Yeah, way above my pay grade.
Two classic unsolved problems:
The Twin Prime Conjecture: Twin primes are pairs of primes p and p+2. Examples 3, 5; 11, 13; 17, 19, easy to get the idea. Are there infinitely many pairs of twin primes? No proof of this has been found, although everyone believes that this has to be true
Goldbach’s conjecture: Every even number larger than 2 is the sum of two primes.
4=2+2
6=3+3
8=3+5
10=3+7=5+5, also easy to get the idea. No proof has been found.
One time I was at an AMS conference and five minutes in my interpreter turned to me and signed, “I’ve been to a thousand academic conferences. In every other one when people greet each other it’s all how’s your family, how was your flight? Here, they start right off the bat with mathematics.” You get the idea. We’re obsessed.