Wow, this is a wild ride. I remember coming across this page because the author was from my alma mater and we were pursing the same (undergrad) degree. At the time, we could do a double major in Pure Mathematics and Statistics so long as we completed the coursework requirements, which is probably why that page even exists.
The page is ~15 years old now, and I think it should be read as though its written by a 22 yr old, more reflecting on their recent university education than a guide to how to become a working mathematician.
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With that note, I would say if someone is eager to engage in mathematics and statistics _at an undergrad level_ (at the time at my university, it was _unusual_ for people to pursue machine learning as a major, and it was in computer science school). I would recommend really focussing on Real Analysis, and the higher statistics courses, try to find the links and the commonality between the proofs and the key ideas. I would also tell myself to not to shy away from martingale theory and link it to measure theory.
Pure mathematics is a weird world. In the moment I hated myself for choosing it in undergrad, it absolutely tanked my grades because of the weird mental state I was in. At the same time when I got to my PhD/research everything starting really started to click. It's immensely difficult to digest and consume all the content in the 12-14 odd weeks that the coursework typically demands.
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