Cambridge mathematics research in subjects like algebraic geometry, number theory and topology is falling fast compared to Oxford, let alone US universities!

Especially in algebraic geometry: Nick Shepherd-Barron moved to KCL, Burt Totaro to UCLA, Mark Gross is mostly based in UCSD now. Thank god Caucher Birkar still stays, for now.

Number theory in Cambridge seems not very good either (I know John Coates, Peter Swinnerton-Dyer and Alan Baker are still in Cambridge but they are not active.) It's behind any top 10 number theory in US (Oxford recently acquired Andrew Wiles and Minhyoung Kim so even it is better than Cambridge.)

Cambridge topology seems ok-ish. Again, cannot compare with top 10 topology in US.

Overall, in these fields Cambridge lacks top-notch people who are actually active (and yes, I know they do still have top-notch people in these fields, albeit scarcely, so please don't give me "counter-examples".)

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Analysis and Combinatorics are still strong in Cambridge. However, Oxford also ups their game in combinatorics with the adding of Ben Green, Tom Sanders and David Conlon.

However, the extremely strong statistics and applied maths departments keeps Cambridge overall ranking in maths research from falling down.

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Then again, undergrad teaching in Cambridge is far SUPERIOR compared with Oxford and as good as Harvard, Chicago, MIT,... Cambridge has the hardest exams, no doubt! In fact, it's so hard that Ben Green couldn't do one of the past exam problems when he supervised us about 10 years ago.

I think most posters before me confused this with actual research quality.