To add onto these answers, there were some notable "outsider art" additions to math around this time.

A few months before this post, Futurama contributed a new proof to the mathematical canon (for "The Prisoner of Benda"), resolving the conflict of the episode.

Almost a year after posting this, a 4chan user solved a previously-unsolved superpermutation (combinatorics) problem in a discussion about anime.

I think everyone who has thought about math seriously has felt similarly to the OP. It was impressed upon me early on that there are combinatorically (hah) many combinatorics problems to be solved and that these were just a few.

a) Individualized teaching methodology. We come with different backgrounds, therefore different types of analogies/examples, different levels of background material, different (but systematized) levels of presentation should be used. The same ask should be applied to kids learning through starting at preschool.

b) Readable mathematics papers where the compact notations are abandoned, and narrative, visualizations are introduced, while preciseness is maintained. It is possible that the same paper (or chapter or topic) should be renderable in multiple ways (for professional mathematicians in the field, for a casual reader, for a student, for an individual reader (as for (a) )

c) Mathematical logic / tooling for differentiable data/event computing. Where there are mathematical tools as well as CS implementation of this tools that allow to act on a difference in state, data, actions.

Typical mathematics (with exception of may be time series), does not view time as 'first class citizen' so to speak, be it abstract algebra and category theory or something else. But, I think, when we go to the 'applied world' we must introduce 'time dimension' as first class citizen. So having the mathematical machinery dealing with this dimension in organic way across many of the areas of mathematics -- will be beneficial to the application of this one of the most valuable human tools.

  - basic visual explanations (for kids)
  - basic algebra steps (for high school)
  - standard explanation (for undergraduate students)
  - compact explanation (a reviee for grad students)

Related. Others?

Bill Thurston's answer to “What's a mathematician to do?” (2010) - https://news.ycombinator.com/item?id=23461983 - June 2020 (21 comments)

Bill Thurston answers: What's a mathematician to do? - https://news.ycombinator.com/item?id=15578866 - Oct 2017 (25 comments)

What's a Mathematician to do? - https://news.ycombinator.com/item?id=8265509 - Sept 2014 (44 comments)

Bill Thurston's answer to "What's a mathematician to do?" - https://news.ycombinator.com/item?id=4419859 - Aug 2012 (1 comment)

Edit: bonus relateds:

https://news.ycombinator.com/item?id=43345503 (March 2025)

It's not mathematics that you need to contribute to (2010) - https://news.ycombinator.com/item?id=36744690 - July 2023 (65 comments)

Knots to Narnia – Bill Thurston (1992) [video] - https://news.ycombinator.com/item?id=34426275 - Jan 2023 (8 comments)

On Proof and Progress in Mathematics (1994) - https://news.ycombinator.com/item?id=31960487 - July 2022 (1 comment)

On Proof and Progress in Mathematics (1994) [pdf] - https://news.ycombinator.com/item?id=12280139 - Aug 2016 (8 comments)

Bill Thurston has died - https://news.ycombinator.com/item?id=4419566 - Aug 2012 (18 comments)

On Proof And Progress In Mathematics (1994) [pdf] - https://news.ycombinator.com/item?id=2582730 - May 2011 (1 comment)

On proof and progress in mathematics (1994) - https://news.ycombinator.com/item?id=982335 - Dec 2009 (5 comments)

Good question, but I'm offended by the egregious misuse of a semicolon. My JIT compilation is throwing an error.

this guy is resigned to feel worthless compared to other mathematicians (suggesting he become cannon fodder in some type of mathematical sacrifice. i wonder if that analogy even makes sense in the field xD).

but, he desperately wants to become a great mathematician who creates completely original work.

from my experience, people tend to or even want to limit themselves. they think they know the ceiling of their capabilities and it becomes some self fulfilling prophecy.

if you really care about doing something great like this guy does, don't limit yourself. push until you achieve the greatness you want to achieve.

it's like that one saying, aim for the stars and you might land on a cloud. you will be surprised at how capable you actually are

I think the answer is to do multi-disciplinary work.

Venture outside of pure theoretical math. Learn some other domain knowledge and combine it with your mathematical ommph. That's the easiest way to make an impact now rather than potentially decades later.

If we see our contributions as brownian motion rather than preconceived trajectories, then, rather than focusing on the Gausses, Einsteins, Patons as providing singular progress, they become the the dominant least energy paths to what we recognize as truth. Without negating the individual’s contribution, the ones we see as truly important are the ones that supported by every other’s attempt, finds the path forward. This should provide hope, if we can leave aside our egos and focus on humanity, we can, and do, all contribute even though a few seems to get all the credit.

This also goes for AI, it may be an accelerant in research, but the probability distribution of reality is large, large enough for humans to wonder, ask questions and stumble upon a new path forward, that computers alone don’t find.

Mathematican here. Writing software because it pays better.

There are many practical jobs left for mathematicians. Time to discover what you like to do with your hands.

Fortunately doing something novel is one of the main things llms can't do.

But unfortunately human knowledge accumulation and advancement over the last many thousand years has been pretty large deep and varied.

Finding something novel for phds or profits or crime or whatever th fk is harder everyday.