One thing I think would be interesting to research is how different people are good in different areas of math. There's lots of anecdotal evidence[0] of people

One thing I think would be interesting to research is how different people are good in different areas of math. There's lots of anecdotal evidence[0] of people saying they tend to be good at either more algebraic subjects (say group theory or algebraic number theory) or more analytical ones (PDEs or measure theory) likewise I would extend this to also include geometric/topological subjects. In general especially as once gets into more advanced mathematics the abstraction level gets much higher quite quickly so it would interesting to know if there is any connection between brain structures and ability to grasp abstract mathematics. As an example I know a physicist who can tell you everything about general relativity and has a solid grasp of differential geometry but one time I was trying to teach him some mathematical logic and he just couldn't grok it no matter how many hours we spent on it. Likewise subjects that use category theory heavily (homological algebra/algebraic geometry for example) are known to be difficult to understand even for professional mathematicians in other areas. [0]: https://bentilly.blogspot.com/2010/08/analysis-vs-algebra-predicts-eating.html https://bentilly.blogspot.com/2010/08/analysis-vs-algebra-pr...