Hi, OP -
STEM academic here.
I am so sorry for the loss of your sister and your nephew’s mum. That surely made him vulnerable already.
Maths is a great degree for employability but it doesn’t have an obvious career path like Medicine or Engineering. Has your DN connected to the Careers Service at Cambridge, both in terns of internships and, more importantly, post graduation plans? It is definitely time to start working with them on the latter.
Your whole family suffered a massive blow. Your DN did extraordinarily well to get to Cambridge - that’s true of anyone, doubly so in his circumstances. But I wonder whether he has been doing the things that the ultra competitive internships rate? Employment, volunteering, involvement in university life etc? How good, in both content and form, is his CV? Would the financial sector even suit him? These are things the Careers Service can help him with.
The disadvantage of the flexibility offered by Maths does mean that after Y2 of uni, Economics students on one side and Computer Science students on the other may have more explicit skills to offer employers. We see a variance acrossSTEM fields at my uni.
If he isn’t sure what he might like to do, I recommend the old classic What Colour is My Parachute? If he might be depressed or anxious, quite understandably, please encourage him to seek help for his MH sooner rather than later.
He is a Cambridge Maths student. He has something tremendous to offer an employer, but a super competitive internship in London this year may not be on the cards. Doing something is very good for his CV. Careers Service, pronto. Hopefully they have a Maths Specialist.
Also the School of Maths and DN’s College should provide networking opportunities. Even if he isn’t the most social by nature, he needs to plug in.
If DN is already taking good advantage of these networking opportunities, I apologise. If he hates the idea, he needs to figure out what he can do comfortably - again, pronto.
Many of the interviews for good jobs in STEM will assess comfort working in groups. It can be hard on introverts; they need to start putting themselves out there - baby steps - as undergraduates.