Do you find some mathematical activities useless?

[Paul Dale]

Currently we believe that \(\pi, e \) and \(\sqrt 2\) are normal numbers but have no proof. One of these searches could provide convincing evidence that the current belief is in fact incorrect. This would have deep implications for mathematics.

The largest prime is another matter entirely. Thanks to some old guy named Euclid, we've a proof that there is always another prime. However, if somebody found the largest twin prime, that would be exciting. We have a proof that the reciprocal sum of twin primes is finite but no proof they are. Interesting but it would likely have fewer implications. A proof that there are finitely many primes of the form \(2^n-1\) would also have implications for perfect numbers. All of the largest primes found thus far are of this form.

How many years was it before conic sections were useful? Over 2,000 years. Who can predict what might or might not be useful in the future?


Pauli