Nah, just study linear algebra (Shilov or Hoffman & Kunze) and baby Rudin. Then read the most famous books in geometry, analysis, and algebra (do proofs + get a mentor). All these roadmap things are meaningless. It’s like “how to join the NBA.” Lift weight, condition, and practice fundamentals. Nothing else matters.
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.
I think about it differently. If you want to become a pure mathematician, you have to publish research in pure mathematics. There are many different routes one can take to accomplish this, and the route that you can stick with and enjoy is the best one.
Before anything one should probably check or at least ballpark their IQ score. The median IQ for mathematics PhD students probably hovers somewhere around 145, about the top 0.2% of the population, correlated with about a 1510/1600 on the SATs, a 34 on the ACTs, etc. Those aren't perfect correlates but you're much more likely to have an SAT or ACT score than a professional IQ score handy.
Math is infamously g-loaded, pure math even more so. An unfortunate fact of life. On the bright side, math is very much a "shoot for the moon and you'll land among the stars" subject to pursue if you even loosely keep industrial or business applications in mind.
These kinds of lists are just completely worthless. Like ok, let’s look at “Stage 1 Elementary Stuff”. It’s a list of 18 books. So what are you supposed to do with that? Figure out which ones are good and useful? Take the next five years working through them all?
Either write a good guide, explaining why you pick each book, what it will teach you and why it’s needed, or just post a link to a university degree and say “just finish all these courses, good luck”.
How to become a pure mathematician or statistician (2008)
(hbpms.blogspot.com)76 points by ipnon 9 September 2025 | 74 comments
Comments
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.
---
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.
I think about it differently. If you want to become a pure mathematician, you have to publish research in pure mathematics. There are many different routes one can take to accomplish this, and the route that you can stick with and enjoy is the best one.
Math is infamously g-loaded, pure math even more so. An unfortunate fact of life. On the bright side, math is very much a "shoot for the moon and you'll land among the stars" subject to pursue if you even loosely keep industrial or business applications in mind.
Either write a good guide, explaining why you pick each book, what it will teach you and why it’s needed, or just post a link to a university degree and say “just finish all these courses, good luck”.