Want it or not, as a mathematician, you’ll be an extreme point in the convex hull of human thinking. Examples abound, and it’s hard to find any serious scientist who was not a bit of an extremist, one way or another.
In good old times, debates and subsequent extremist opinions were usually philosophical, or religious. Nowadays, it’s all about politics.
One thing to know about politics is that, at least for most applications, this is something 2D. A standard choice for the coordinate axes are economic left/right, and libertarian/authoritarian. You can also rotate by 45.
So, where are you in this 2D scheme? There have been serious guys all around the spectrum, and knowing where you are is definitely good to know.
Interestingly, the 3D political theory does not seem to be really developed. I am currently working on this, as an amateur, and if I find something interesting, I will probably write a blog, and link it here.