Search is hidden behind registration wall AND I was not allowed to register (without affiliation). You should open search or registration.
Agree on search, it is now open for non users. Affiliation is to avoid content dilution. Any alternative ideas are welcome (and as you can see with search, implemented)
You don't any users, you have an incredibly tiny niche, and starting a new forum these days is already ultra hard.
You should be working on getting users at all costs, not planning for the glamorous problems you might have if your moonshot happens to land, like having too many math novices cluttering up the high brow academic discussion.
lol, c'mon.
You need to understand that right now your forum is about as enticing as installing vBulletin on localhost to talk to yourself, just without the arxiv.org bot.
I started a large forum over a decade ago when it was easier. I spent almost a year sockpuppeting with myself so the first users didn't arrive at an empty forum. And that was in a popular forum-faring niche.
I look at your forum and you couldn't even be bothered to write a single comment on launch day. What's the plan?
As for affiliation, make it optional. Affiliated users get a little icon next to their username.