What college to apply for at Cambridge?

I'm applying for the mathematics course and I from what I heard, Trinity is the best for maths and also the most academically competitive among students but the concerning matter is it's the most anti-social.

Says who? What are you basing this on? It's an odd assertion from someone thinking of reading mathematics...

There is really no difference between colleges in terms of academics because a) lectures are organised centrally by the department and b) while you have tutorials in-college usually, you may also be "farmed out" to another college for tutorials if your director of studies thinks there is a better suited tutor for the topic you are studying elsewhere. So if you go another college you may still have tutorials at Trinity anyway (and even if you're at Trinity you'll probably have some tutorials at other colleges).

The reputation of Trinity for maths is largely historical, and while it persists I don't think there is a significant difference in the academic performance of those at Trinity vs those at other colleges for maths. There is however a significant difference in the number of applicants to Trinity and hence the proportion of applicants they interview - which is far lower than most other colleges. There are lots of anecdotal stories of people with basically flawless grades applying to Trinity and not even getting interviewed, which also makes them ineligible to be pooled. Therefore you should only really apply to Trinity for maths if you really are an exceptional applicant, even by Cambridge standards.

Graduate employers don't know or care about the differences between colleges so it won't make any difference in that regard. Realistically I'd suggest you just pick your college based on things like location, facilities/amenities, cohort size (if that's important to you), architectural style (if that's important to you), etc, rather than what is "prestigious" for some particular subject or not. At the end of the day, employers just see that it's Cambridge and don't care about your college, and the differences between academic outcomes at the colleges are honestly pretty narrow.

As someone who applied for trinity (based on academics, music/choral scene and general amazing-ness), I would definitely think hard about whether you prioritise getting into Cambridge as a whole or if the college really matters to you. I’m doing architecture, which is a really tiny year group and this pretty difficult to get in, and I didn’t really think twice about the level of competition and luck i would be dabbling with , especially for a course which doesn’t really vary depending on the college (we would work as a year group rather than college - compare 30-50 people with much more for NatSci, for example) - and so I shouldn’t have placed so much weight on music scene (I had applied for a choral scholarship) and academic ranking. I’m happily going to Bath this year, but I would certainly think twice how important Cambridge as a whole is rather than if you get in you favourite college (the initial is probably more likely - the oxbridge names are very valuable). After being rejected I am quite content with going to bath as my first step in becoming an architect, but I do realise that’s different for those with a bigger weight/priority on undergrand courses.

Which colleges are closer to where undergraduates will be lectured in maths?

Also, it's a bit of a myth every maths student is anti-social which is what you're suggesting