When I go to research Trade or Mathematics in the Research Table, it will not work. I put in the appropriate items, gold, emeralds, diamonds and books for Trade, and some other stuff for Mathematics. I have finished every other tree, just for some reason this won't work at all.

I'm having the same issue:

The oddest part is that it worked fine for my other Minecraft account. I ended up just getting myself one of the research notes and chucking out the mats. Ended up that nothing in those particular trees (Trade & Mathematics) was researchable by that one particular account, but other accounts could.

That sounds curious. I just checked this both in a fresh world with v2.4.111 with only NEI and with my usual bunch of mods, and those research topics drew their required items from an adjacent chest without a problem.

Has this account name "uncommon" characters, like backslash or underscore ?

No, it is ArackChoo. Nothing unusual. I'll see if I can replicate it in a different build and take screen shots or something.

Likely the ore dict issue that got fixed in 1.12 so closing. If anything like this come up again feel free to open new issue.