I was wondering how Euclid showed that there are infinitely many primes by generating a prime number from finitely many primes, and if it could be used to answer if there are infinitely many pairs of primes whose difference is 2. I show my approach in my - short - article here (I know I should co...

If $\pi_2(x)$ is the number of twin primes of magnitude less than or equal to $x$. We want to prove that $$\lim_{x\,\to\,\infty}\pi_2(x)=\infty$$ which should be easier than finding and proving an asymptotic formula like $x/\log(x)$ for $\pi(x)$. How is it that modern mathematics cannot prove eve...

Im currently wondering whether one can define a cubic function in a similar way to a parabola, a parabola being a set of points equidistant to a point and a line. Maybe a cubic function would be equidistant to a line and a parabola?