Gian-Carlo Rota’s legacy and modern AI (Re: Would Poincaré miss the AI Boom?)

Hi,
Spotting Trojan Horses is a nice example
of creativity that also needs ground truth.
Gian-Carlo Rota was phamous for this truth:
"The lack of understanding of the simplest
facts of mathematics among philosophers
is appalling."
You can extend it to GitHub acrobats,
paper mill balerinas and internet trolls.
But mathematics itself had a hard time,
allowing other objects than numbers:
- Blissard's symbolic method
   He was primarily an applied mathematician and
   school inspector. His symbolic method was a way
   to represent and manipulate sequences algebraically
   using formal symbols.
- Gian-Carlo Rota (in the 1970s)
   Gian-Carlo Rota (in the 1970s) gave Blissard’s
   symbolic method a rigorous algebraic foundation. Rota
   admired the symbolic reasoning of 19th-century mathematicians
   and often described it as having a “magical” or “mystical”
   elegance — again hinting at interpretive, almost poetic, qualities.
- Umbral calculus
   Modern formalization of this method, often involving
   linear operators and algebraic structures. "Umbral"
   means “shadow” — the power-like expressions are
   symbolic shadows of actual algebra.
Bye
Mild Shock schrieb:

Henri Poincaré believed that mathematical
and scientific creativity came from a deep,
unconscious intuition that could not be
 captured by mechanical reasoning or formal
systems. He famously wrote about how insights
came not from plodding logic but from sudden
 illuminations — leaps of creative synthesis.
 But now we have generative AI — models like GPT — that:
 - produce poetry, proofs, stories, and code,
 - combine ideas in novel ways,
 - and do so by processing patterns in massive
    datasets, without conscious understanding.
 And that does seem to contradict Poincaré's belief
that true invention cannot come from automation.