For all of the notable unsolved problems I'm familiar with, most mathematicians seem to generally agree that one outcome is more likely than the other. People are very confident that the Riemann Hypothesis is probably true, and that P probably doesn't equal NP, and that odd perfect numbers probably don't exist, et cetera. We have more than enough reason to believe these things, but we just don't have the tools to definitively prove them. But are there any conjectures where there isn't a consensus and mathematicians are more or less equally divided on whether they believe them to be true or false? submitted by /u/footballmaths49 [link] [comments]