Comment by mdnahas | Hacker News Reader

Comment by mdnahas | Hacker News Reader

As a consumer of mathematics, I want to attack the author’s idea of “what that work was meant to achieve in the first place”.

I do a lot of programming that uses mathematics. I designed the error recovery file format “par2”. I worked as a quantitative trader.

What do I want from math? To be able to search math results, understand them, and apply them. But academic mathematicians are so inwardly focused - as these authors so obviously are - that it does all of these badly! Search is still with words, not symbols and formulae. As for comprehension, many math papers are unreadable to those not in the cliche of mathematicians in that specialty. And even applied math papers don’t ship code or specify the operations explicitly.

I wanted to fix this and in 2013 I worked on formal proof. It makes symbol search and application easy. I found out that the tools had been usable for decades at that point. But mathematicians didn’t use them because they had that inward focus and didn’t give a damn about math consumers.

AI is enabling formal proof. It will carry mathematics into the computer age, which the field should have joined with every other industry in the 1970’s! I welcome it. Math will get used more and that is what the work was meant to achieve in the first place.

I've had a similar experience.

LLMs doing math has made math far more accessible to me than it was pre-LLM.

Not just using existing math, but developing new math. (For example, I developed an alternative to NURBS surfaces for geometric kernels using LLMs.)

It's really annoying that anyone, anywhere is talking about halting math progress with AI.

different fields have different communication cultures, that’s not inherently bad. sacrificing inward focus is expensive from the pov of the insider; i see your points but not everything can be written for a general/wide audience. after all, the audience of the author are the specialists, since only specialists spent the effort to be able to engage with the work in depth. perhaps we disagree that mathematics is not a product that mathematicians are making?

what the work was meant to achieve in the first place is what the work was achieving in the first place. it was developing mathematics. if someone wants to use it, they are free to do so, or to write a blog article how it can be used by non experts. mathematicians do that themselves sometimes, but it’s not their job. myb there should be more incentives for them to do more of such work

i keep seeing this myth that mathematics has some purpose to do this or that, but somehow its purpose is least known to mathematicians, everyone else seems to know better

> what the work was meant to achieve in the first place is what the work was achieving in the first place. it was developing mathematics.

Meant by who? Were the people footing the bill aware of this? People can like and do a lot of things. When money enters the picture it gets more complicated because usually the people who pay do that because they derive some gains from it. Historically scientists and mathematicians were employed by various patrons, sometimes doing astronomical calculations for horoscopes, Easter calendars and whatnot. Pure for-fun math was usually done by already wealthy individuals and not salaried employees like today. So it's fine that mathematicians feel this or that is their purpose, but they are coming to us asking for tax money, and so there is a bit of burden on them to be convincing. Before AI they used to argue how it helps physics, engineering technology, computer tech, optimizing logistics and telecom, cancer cures etc. Now the tune changed and it's retroactively now obviously just pure recreation and spiritual elegance. I also like math don't get me wrong. I think it's a great intellectual pursuit. But it's arrogant to expect that the money can flow by default.

mathematicians are primarily paid for teaching, and that's their primary function from the pov of the general society. i don't think anybody is debating that part of their profession? i read somewhere that the annual nsf grant budget for mathematics is 57 million, in total. even if it was just spiritual elegance, that's a reasonable number no?

Yes, that amount seems fine if true. They may be seen as teachers by the outside world yet they hire and promote and award internally based on research. Status and prestige is rarely allocated based on teaching. This is already a discrepancy. And note that the post doesn't much talk about teaching courses, but mentorship of grad student researchers who already work at their labs.

my response is not to the post, but to the parent comment i replied to. the internal structure of mathematicians is their thing, if someone should step in, who? do you think that discrepancy matters?

You mean who should pay? Whoever they can convince, of course. Historically it was wealthy patrons, royal courts, etc. Teaching indeed used to be the main thing a professor was expected to do, this changed in the 19th century with Humboldt's model of the research university, with the explicit purpose of not just passing on knowledge but constantly producing new knowledge as a core part of the operations. It could go back to the teaching model, if that's acceptable to them. Then they would have to do the research part on the side, as a hobby, like it was back in the day.

In case of public universities, the mathematicians would ultimately have to convince the public, but of course in practice that means politicians and national grant agencies, who indeed report to politicians and the politicians chase popularity to the extent needed for reelection, so public sentiment has some relevance.

Generally when you come to someone holding out your hand asking for money, being humble is a good first step, instead of getting angry at people for not sufficiently appreciating the big myterious value of what they are doing. Explain the spiritual value of the pursuit, they may or may not be convinced. This may be called a deficiency of democracy if your aesthetic values are different, but typically people don't like to fund abstract disconnected things, like expensive space travel unless it's embedded in some tribal jockeying like during the Cold War. In normal times people just want research that has life enhancing practical outputs. Nevertheless currently the West is structured as electoral democracy, so convincing the plebs is indeed necessary, no matter how lowly that feels from the ivory tower.

> In normal times people just want research that has life enhancing practical outputs

what about people who study birds, or say, olms? people want that kind of research? the people who are doing it surely do. astronomy and eg star watching in deep space? i could go on for days

people like doing mathematics, similarly to studying endemic organisms or other stuff of no direct utilitarian value

how many parents are happy to pay the fraction of taxes that go into something that their children might want to choose as a calling and fall in love with?

it’s okay to discuss whether something should be publicly funded, using “people want x kind of research” as a supposedly obvious or common sense argument is fallacious in the sense that it implies an idealised steelman model of the general public. that model is divorced from reality

One key idea to understand about human behavior is that people are focused on their status among their peers and their next level superiors with power to lift their status. You are not among either, so you don't matter to them. This is nothing special about mathematicians, though, people work the same way everywhere, in every field, community etc.

Yes, that’s very true. I recognized that in 2014. It was hard, but I stopped doing research on formal proof.

I got an economics degree and found that the City of Austin to pay off its $3 billion dollar pension debt … and encountered the same problem you mentioned, again. Except this time my plan is to run for City Council and be their next-level superior.

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