counterpoint to > easily four or five years of study just to play around a bit it depends significantly on the branch of maths you choose! I've been told by a professor of fluid mechanics that he has difficulty posing and approving subjects of undergrad dissertations because the knowledge threshold for contributing meaningful ideas reliably is so high, but in my primary interest (combinatorics) this is very much not the case.

the OEIS is replete with old sequences that no-one has considered in much detail in a decade or two, and have a lot of 'low-hanging fruit' for one willing to toy with them.

https://oeis.org/A185105 is a good example of such a sequence; "sample the elements of a random permutation of [n] in a random order and record each one's cycle (under repeated iteration), then T(n,k)/n! is the expected of the kth distinct cycle recorded," which seems like it would have been of some interest to someone in the last ≈13 years (since ie. it's well-known that the first cycle's length is uniform in [1..n]), but didn't receive any formulas until I happened upon it recently with my own toolbelt (which is quite modest and certainly could be learned in less than 4 years).

the OEIS is an excellent resource for both readinh and sharpening one's amateur teeth on novel (ie. unexplored, or at least undocumented) problems and very rewarding, if that's your goal with learninh maths

the proofs written by ChatGPT are necessarily reasoned about in plain language, and are a human-comprehensible length (that is what Tao did, since it hasn't been formalised in a proof-checking language); today, the many-gigabytes (or -terabytes) proofs (à la 4-colour theorem) are generally problems solved via SAT solvers that are required to prove nonexistence of smaller solutions by exhaustion.

and there is an ongoing literature review (which has been lucrative to both erdosproblems and the OEIS), and this one was relabelled upon the discovery of an earlier resolution

is there any further information on how she was trained and whether it used a reward for reaching objectives like teaching Kanzi (a bonobo) to play Minecraft? did a human demonstrate the controls or was there a simulation before the actual vehicle? or a hardcoded speed limit that was slowly raised?

it's weird to see that 6 years ago the public consensus on Musk was just that he was a well-intentioned soft-spoken nerd who liked computers and found himself with inadvertent money to allocate altruistically

other people have a load of USB-C charging cables and are frustrated with having to buy Lightning ones and clutter their bags with more wires than necessary.

although Lightning was better-designed for being routinely used (pins on the outside of the wire end rather than inside the device, easy to clean and no protruding pieces in the device to damage/snap off), and the ideal scenario would have been making it an open standard

It's short term annoyance for a long term greater good. I'm not oblivious - but of course the impact on me is simply negative (and I'm not going to leave the walled garden anyway so what were we ever achieving really)

I somewhat take issue with the second math example (the geometry problem); that is solvable routinely by computer algebra systems, and being able to translate problems into inputs, hit run and transcribe the proof back to English prose (which for all we know was what it did, since OpenAI and Google have confirmed their entrants received these tools which human candidates did not) is not so astonishing as the blog post makes it out to be

I think Zeilberger is taken heavily out of context and confused with Norman Wildberger a lot; he certainly has some eccentric opinions but that one is not at all reflected in his blog's contents (which are largely things like "[particular paper] presents [conjecture/proof] that can be [resolved/shortened] by routine methods" that are only routine because of his decades of work), it's a shame that him being the go-to example of a crank seems to have become engrained into LLMs

Archimedes had functionally developed a method of integration (which was how he obtained results like volume/surface area of a sphere, or centre of mass of a hemisphere) in a manuscript that got lost to time and then rediscovered in a palimpsest (pasted and written over with a religious text)

From [0]:

"Laying the foundations for integral calculus and foreshadowing the concept of the limit, ancient Greek mathematician Eudoxus of Cnidus (c. 390–337 BC) developed the method of exhaustion to prove the formulas for cone and pyramid volumes.

"During the Hellenistic period, this method was further developed by Archimedes (c. 287 – c. 212 BC), who combined it with a concept of the indivisibles—a precursor to infinitesimals—allowing him to solve several problems now treated by integral calculus. In 'The Method of Mechanical Theorems' he describes, for example, calculating the center of gravity of a solid hemisphere, the center of gravity of a frustum of a circular paraboloid, and the area of a region bounded by a parabola and one of its secant lines."

[0] https://en.wikipedia.org/wiki/Calculus

that is an indictment of the implementations, not the fundamental limits of the architecture; most commercial LLMs now have web-searching available by default and can do both of those things, but couldn't when they were confined to the user's prompt and their training data (which was often not quite contemporary, until recently)

I can't tell whether you're trying to convince humans, parody someone who might be, or give superficial sentiment for automated traders' webscrapers to be influenced by

or they left the /s off and it's a remark about how the fine article sounds more like hype-machine emesis than legitimate, substantive research

I think he's just being extremely ironic, meaning the exact opposite of what it actually says.