not aiming above my range. It is almost like what I finally produce is too simple, and what I can not do is to difficult.

Finding a good math problem to work is indeed a really difficult matter. Over the three years of my phD program, I followed the same path several times: I was given a problem that was too hard, then spent six months almost doing nothing (but still working 6/8 hours a day, always trying the same ideas that did not work) and ended up proving results that I knew how to prove at the start of the project. This is very frustrating, and it has a tendency to happen every time, even after the completion of the phD. I feel like I am not a real mathematician, in the sense that I do not improve the difficulty of the problems I am able to solve. To be fair, I identified a number of problematic situations:

(i) I am not able to ask problems outside my very narrow field (despite the fact that I attend a lot of talks and conferences). Indeed I often have the impression that other fields are blocked. For example, I am working in a field very close to dispersive PDEs, but I am not able to find any problem on which to work on in dispersive PDE, a sort of problem that would extend my range and introduce me to this field (although I read courses on the matter, that does not help more than understanding line by line the papers of the field). It is almost like other fields seem “blocked” to me.

(ii) I tend not to see doable problems when they exist, even in my very field of expertise. I had the feeling that some problems in my field were out of reach; but some mathematicians looked at the very same problem, used quite the same techniques as the one I knwo and solved the problem.

(iii) I attended several conferences, some of which with the idea to discuss with people about their work and possibly launch work together: I read the papers in details, “learned” some of the techniques. But again, after reading the papers I had the (wrong) feeling that nothing more can be done. None of these attempts to work with other people has worked.

(iv) I also know some people working in related fields and discussed various works with them, but yet, after 4 years of mathematics, not a single question to work on with other people, or mysels has emerged. Compared to what other mathematicians tell me, that is a strange situation.

(v) I also feel like I need to rush and fear the non productive times, because I do not have a tenure position, so I need to prove that I am able to solve problems. But this has the drawback that I would not spend too much time on a problem without a serious lead, otherwise I would be afraid to not produce any paper by the end of the year.

All of that shows that, even if I try a lot, I must not have the right approach on how to find problems to work on. I am also often told that many mathematicians work on problems that turn out to be too hard but manage to use what they proved to solve a part of the problem, or another problem resulting in a nice work (not oustanding, but nice). This seems like a very nice way of working, which never happened to me.

Do you have any advice that would help me to find tractable interesting problems?

Thank you.

]]>https://terrytao.wordpress.com/career-advice/on-the-importance-of-partial-progress/

]]>Thank you

]]>If Google+ can be closed down and you can’t read things on it anymore then that could happen to anything. I wonder if anyone is saving the text from this WordPress site.

]]>I happened to have saved the text before Google+ was taken down. It can be found here: https://pastebin.com/MkzSrdYm.

]]>do you happen to have a copy of your Google+ post “value partial progress, as a crucial stepping stone to a complete solution” that you could re-post on this blog? I just wanted to look it up but since Google+ closed down I can’t read it anymore.

Regards,

Andreas