I'm not a math major. I'm somebody who thinks math is the solution to all the worlds problems. (I know, not very realistic.) Anyway my bent has to do with the difference between exact equations and approximations. If you tell me the arc of the cycloid is the solution to the problem of the tautochrone, I'm happy. If, on the other hand you tell me the arc of the circle is good enough for pendulum clocks because the circle is tautochronous when the motion is held to 15 degrees either side of botton dead center, I'm not happy.
Another issue, I abhor fitting data sets to the so-called 'Normal Curve'. The normal curve is nothing more than an approximator for a binomial distribution composed of six permutables (coins) with an equal probability of landing either a head or a tail (n = 6, p = 0.5). I think we need to go back in time in statistics and fit distributions to the binomial as Jacob Bernoulli first defined the binomial.
I have lots more opinions like this, too numerous to count.