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?
Can you list some of them in your answer?