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I work as a senior academic in an important university in Europe. My name is in several publications in top journals in my field.

I have always published papers together with brilliant collaborators who really made the difference but they are not there any more.

I am working on a new paper as a solo author but I am suffering a mental blockage and serious problems of anxiety.

I have previously published some papers as a solo author but I need help with this new paper. The difference now is that I am not able to start writing the proof demonstrations and therefore I cannot attract collaborators. Blank page syndrome. When I try to work on it, I have panic attacks. It's not a lack of skills because I have previously performed at a high level, I am blocked because I am used to collaborative work and talk about work helps me develop my ideas. I am now in a vicious loop, without proofs to attract collaborators and without collaborators to develop proofs

I was invited to give a seminar on my previous paper in an American university. I could use that opportunity to talk with them about my new ideas. I also spoke with some of my department colleagues. They are waiting for me to develop a bit more the proofs to decide whether my idea is feasible and collaborate. They are busy and will not help me at the moment. Right now, I am alone with my unsolved proof and my panic attacks.

Two questions:

• How can I overcome this mental block when working with theoretical mathematics?




• My job is my life, I don't want to leave academia but this situation is killing me. Should I leave academia or stay regardless the consequences?

I am an academic with tenure. I experienced difficulties with research at one point. I had been working on mathematics for about 30 years. I share below what helped to tackle it. I am back in a creative zone, happily producing results--in fact delivering some of my best results.

Others have given great advice, including finding new research partners to work with. Can you take on a grad student? I always found conversations with grad students very stimulating.

Panic attacks can be addressed via breathing techniques (very helpful and simple to apply). There could be other causes for stress or blank page syndrome too (e.g. conditions affecting sleep such as apnea etc), so perhaps check your health with a GP.

Others suggested engaging in sports. I find swimming energizing and super useful prior to a research session.

A creative activity (other than maths), such as sculpting or writing (or drumming or portrait drawing as Feynman did) will help to regain creativity elsewhere, which you can bring back to research in due time. It worked for me.

Gain distance. If one is too close to the work and attaches too much importance to it, then the work can suffer. I work with far more detachment now on a topic that I find more important than any other I worked on before. I keep perspective, humor and balance in the work. I found better pacing than when I was younger. If you change your life style and get more distance from your work by socializing, sports or creative undertakings, then the distance and added perspective this brings will help to overcome stress. I never stress in research at this stage. It is delightful (again and far more so than when I was a younger scientist).

Get a sabbatical to work with a mentor. Finding the right mentor to work with can make all the difference. I found a mentor who is very active, yet retired for quite a while. He is an inspiration and working with him and seeing him in action has changed my work practice.

All of the above helped me to move forward. Life always brings many challenges. A research block can be a sign that you require something different. So perhaps consider it as the opportunity that it is to regain what you are looking for...

Forgive me but I'm going to just wildly speculate here and hope that you find a bit of value in it. Perhaps you are just the sort of thinker that thrives on the synergy of working with others and getting ideas bounced around and reinforced (or shot down). That doesn't make you less of a mathematician, of course, but just represents one way of getting all of the pieces together.

It seems like you thought of yourself up to now as the 'junior' member of your circle and now the others have died or retired and so you are left 'alone'. In fact, IMO, you are left, now, as the senior member, but you don't need to continue to be the 'only' member.

Try to build up the circle again with new junior members with whom you can interact, building up their ideas as well as your own. It will give you that synergy again, if this is indeed the issue (like I said, speculative). A local circle is best, of course, but today's communication resources give additional options if learn to use them intensively.

And you have the opportunity to become the master that those younger scholars look up to and revere as they grow into the profession. Very cool.

One additional factor might be at play. When a person tries too hard for too long at intellectual activity, the brain sometimes rebels and shuts down. A break is called for, especially a break that gets the blood flowing, such as physical exercise. Physical exercise that also engages the brain but in a different way from the normal research mode can be helpful. I use Tai Chi for this as it is a mind-body fusion exercise, though not aerobic. When younger, I used cycling and x-c-skiing and such though they didn't have the same mental component. But an hour or so break for physical exercise can sometimes invigorate you.

And since the mind works subconsciously as well as when forced, sometimes insights magically appear during or immediately after a break. Even a sleep break.

_{Note: after the OP updates the question, I feel this answer doesn't answer it much. Nevertheless, it's still applicable in a general case I think.}

The method to solve mental block is very easy: take a break. Everyone has it, even your brilliant collaborators, so there is no need to be anxious about it. (The more you are anxious, the more likely you have it).

My experience is that if you don't know what to write, read more books/papers. During the reading if you catch relevant idea, then it will invoke the idea that you are looking for, and then it will come as flood. If it still doesn't come, then perhaps ideas for other problems will come?

Other resources:

• Writer's block


• 
  Occupational burnout (for a psychology approach on this)


• 
  Process theory of composition (for those who is interest in the field studying about writing: composition)

It's okay to need help on a particular project. It's natural to become interested in questions that are not entirely within one's expertise. But I think this idea that you need to have X amount of the proof done before you're "allowed" to bring on coauthors is not necessarily true. I can think of two other ways to get people interested: first, get better at selling the question itself, and second, work out a particular example or toy problem in detail. (Toy problems are a good cure for being stuck, in general.) If you do that and still can't find anyone to work with you, you can get help from the literature. It's not as efficient as working with coauthors, but reading is better than staring at a blank page.

Maybe you could try out a method from another field ! (Computer Sciences.)

It does not help with the exact same problem, but you could try out the rubber duck method, usually used to find a problem in some code, but it works by explaining what [the code] does to somebody else [which happens to be a toy].

Maybe it could stimulate you to just talk to a rubber duck, as long as you haven't got anybody else to talk to.

Here is an excerpt from 'Surely You're Joking Mr. Feynman!'. Copy from here

When I was at Princeton in the 1940s I could see what happened to those great minds at the Institute for Advanced Study, who had been specially selected for their tremendous brains and were now given this opportunity to sit in this lovely house by the woods there, with no classes to teach, with no obligations whatsoever. These poor bastards could now sit and think clearly all by themselves, OK? So they don't get any ideas for a while: They have every opportunity to do something, and they are not getting any ideas. I believe that in a situation like this a kind of guilt or depression worms inside of you, and you begin to worry about not getting any ideas. And nothing happens. Still no ideas come.

Nothing happens because there's not enough real activity and challenge: You're not in contact with the experimental guys. You don't have to think how to answer questions from the students. Nothing!

In any thinking process there are moments when everything is going good and you've got wonderful ideas. Teaching is an interruption, and so it's the greatest pain in the neck in the world. And then there are the longer period of time when not much is coming to you. You're not getting any ideas, and if you're doing nothing at all, it drives you nuts! You can't even say "I'm teaching my class."

If you're teaching a class, you can think about the elementary things that you know very well. These things are kind of fun and delightful. It doesn't do any harm to think them over again. Is there a better way to present them? The elementary things are easy to think about; if you can't think of a new thought, no harm done; what you thought about it before is good enough for the class. If you do think of something new, you're rather pleased that you have a new way of looking at it.

The questions of the students are often the source of new research. They often ask profound questions that I've thought about at times and then given up on, so to speak, for a while. It wouldn't do me any harm to think about them again and see if I can go any further now. The students may not be able to see the thing I want to answer, or the subtleties I want to think about, but they remind me of a problem by asking questions in the neighborhood of that problem. It's not so easy to remind yourself of these things.

So I find that teaching and the students keep life going, and I would never accept any position in which somebody has invented a happy situation for me where I don't have to teach. Never.

There are those who do not do well with theoretical mathematics. And they always consult a mathematician for that work when it comes up in their research. This situation is OK. (It is said that Einstein always had a mathematician handy to help him with his math.) It may mean sometimes that the mathematician will be added as a co-author; and other times it may not.