My impression, based on using LLMs, is that their effectiveness in solving mathematical problems depends heavily on the quality and untapped potential of the existing literature underlying those problems. If that is correct, I wonder what will happen once that potential has been exhausted, especially if mathematicians become overly reliant on LLM assistants and the literature is not replenished by genuinely new, sufficiently deep insights. In other words, I’m not entirely sure we aren’t entering a creative rabbit hole.
— Francesco Maggi (@Frances01896069) November 10, 2026
Wednesday, November 11, 2026
LLMs, math, and the well of human insight
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Bill, no need to provide sans empathy Elon Musk with content.
ReplyDeleteTry a no gate, surveillance, or cesspool associated link.
"Will it be a golden age or a dark age for mathematics (and science)?
Posted by Terence Tao
[This is a guest post by Francesco Maggi.
...
"Reality will likely combine these scenarios. In eight points, I will examine the choices shaping that outcome, moving from mathematics to science more broadly, and closing with actionable proposals.
...
"(7) Private control of frontier LLMs is potentially dangerous."
...
https://terrytao.wordpress.com/2026/10/18/will-it-be-a-golden-age-or-a-dark-age-for-mathematics-and-science/
Private control of common knowledge and dissemination is also potentially dangerous.
X (pronounced shitter) being an archetypal example.
I can't understand why Francesco Maggi uses Xitter. As Francesco Maggi says in the Tao link... "In the “dark age” scenario, scientific and technological output would still increase spectacularly in the short term, but, at the same time, independent human scientific activity would progressively weaken, the production of new knowledge becoming increasingly concentrated in a small number of hands" ...
And a toll booth, a gate and a dark mirror placed abound new knowledge by the likes of Musk, as people provide Xitter with content for free.
Frank Wilhoit has coined a term for this, applicable to Xitter, as with the good comes plenty of violence providing...
"whateverthefuckkindofstupidnoise-ism".
Besides the many good tweets reside the dangerous, and so posting links to Xitter is imo, encapsulated in the term...
whateverthefuckkindofstupidnoise-ism.
Frank Wilhoit..."...All that is left is the core proposition itself — backed up, no longer by misdirection and sophistry, but by violence.
So this tells us what anti-conservatism must be: the proposition that the law cannot protect anyone unless it binds everyone, and cannot bind anyone unless it protects everyone.
Then the appearance arises that the task is to map “liberalism”, or “progressivism”, or “socialism”, or whateverthefuckkindofstupidnoise-ism, onto the core proposition of anti-conservatism.
No, it a’n’t. The task is to throw all those things on the exact same burn pile as the collected works of all the apologists for conservatism, and start fresh. The core proposition of anti-conservatism requires no supplementation and no exegesis. It is as sufficient as it is necessary. What you see is what you get:
The law cannot protect anyone unless it binds everyone; and it cannot bind anyone unless it protects everyone.
— Frank Wilhoit, 03.22.18 at 12:09 am
https://crookedtimber.org/2018/03/21/liberals-against-progressives/#comment-729288
SD