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Comment by paulpauper | Hacker News Reader

I think the gulf between research math and teaching math is so wide that it may as well be a different subject altogether. The vast majority of mathematicians are teachers, not researchers. If all mathematicians have at the very minimum PHDs, then is the difference in ability so great?

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I was ABD in math at a top 25 program when I went to a talk given by a graduate student from Berkeley. He was in my area and we had the same length of them spent on the subject. As close to equals in terms of experience and area of study as one can get. He was far better than me and I knew that I’d never understand the subject as well as him. Shortly after I quit the Ph.D. program. I realized I would never do anything worthwhile in the field. There is a large variation in talent within the community of professional mathematicians. Outliers amongst outliers.

In trained in MMA for a number of years and sparred against some local fighters. They were better than me but I could get some hits in. I could cause them to expend some effort. Once I sparred with a low level UFC fighter. He thoroughly destroyed me. It was like I was 5 years old. Outliers amongst outliers.

It's not so hard to get a PhD in math, in the sense that if you're willing to attend a low-ranked program and have at least a moderate affinity for mathematics, you could probably do it. It takes a lot of time to learn all the prerequisites, but that's why the undergrad degree is 4 years and the PhD typically 5+. Then you just find a suitable advisor, ask to be handed a dissertation problem and some ideas for the solution, write down that solution, and graduate. Anyone who's been doing math research for a few years has a collection of problems they know how to solve but haven't written up for various reasons, which they can give for this purpose. (Usually: the question is too boring or simple, no one cares, and there are bigger impact things to do instead).

Doing research that meaningfully advances mathematics, as opposed to being make-work in service of getting a degree? Much harder.

The higher up you go the tower of abstractions the more you notice difference in skill. A person with even just a slightly worse foundation will soon find that their tower is unstable and it is hard to add more on top. I'd say that mathematics is currently the field with the tallest such towers, it is just abstractions on top of abstractions over and over and you have to understand every step thoroughly, so difference in skill should be about as high as it can get in any mental field.

The math most STE (not M) people learn in college was mostly well understood 200 years ago. A lot of things happened in those 200 years just adding more and more on top, getting to the forefront today requires you to build your understanding extremely high.

I wouldn't consider someone a mathematician unless they were a researcher. Otherwise what does a mathematician do? Many people have undergraduate or advanced degrees in math, but most of them don't "do math" for a living (i.e. research).

Same for most science - physics, chemistry, etc… I have a Physics PhD and I still wouldn’t consider myself a physicist as applying the physics skills is not what I do day to day.

with a bachelor's in Biochem, in my head I say I'm formally trained in biochemistry. But iut loud I just say "my bachelor's was in biochem"

often as large as a draft prospect and nba player with years of experience

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