Also because nobody has a great solution yet for alignment, I can see that it is very easy for any work to be heavily critiqued. In other domains, you can feel like you are contributing something valuable even if you aren't doing anything ground-breaking. This is slightly different from not feeling smart enough I think. Although it hasn't happened to me (yet!) because I haven't shared any of my ideas publicly, I can see that the constant critique is something that could be quite demotivating.
As a newcomer too, my experience of the community is that is has felt much less supportive than in other technical fields I have worked in (although I have also met some people who are lovely exceptions!). It has certainly made me question somewhat if it is an area that I want to work in. I'm not sufficiently convinced that I'm going to solve alignment that it feels imperative for me to work in the field and I still feel I have lots of agency about whether I do or not. However, for somebody who doesn't feel that sense of agency or who hasn't experienced different communities, I can imagine that it might affect their mental health slightly subtly and perniciously without them realising its impact.
Really enjoyed this post. I have been talking about this sort of idea a great deal with my physio lately - people often put lots of unnecessary effort into actions that that they don't need because somehow they have a belief that 'effort is good'. He has had cases where he has e.g. shown more elderly patients easier ways to get up from a chair and they have refused because 'it is too easy'. As children most of us were taught to put in 'effort' and 'try harder' whereas usually what you actually want is to find a better way of doing whatever you want to do, rather than to 'look as though as you are trying really hard'.
I realised that I do find myself saying things to my children along the lines of 'I know you find your art lessons really hard, but as long as you are trying your best that is ok'. Their school reports include an effort grade for every subject and it's hard when I read their reports to them, not to say nice things about good grades for effort!
I am trying to figure out how this reconciles with growth mindset vs fixed mindset ideas. I guess perseverance and effort are subtly different things, and that one can grow instead by considering different options and doing the type of brain-storming you are talking about. As a parent, I'm still trying to figure this all out. I guess the first step is just to be aware of when I am suggesting 'trying' and 'effort' - both to them and to myself!
Did a PhD and post-doc in maths and also have a 10 and 12 year old so have been interested in watching them and their peers learning mathematics at school and have even been in to help at school a little bit.
I think understanding and problem-solving are different, although the former is a prerequisite for the latter. I can imagine understanding areas of mathematics but not having a good ability to solve novel problems.
Abstraction is a massive part of mathematics. Some people seem to find abstraction much easier than others. I don't know to what extent it is a learnable skill, but I think without it more advanced mathematics is almost impossible.
Also some people (and I see this in children) seem to have real blocks with aspects of logic. The difference between 'if' and 'only if' seems to not exist for some people and yet is obvious for others. The idea of mathematical induction likewise I remember really stumping some of the other students in my class. Again, I don't know how learnable this is!
I also suspect there are certain mental models related to number and geometry one acquires early on that either make aspects of maths very easy or very hard depending on whether one acquires them. Jo Boaler's work in this is interesting - I like her 'Mindset Mathematics' activities for school-level mathematics.
I suspect most people who don't get some of these things naturally lose motivation for mathematics making it hard to know how learnable they are. There are examples though of successful research mathematicians who weren't like that, Mirzakhani being an obvious example. Mathematicians do gravitate towards different fields as well - I do know some mathematicians who don't like geometry.
I do find it interesting how from a very early age, there are huge differences in how much different children 'get' mathematics. Either there is something genetic going on or is there are critical things one can do in those first few years that make a difference! I'm sure working memory helps, but I'm inclined to suspect that it is not just that. I have a reasonably good working memory but it wasn't one of my strong points. I was fine at mental arithmetic but not the best person in the class for example, but by the time I was 16-17, I was way better at mathematics than anybody else at school.
I'm reminded of the book What is Mathematics, Really? by Reuben Hersh. I read it too long ago to be able to summarise it well or debate the arguments, but it takes a fairly similar stance to mathematics and is very readable from what I recall.
I've just been reading Anxiety Rx by Russell Kennedy (which applies to troublesome thoughts in general not just anxiety so think it is rather unfortunately titled!) and I think some of the ideas in it might be relevant here.
His assertion is that it is easier to use the body to calm the mind than to use the mind to the calm the body. If you are a very cognitive person it is tempting to do the latter rather the former - you believe (falsely!) that you can talk yourself into feeling safer.
He makes an interesting distinction between anxiety as the thoughts in the mind and alarm as the corresponding sensations in the body. You then have a looping feedback cycle between the two, where they can each make the other worse.
However, the cycle is generally initiated by alarm (and he talks about two different types of alarm - foreground and background, with foreground being the universal fight-or-flight response and background being caused by trauma). Often alarm is initiated unconsciously, and then our brain tries to come up with an explanation for that alarm. It sounds like it your case perhaps you have some unconscious trigger actually related in some weird meta way to thinking or the possible social consequences of thinking.
His solution for breaking the feedback loop involves awareness of the sensations in the body, breathing and self-compassion, but I think other therapies that focus on the 'alarm' rather than cognitive strategies might just as valid. For me the ideas in the book fit very nicely with Internal Family Systems therapy and also with Acceptance and Commitment Therapy for example. Kennedy is clearly a big fan of Somatic Experiencing Therapy which I suspect has influenced his approach.
This reminds me of iRest yoga nidra. One part of it involves identifying a belief that you want to work with and then alternating between the 'felt sense' of that belief and it opposite (using a memory you have chosen to access the 'felt sense' of a belief). After alternating, you then hold both the 'felt sense' of the belief and its opposite in you attention at the same time. Sometimes (but not always), I've had the original belief melt away in that process and I wonder if this explains what is going on there.