"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.

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kronicum2025 3 days ago | parent | next [-]

As a young person growing up in India, enrolled in engineering in a small desolate city, when I wanted to be a mathematician, with no real path in sight, this blog post is actually what I followed, and learnt everything that is mandatory on this blog post during my undergraduate on my own, and then applied for entrance examinations for grad institutes in India, and now have successfully finished my PhD nicely in US.

So, in that sense, this blog post is for people like me, who had no exposure to research scientists in around 2012 in the places we are growing up. (I didn't yet have stable internet then, only once an hour every evening). They still have some years before they could actually come in contact with researchers who can give them good problems to work on. and the local universities are horribly out of whack in their skill/desire to teach the students properly.

And so, in the meantime, till you get access to good research problems, you prepare yourself to be ready for the problem when the day finally comes. And this blog post along with another one: https://webspace.science.uu.nl/~hooft101/theorist.html was what kept motivating me when I was studying.

The list of books is as important as anything else. To be fair, in 2012, math.stackexchange.com had grown up quite a bit, but I was not aware of it for various reasons.

	▲	yu3zhou4 2 days ago \| parent [-]
		Very inspiring story, congrats on your journey!

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guyman16 3 days ago | parent | prev | next [-]

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.

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throwaway652368 3 days ago | parent | next [-]

I've never seen a math journal that requires academic credentials or affiliation to submit a paper, and I've published several math papers without an academic affiliation. You can put your employer as your affiliation or even "Independent Researcher". The hard part is writing the papers themselves. Getting a paper in a decent math journal as an outsider is rare, not because the journals ban or are biased against outsiders, but just because it's rare for an outsider to write a decent math paper.

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gus_massa 2 days ago | parent | prev | next [-]

The sibling comments are good. Some additional info:

It's hard, there are a lot of i to dot and t to cross (and remember the j and f too).

The paper must have the correct length, a relevant introduction, conclusions and a lot of other form stuff, detailed but not too much detailed, the correct references, ...

And you must solve an interesting problem. The famous problems are too hard, a lot of people already tied to solve them. And "interesting" means what the community consider to be interesting, that sometimes it's what is interesting for the application and sometimes is something completely different.

And must be correct, in my university we got a few independent people (5?) claiming to have solved the Goldbach conjeture a few years ago. Unsurprisingly all had big mistakes.

My suggestion is to partner with someone already publishing math papers. Do you have a friend that is mathematician? Do you have a friend that has a friend that is mathematician? If your friends work in an uninteresting topic, you can ask for help to contact someone else that is working in something you like.

Be aware that there are abusive people, but most horror cases I heard are about experimental physics where a few extra hands are more helpful, mathematician usually don't lock people in the basement until they finish the experiments.

Once you understated how to publish, which journals are good, which journals are run by idiots, you can try to publish independently.

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Ivan92 3 days ago | parent | prev [-]

I don't know what your current industry is, but Google publishes their research and collaborates with academic institutions is one that immediately comes to mind. The government (NASA, NSA for one), tech companies (IBM, Microsoft, etc.), medical companies, aerospace/defense (JPL), just to name a few. I am sure there are way more than I could think of and I am sure others will care to fill in as well.

Research is not exclusive to academia.

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unixbeard1337 3 days ago | parent [-]

Yeah, but this is specifically about pure mathematics. Do Google and medical companies publish pure math research?

	▲	nativeit 3 days ago \| parent [-]
		Sure, this was the first result: https://www.nature.com/articles/s41586-021-04086-x

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kbrkbr 3 days ago | parent | prev [-]

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.