You might not say that if you’ve seen some of the amateur “proofs” of Fermat’s Last Theorem, the Riemann Hypothesis, or other famous statements. Really, in orde

You might not say that if you’ve seen some of the amateur “proofs” of Fermat’s Last Theorem, the Riemann Hypothesis, or other famous statements. Really, in order to contribute to mathematics, one needs, at minimum, a serious mathematical education, intelligence, and lots of persistence. Nobody can provide anyone with intelligence or grit, but the easiest way to get the required education is graduate-level study in mathematics, which is most easily done within the system itself. Beyond that, knowledge of and ability to navigate the culture of mathematics is helpful. There is a reason that not using Tex/LaTeX, and presenting standard material as if it were new are among the 10 signs Scott Aaronson lists that a paper supposedly presenting some mathematical breakthrough is wrong[0]. [0]: https://www.scottaaronson.com/blog/?p=304 https://www.scottaaronson.com/blog/?p=304