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
and wars can be led in such ways that it never seems like the enemy is attacking the thing over which you would be willing to end the world. aka salami tactics
oof same here brother. chess is killing me. i go cold turkey but i come back eventually. one idea is to replace it with something and then ditch the replacement. or just capitalise next time there’s enough momentum built up for wanting to get rid off of it. i did do it before though, went not playing for months. but when it’s it’s back for good
didn’t open the video, but you can also set double or triple tap on back of your iphone shortcut for this. i have a red filter set up for late night doom scrolling
spend 1-2 years learning consistently _any_ undergrad math. id recommend focusing on “mastering” multivariable calculus, dependencies included. but keep taking peaks of higher level stuff or just articles as these. doing this is important as the math can be contextualised in many ways and being exposed to those ways helps you internalise intuitions
would you say that 3 reformulates 1+1+1 in another language? because if yes, such reformulations shouldn’t be disregarded just because they’re “reformulations”. so we can say there are kinds of reformulations which make things incredibly easier, and category theory is one of them
Why do you think category theory makes it easier? That's one thing category theory does not do. How well do you understand the subject?
There is a category theory "school of thought" in many subjects, which believes without solid evidence that category theory must be immensely useful to their subject. But it's often just that: a school of thought. This is the situation of category theory in CS. My concern is that people aren't being honest about this.
you’re right, and I’m in that school of thought, but mainly for math. In essence, I know people who use it in their reaearch and I trust them (and there’s a lot of good people doing good stuff with CT—it’s ubiquitous, so I’m fine with trusting them). I have a beginner understanding of CT, actually I finally started studying it seriously a month ago, after being exposed to it sporadically for some time. I’m not claiming anything about CT in CS, but I’m optimistic about that it can have a more widespread positive effect in it
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
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