# What are some of the unsolved mathematical problems posed and stated clearly prior to the year 1900?

I chose year 1900 because of:

"Hilbert's problems are twenty-three problems in mathematics published by German mathematician David Hilbert in 1900. The problems were all unsolved at the time, and several of them were very influential for 20th-century mathematics. Hilbert presented ten of the problems (1, 2, 6, 7, 8, 13, 16, 19, 21, and 22) at the Paris conference of the International Congress of Mathematicians, speaking on August 8 in the Sorbonne. The complete list of 23 problems was published later, most notably in English translation in 1902 by Mary Frances Winston Newson in the Bulletin of the American Mathematical Society."

I know about some of them, to mention:

5) Are there any odd perfect numbers?

7) Are there infinitely many Mersenne primes?

But, I am not so sure is there a huge number of mathematical unsolved problems posed prior to the year 1900 or just a "few" of them?

• I just noticed that the irrationality of $\gamma$, the Euler–Mascheroni constant, is not mentioned under any links provided so far. Wrote Euler in 1768:"This number seems also the more noteworthy because even though I have spent much effort in investigating it... the question remains of great moment, of what character the number O is and among what species of quantities it can be classified". In 1776 he asked the same question about $e^\gamma$, see Ufuoma – Conifold Jul 3 '19 at 8:36