It was so infuriating to see everyone in the class absolutely fail on a specific subject and the "teacher" assumed that everyone must be stupid then. No self reflection, no questioning himself why he is not getting gaussian distribution in marks, just straight Fs.
I higly doubt that. Maybe in university level courses. Most people’s only experience with mathematics is an elementary or high school teacher who were probably themselves at best mediocre at the subject. Simply because of selection factors. Those who are good at math are encouraged to go into STEM. There will be of course exceptions everywhere, but that is not what “usually” happens.
And thats just about being good at maths the school subject, which is distinct from being “ good mathematicians” the science / research topic. Mathematicians are few and far between, simply because it is a specialist subject. There just aren’t enough of them to go around for them to be the formative experience around math for most people.
socratic method exists. almost none follows it.
I have a hatred for people who think they can use this method.
If used incorrectly which it is a great percentage of the time it confuses the student. The person employing the socratic method must actually know the answer and where the student is in their mind. Failure on either account makes it pointless.
Ask anyone unfortunate enough to ask for help on IRC
The moat for coders now seems to be that AI can automate tasks but not a full job (unclear how long that will hold). But in math, doing the math really was _the_ job, my PhD certainly was. Since this is academically funded, they now have to attempt to pivot that to save their profession. I am not optimistic myself.
We are all staring at the same existential dread, just seeing it unfold a bit slower. We're being told that utopia is being obsolete, and that is difficult to accept.
Math that only resides in the weights of models, or arcane forms such as a long lean proof or even an unread textbook .. is not the math that we should be striving for.
Likewise all other technology [ and culture ].
LLMs and AI / AGI / ASI could lead to a new renaissance of math discussion and expansion of human math and science. Or the opposite, where we outsource all our thinking to the AI, and no new generation of artisans is trained by doing hard problems, and in a generation we have killed off human math.
Likewise all of the fields of human intellect. We need to make sure we protect future generations of doctors, biologists, software developers, architects, engineers, librarians, musicians, artists ...
A moratorium on AI development might be the only way to achieve this preservation of human culture.
So many thoughts come to mind at once, they're a jumble in my head rather than a single coherent narrative.
John Henry comes to mind. As does Agent Smith's "I say your civilization because as soon as we started thinking for you, it really became our civilization, which is, of course, what this is all about" monologue in The Matrix. I've not read (or listened to) "With Folded Hands ..." or "The Machine Stops", but I have read the Wikipedia plot summary of both.
Do we want to have comfortable lives, or do we want to serve each other?
"Computer" used to be a profession; I grew up around adults bemoaning that "kids these days can't do mental arithmetic", the Pi Zero I've not switched on for probably a year now could beat all humans simultaneously at that (even if everyone was as good as the current world record holder) and yet we still teach arithmetic in schools.
Nobody needs to knit, and yet we do so for fun. Youtube's "Primitive Technology" channel, which has spent around a decade speechlessly making iron from bacterial slime found in a creek, using only clay and sticks naturally found next to that creek.
Like I said, no coherent narrative. It's been a while since my stream of consciousness became a river delta.
Tao is speaking of a very particular kind of mathematics, that done out of pure curiosity.
But maths, even at the highest levels, often finds applications sooner or later.
It will be economically impossible to justify boycotting correct mathematics that no humans understand on grounds only of purity.
This may happen very soon: one of the obvious applications of novel mathematical results is in building stronger AI models.
Mathematics is suffering from Goodhart's Law:
"When a measure becomes a target, it ceases to be a good measure."
a- understood it and all the background information it requires
b- internalized techniques and methods that are helpful in problem solving in general
Now it just means nothing
So, we are talking about a field that already does not use that much funding anyway, and most high end theoretical mathematicians probably would make much more money in the industry anyway, so this seems like missing the forest for the tree imo.
[0] Table in page 1 in https://nsf-gov-resources.nsf.gov/files/71_fy2025.pdf?Versio...
[1] Figure DISC-13 in https://ncses.nsf.gov/pubs/nsb20257/academic-r-d
The theorem thing is invented by human to help other people better understand Math structure in a easier way.
> Sorry, only epic problem solvers allowed here
Math academia 2026
> We were more than just problem solvers
I think people are overblowing this though. Wake me up when GPT-whatever writes gcc from scratch, then by the Curry-Howard I'd be impressed
It's interesting because, as far as I'm aware, the vast majority of people already believe that math is more than proof. A slightly smaller but still very large majority don't even include proofs in their mental concept of what math involves.
Technically, the largest majority are the people who go: "What are proofs?" :P
At university level introductory calculus, the person teaching class had to reassure students that math wasn't entirely arithmetic or adding up numbers. He did this because it's a common misunderstanding.
[1] https://youtu.be/H7_d_sgui6o?t=4436 (timestamped url)
Personally, I doubt AI can surpass a good human explainer because explanation requires empathy, which benefits from being an instance of the kind of entity you are explaining the thing to. That gives you a way of exploring and evaluating the space of possible explanations that isn't available to an LLM.
not really. You can consider positive proof as an experiment confirming your theory and the negative proof and counter examples as an experiment falsifying your theory.
no. Positive proofs have nothing to do with falsification. They just tell you that there is no point in spending effort on searching for negative proofs and counter examples. They don't prevent nor prohibit you from spending that effort. They just advise you that that effort will be wasted.
It is like nobody prevents from experiments to turn lead into gold. Of from searching for a right angled triangle violating Pythagoras.
It seems now that NS is solved he is mobilizing the community to convince taxpayers continue to pay even though AI may do a better job in his work.
Also, his opinion of AI has continually changed in the past years, after the capabilities were demonstrated.