Basic mathematical research pursues questions that are often quite far from actual practical application; but they contribute, in a largely invisible way, to the broader research ecosystem that eventually does generate such application. For instance, consider the problem of packing spheres into space as efficiently as possible - a question first proposed by Kepler in 1611. At a practical level, the solution to this problem has been "known" to greengrocers for centuries - one should stack the spheres in a hexagonal close packing. But mathematicians spent decades to work out how to establish the optimality of this packing, culminating in a formally verified proof in 2012.

Mathematicians also explored variants of this sphere packing problem in other geometries than three-dimensional Euclidean space: for instance in higher dimensions, with the famous recent breakthroughs of Viazovska in 8 and 24 dimensions, or in more discrete geometries over finite fields. Such curiosity-driven questions appear to lack immediate application - nobody had a need to pack eight-dimensional oranges together, for instance. (2/3)

@tao That diagram looks like an illustration of the Banach-Tarski paradox.

How does it go again?

Ah yes: if you accept the Axiom of You Have No Choice, it follows that for all agencies under public ownership, there exists some series of political manoeuvres such that an agency can be disassembled and the pieces looted, ransacked, destroyed, pillaged, and privatised until the agency provides no more than half of its previous services; all the while claiming that the remnants are somehow at least as effective as the original.

The only way to avoid the paradox is to reject the Axiom of You Have No Choice. #HandsOff

@tao to put it bluntly, using chatbots which require calling out to third party corporate servers to regurgitate mathematical fragments without credit or citation is not a terribly good example of the kind of research actually under threat right now since it's indistinguishable from corporate PR and part of a field receiving immense levels of funding at the moment for this reason. you could certainly do better than to siphon from the same competitive sources that failed to allocate funding for my own phd application this year.

it's not terribly convincing to claim that an effective response to government imposed austerity is to invest in tools like LLMs which are directly intentionally created to foster said austerity—to deskill and to replace expensive researchers with graduate degrees. it's insult added to injury to claim that this is a form of fundamental research desperately worth preserving, in an environment where LLMs are literally the only thing getting grant money at the moment, causing many researchers to simply leave the field they have developed a unique and irreplicable expertise in. none of this is remotely contentious to people who have read a single book.

did you know all production LLMs use regular expressions to filter and censor their outputs, since the token prediction machine is fundamentally incapable of understanding the intricacies necessary to do so? do you know how difficult those filter expressions are to write and how difficult they are to debug? this task is so thankless because the field of parsing and formal languages has starkly diverged from practice for half a century and extant regular expression engines measure only farcical ideals of decontextualized performance, much like the "objective" function which substitutes for intelligence in LLMs.

that's my field, and that's my thesis (i actually have a novel formulation of linguistic complexity and a grammar language with qualities you wouldn't be able to appreciate). research like your project proposal in OP displaces exactly that which holds it up. calling LLM usage the kind of fundamental research under threat in this environment steals valor from those who would actually advance many separate fields at once. reconsider.