Hello ConcussedMathGuy,

I am facing similar problems, with the difference that I am older than you (31) and already established in academia as a mathematician. My concussion history is also worse than yours. I work on complicated fields that require both intuition and long formal proofs.

I think that some of our cognitive difficulties are anxiety-driven. After my concussion number 2, I had trouble going through complex reasoning, keeping track of variables, etc. Now in retrospect I think that these problems were self-generated. I was so stressed out about permanent brain damage that I was over-obsessing about any mild form of cognitive impairment, even the kind that probably happened also before my accidents when I was tired, anxious, not rested, etc. This not only impaired my healing, but it also made my cognitive performance itself worse, as I was seeing every cognitive effort as a diagnosis test to evaluate how screwed I was. When I realized it and decided to let it go and simply "enjoy" doing math again without any pressure, my cognitive symptoms faded away and I quickly came back to my pre-accident levels (the physical symptols stayed though).

After my concussion number 3 (4 months ago), my cognitive problems have become more severe (trouble reading, concentrating in seminars, etc.) and I start doubting that I have a future in academia. This also generates negative feelings, as math was also my passion and I was very good at it. That said, even now, when I am unable to do research on my own, I still have found some workarounds to try to stay productive while I am waiting and hoping to recover a bit more. I now give some of my ideas to my colleagues, post-docs and PhD students. They do the "dirty work" (proving theorems, algebra, etc.), while they benefit from my knowledge of the field and from my intuition (which, surprisingly, is intact). This is not a sustainable arrangement in the long term but it allows me to stay active in this business and to give myself more time before making an irrevocable decision (quitting, which I will perhaps be forced to do).

For you the problem is a bit different since you still have to acquire education but I think your concussion history is still too short for you to worry about your math skills. One of our post-docs received two severe concussions from skiing (without a helmet) when he was between 20 and 25. He took several months off work to recover from each. He is completely symptom-free now and he is even the most productive guy in our group. He got a lot of recognition for his work. Of course every concussion history is different but I hope this example will allow you to break the automatic association "concussion -> permanent inability for math" that you seem to have developped.

I wish you all the best. I am happy to talk more about it if I can help you.