How to Become a Pure Mathematician (Or Statistician)
53 comments
·September 9, 2025hiAndrewQuinn
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fine_tune
I got rage baited by this so hard, cant comprehend thinking this way.
Hung out with PhD's, economists, bankers, trust find kids, scientists, and artists - who maybe weren't top tier enough, but none thought this way.
Literally the weirdest take on a forum filled with dreamers, but every take is valid.
Ivan92
Same lol. By the OP's logic, every student pursuing this field in a university as an undergrad/graduate student should be taking an IQ test before proceeding to the upper level math courses covering these topics. Anything less than the threshold will mean they have to focus on something different.
the__alchemist
It's not comfortable, but this seems to be what the priors point to. I suspect that pure mathematics is one of the most intelligence-dependent fields; one where hard work, practical solving problems and a large knowledge base is less of a substitute.
thr0waway001
> one where hard work, practical solving problems and a large knowledge base is less of a substitute.
I have seen this first hand. I remember when I was in university doing my math major. This one older adult lady (she seemed 40yrs old, and very attractive too), she had decided for some reason or other she wanted to do a major in mathematics. Not for a job or anything but just to do it.
Whereas the rest of us, let’s face it, we just wanted a good job in STEM.
Bless this lady, she was so determined and hard working. She would show up to every lecture, first in, last out, and she would show up to every study session and give it her all.
But unfortunately, she was not good at grasping the concepts nor solving the problems. It was shocking how little she grokked the introductory concepts for the amount of effort she put in. She worked harder than anyone in our group.
I don’t think any of us had the heart to tell her that maybe a math major was not in the cards.
I never saw her on campus in my 3rd year and on so imagine she dropped off.
But I was rooting for her.
nartho
Two things :
> The median IQ for mathematics PhD students probably hovers somewhere around 145
Does that mean the 145 figure is only a guess on your end ?
Second, as far as I know, an individual's IQ is not something set in stone, and can absolutely be improved with training. I remember reading (that's an anecdote so correct me if I'm wrong) that rewarding a good score with money was able to improve the outcome by up to 20 points. It doesn't sound absurd to me that someone with a slightly above average IQ could get close to 140 after 6, 7 years of high level math training.
hiAndrewQuinn
>Does that mean the 145 figure is only a guess on your end ?
It's not quite a guess, but I don't have precise data on this exact thing either. Previous studies in this field have consistently found a range of between 140 and 150, and you can probably find those with some Googling if you want to corroborate it yourself. I have a long cached memory of seeing a study where theoretical physics PhD students had an average IQ of 150, which also loosely supports this, since theoretical physics is almost its own form of pure mathematics.
>an individual's IQ is not something set in stone, and can absolutely be improved with training
Most psychological research I've seen says no such thing, unfortunately. Believe me, I would love for that to be the case - one extra point of IQ correlates to roughly $1000 extra income per year in the US, and so if your 20 point claim were really true we could potentially cause a double digit spike in GDP over the next few months just by implementing it in smart ways. But my baseline belief is that study is almost certainly an outlier in a sea of similar studies which support the null hypothesis.
BeetleB
Did a Google search, and the only actual, definitive thing I found was this:
https://pmc.ncbi.nlm.nih.gov/articles/PMC5008436/#tbl1
Note that it's an IQ of 128 vs 125 for humanities. With the small sample size, it's basically noise. And given that this is Oxford, I would expect the average PhD student to have less than these numbers.
nartho
Maybe, but let say you're right. I still don't understand your suggestion of doing an IQ test before you decide to study math. If you can't go further than a masters, like you said there are still a lot of industries you can go too and have an interesting, lucrative job. And if you do succeed to finish your PhD then that's great news. There are no benefits that I can see in doing an IQ test like you suggested before you make your decision. If you love math and are good at it, chances are you're moderately smart at least. Might as well go as far as you can if that's what you want.
mikebenfield
What's much more sensible than taking an IQ test is looking at your experience with math to date.
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viccis
My experience with pure math is that this is not necessary to get job as one, even at good institutions, but you will be terrorized by the arrogance of the ones you mention. Learning to deal with the "brilliant jerk" is a problem in many fields, but the ones I've met in pure math are some of the weirdest (and most vicious)
qsort
At least from my point of view (in the industry, not academia) this is actually the opposite. Math graduates tend to be smart and humble and I respect them a lot. Sometimes it almost feels like math and physics are the last "real" degrees left.
BeetleB
Similar - I found math majors to be fairly humble. Yes, there's always the exception, but I found them to be fairly fun folks.
Physics majors, in my experience, had a significantly higher arrogance level.
monkeyelite
Yes, and those are the ones who didn’t make it to researcher.
monkeyelite
A corollary of this is that many professional mathematicians are not actually competitive in research.
It’s just different leagues of intelligence: social studies undergrad vs math undergrad vs math grad vs competitive researcher.
hiAndrewQuinn
This is what I've observed as well. By my own metrics and grades, I was a somewhat bright math minor (near-perfect score in abstract algebra, etc), would have been middle of the pack as a PhD student, may have been below par if I managed to complete the PhD, and almost certainly would have been deadweight as a pure mathematician myself. That's just how the scaling and competitive dynamics have worked out; it's not really something to feel personally bad about, any more than you might feel personally bad about not having the potential to be a competitive figure skater.
Ar-Curunir
The definition of professional mathematics is research. That’s what they are trained in and that’s what they are competent at. I don’t understand your comment.
FranzFerdiNaN
The dumbest people I’ve ever encountered in university were the math and physics majors who thought they could score some easy points by taking humanities classes, because just like you they considered that below their level. I’m sure they were smart on an IQ test but they couldn’t reason their way out of a paper bag, and their writing skills were just laughable.
The smartest ones were usually the philosophy majors. Also some of the weirdest (in a good way) folks.
HSO
> "shoot for the moon and you'll land among the stars"
I´ve never been able to wrap my mind around this saying.
hiAndrewQuinn
Ha, yeah, it's a weird saying. I think it makes more sense if you imagine the sky as like a static painting you shoot yourself into with a cannon or something.
tea-coffee
Imagine if Richard Feynman used his IQ as a metric for deciding whether he should become a physicist. Physics would not be the same.
I am certain that there are mathematicians below, near, and above an IQ of 145 that all have great research productivity. IQ tests do not approximate the creativity, effort, and collaboration required in a mathematician. Not to mention the dubious nature of the 145 claim.
Of course, there are some people that will have a greater aptitude for mathematics than others. But you do not need to be a genius, and this is echoed by Terence Tao [0].
[0] https://terrytao.wordpress.com/career-advice/does-one-have-t...
impossiblefork
Also possible that Feynman had superb verbal-mathematical ability and bad visual-spatial ability and took a visual-spatial test. It's unusual but not incredibly so. I am the same way.
Ivan92
Just to complement your post, Richard Feynman's quote on the topic:
“I was an ordinary person who studied hard. There are no miracle people. It happens they get interested in this thing and they learn all this stuff, but they’re just people.”
― Richard Feynman
nphardon
"Just follow this simple road map".
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.
kbrkbr
I could not agree more. I am on my second try to master mathematics (30 years after the first), and I can see, understand and appreciate mathematics mainly from the constructive standpoint.
Nothing wrong with classical mathematics, as also used in this roadmap. Having axioms and drawing logical conclusions or searching proof does just not click for me.
Give me 0: N and suc: N -> N and I see how to construct stuff. Induction makes sense right away as a case distinction on those two constructors.
guyman16
What different routes are there to publish research besides academia? I would love to work on publications but it is not practical for me to return to an institution right now.
kronicum2025
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atulvi
What timing. I just got Schuam's Trigonometry to practice over the weekend and start a pure mathematics journey today and I see this article.
Caelan22
Unfortunately, most links are dead. At least the pages related to real analysis.
barrenko
Also a great way to lose your mind.
FranzFerdiNaN
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”.
cobbechampo
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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.