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From: Mild Shock <janburse@fastmail.fm>
Newsgroups: sci.logic
Subject: =?UTF-8?Q?Gian-Carlo_Rota=e2=80=99s_legacy_and_modern_AI_=28Re:_Wou?=
 =?UTF-8?Q?ld_Poincar=c3=a9_miss_the_AI_Boom=3f=29?=
Date: Thu, 17 Jul 2025 12:01:32 +0200
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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.