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.
Hi,
So StackOverflow has already fallen, and
GitHub will be the next one. StackOverflow
was eclectic, insuinated a high Signal
quality but repelled its newcomers by
strick language rules and deletism.
StackOverlow is suplaned by ChatGPT, etc..
They are more tolerant and can deliver
excellent Signals, much beter than
StackOverflow. ChatGPT and other assistants
flipped the model: No downvotes.
No “duplicate question” shaming. Conversational,
exploratory, and often faster than Googling +
scanning SO threads. Most importantly: they don’t
punish incomplete knowledge, which is where
most human learning happens.
LLMs give a more forgiving learning curve.
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.
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.
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.
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.
Hi,
Rota often celebrated symbolic, analogical, and
conceptual understanding over brute calculation.
This philosophy has come full circle in modern AI:
- Large Language Models (LLMs) like GPT-4 don't
just store facts — they recognize patterns,
make analogies, and generate new structures
from old ones.
- Rota’s work in combinatorics, symbolic logic, and
operator theory is essentially pattern-based
manipulation — exactly the kind of reasoning LLMs
aim to emulate at scale.
Rota had a clear aesthetic. He valued clean formalisms,
symbolic beauty, and well-defined structures. Rota wanted
mathematics to mean something — to be not just correct,
but intelligible and expressive.
In contrast, modern AI (especially LLMs like GPT) thrives
on the messy, including: Noisy data , Inconsistency ,
Uncertainty, Contradiction. AI engineers today are mining
meaning from noise.
What counts as “structure” is often just the best
pragmatic/effective description available at that moment.
Bye
Mild Shock schrieb:
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.
Hi,
An example of human intelligence, is of course the
name "Rational Term" for cyclic terms set forth by
Alain Colmerauer. Since it plays with "Rational Numbers".
A subset of cyclic terms can indeed represent
rational numbers, and they give a nice counter
example to transitivity:
?- problem(X,Y,Z).
X = _S1-7-9-1, % where
_S1 = _S1-6-8-0-6-2-8,
Y = _S2-1-6-1-5-4-6-1, % where
_S2 = _S2-0-9-2,
Z = _S3-3-0, % where
_S3 = _S3-8-1
The Fuzzer 2 from 2025 does just what I did in 2023,
expanding rational numbers into rational terms:
% fuzzy(-Term)
fuzzy(X) :-
random_between(1,100,A),
random_between(1,100,B),
random_between(1,10,M),
fuzzy_chunk(M,A,B,C,X,Y),
random_between(1,10,L),
fuzzy_chunk(L,C,B,_,Y,Z),
Z = Y.
% fuzzy_chunk(+Integer,+Integer,+Integer,-Integer,+Term,-Term)
fuzzy_chunk(0, A, _, A, X, X) :- !.
fuzzy_chunk(N, A, B, C, Y-D, X) :-
M is N-1,
D is A // B,
H is 10*(A - B*D),
fuzzy_chunk(M, H, B, C, Y, X).
Bye
Mild Shock schrieb:
Hi,
Rota often celebrated symbolic, analogical, and
conceptual understanding over brute calculation.
This philosophy has come full circle in modern AI:
- Large Language Models (LLMs) like GPT-4 don't
just store facts — they recognize patterns,
make analogies, and generate new structures
from old ones.
- Rota’s work in combinatorics, symbolic logic, and
operator theory is essentially pattern-based
manipulation — exactly the kind of reasoning LLMs
aim to emulate at scale.
Rota had a clear aesthetic. He valued clean formalisms,
symbolic beauty, and well-defined structures. Rota wanted
mathematics to mean something — to be not just correct,
but intelligible and expressive.
In contrast, modern AI (especially LLMs like GPT) thrives
on the messy, including: Noisy data , Inconsistency ,
Uncertainty, Contradiction. AI engineers today are mining
meaning from noise.
What counts as “structure” is often just the best
pragmatic/effective description available at that moment.
Bye
Mild Shock schrieb:
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.
Hi,
Ok I have to correct "Rational Term" was less
common, what was more in use "Rational Trees",
but they might have also talked about finitely
represented infinite tree. Rational trees itself
probably an echo from Dmitry Mirimanoffs
(1861–1945) “extraordinaire” sets.
Dmitry Semionovitch Mirimanoff (Russian:
Дми́трий Семёнович Мирима́нов; 13 September 1861, Pereslavl-Zalessky, Russia – 5 January 1945, Geneva,
Switzerland) was a member of the Moscow Mathematical
Society in 1897.[1] And later became a doctor of
mathematical sciences in 1900, in Geneva, and
taught at the universities of Geneva and Lausanne. https://en.wikipedia.org/wiki/Dmitry_Mirimanoff
This year we can again celebrate another researcher,
who died in 2023, Peter Aczel R.I.P., who made
as well some thoughtful deviance from orthodoxy.
Peter Aczel Memorial Conference on 10th September 2025.
Logic Colloquium will take place at the University
of Manchester (UK) from 11th to 12th September 2025 https://sites.google.com/view/blc2025/home
Have Fun!
Bye
Mild Shock schrieb:
Hi,
An example of human intelligence, is of course the
name "Rational Term" for cyclic terms set forth by
Alain Colmerauer. Since it plays with "Rational Numbers".
A subset of cyclic terms can indeed represent
rational numbers, and they give a nice counter
example to transitivity:
?- problem(X,Y,Z).
X = _S1-7-9-1, % where
_S1 = _S1-6-8-0-6-2-8,
Y = _S2-1-6-1-5-4-6-1, % where
_S2 = _S2-0-9-2,
Z = _S3-3-0, % where
_S3 = _S3-8-1
The Fuzzer 2 from 2025 does just what I did in 2023,
expanding rational numbers into rational terms:
% fuzzy(-Term)
fuzzy(X) :-
random_between(1,100,A),
random_between(1,100,B),
random_between(1,10,M),
fuzzy_chunk(M,A,B,C,X,Y),
random_between(1,10,L),
fuzzy_chunk(L,C,B,_,Y,Z),
Z = Y.
% fuzzy_chunk(+Integer,+Integer,+Integer,-Integer,+Term,-Term)
fuzzy_chunk(0, A, _, A, X, X) :- !.
fuzzy_chunk(N, A, B, C, Y-D, X) :-
M is N-1,
D is A // B,
H is 10*(A - B*D),
fuzzy_chunk(M, H, B, C, Y, X).
Bye
Mild Shock schrieb:
Hi,
Rota often celebrated symbolic, analogical, and
conceptual understanding over brute calculation.
This philosophy has come full circle in modern AI:
- Large Language Models (LLMs) like GPT-4 don't
just store facts — they recognize patterns,
make analogies, and generate new structures
from old ones.
- Rota’s work in combinatorics, symbolic logic, and
operator theory is essentially pattern-based
manipulation — exactly the kind of reasoning LLMs
aim to emulate at scale.
Rota had a clear aesthetic. He valued clean formalisms,
symbolic beauty, and well-defined structures. Rota wanted
mathematics to mean something — to be not just correct,
but intelligible and expressive.
In contrast, modern AI (especially LLMs like GPT) thrives
on the messy, including: Noisy data , Inconsistency ,
Uncertainty, Contradiction. AI engineers today are mining
meaning from noise.
What counts as “structure” is often just the best
pragmatic/effective description available at that moment.
Bye
Mild Shock schrieb:
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.
Hi,
I am trying to verify my hypothesis
that Rocq is a dead horse. Dead
horses can come in different forms,
for example a project that just
imitates what was already done by
the precursor, is most likely a
Dead horse. For example MetaRocq,
verifying a logic framework inside
some strong enough set theory,
is not novell. Maybe they get more
out of doing MetaRocq:
MetaRocq is a project formalizing Rocq in Rocq https://github.com/MetaRocq/metarocq#papers
#50 Nicolas Tabareau
https://www.youtube.com/watch?v=8kwe24gvigk
Bye
Mild Shock schrieb:
Hi,
Ok I have to correct "Rational Term" was less
common, what was more in use "Rational Trees",
but they might have also talked about finitely
represented infinite tree. Rational trees itself
probably an echo from Dmitry Mirimanoffs
(1861–1945) “extraordinaire” sets.
Dmitry Semionovitch Mirimanoff (Russian:
Дми́трий Семёнович Мирима́нов; 13 September 1861, >> Pereslavl-Zalessky, Russia – 5 January 1945, Geneva,
Switzerland) was a member of the Moscow Mathematical
Society in 1897.[1] And later became a doctor of
mathematical sciences in 1900, in Geneva, and
taught at the universities of Geneva and Lausanne.
https://en.wikipedia.org/wiki/Dmitry_Mirimanoff
This year we can again celebrate another researcher,
who died in 2023, Peter Aczel R.I.P., who made
as well some thoughtful deviance from orthodoxy.
Peter Aczel Memorial Conference on 10th September 2025.
Logic Colloquium will take place at the University
of Manchester (UK) from 11th to 12th September 2025
https://sites.google.com/view/blc2025/home
Have Fun!
Bye
Mild Shock schrieb:
Hi,
An example of human intelligence, is of course the
name "Rational Term" for cyclic terms set forth by
Alain Colmerauer. Since it plays with "Rational Numbers".
A subset of cyclic terms can indeed represent
rational numbers, and they give a nice counter
example to transitivity:
?- problem(X,Y,Z).
X = _S1-7-9-1, % where
_S1 = _S1-6-8-0-6-2-8,
Y = _S2-1-6-1-5-4-6-1, % where
_S2 = _S2-0-9-2,
Z = _S3-3-0, % where
_S3 = _S3-8-1
The Fuzzer 2 from 2025 does just what I did in 2023,
expanding rational numbers into rational terms:
% fuzzy(-Term)
fuzzy(X) :-
random_between(1,100,A),
random_between(1,100,B),
random_between(1,10,M),
fuzzy_chunk(M,A,B,C,X,Y),
random_between(1,10,L),
fuzzy_chunk(L,C,B,_,Y,Z),
Z = Y.
% fuzzy_chunk(+Integer,+Integer,+Integer,-Integer,+Term,-Term)
fuzzy_chunk(0, A, _, A, X, X) :- !.
fuzzy_chunk(N, A, B, C, Y-D, X) :-
M is N-1,
D is A // B,
H is 10*(A - B*D),
fuzzy_chunk(M, H, B, C, Y, X).
Bye
Mild Shock schrieb:
Hi,
Rota often celebrated symbolic, analogical, and
conceptual understanding over brute calculation.
This philosophy has come full circle in modern AI:
- Large Language Models (LLMs) like GPT-4 don't
just store facts — they recognize patterns,
make analogies, and generate new structures
from old ones.
- Rota’s work in combinatorics, symbolic logic, and
operator theory is essentially pattern-based
manipulation — exactly the kind of reasoning LLMs
aim to emulate at scale.
Rota had a clear aesthetic. He valued clean formalisms,
symbolic beauty, and well-defined structures. Rota wanted
mathematics to mean something — to be not just correct,
but intelligible and expressive.
In contrast, modern AI (especially LLMs like GPT) thrives
on the messy, including: Noisy data , Inconsistency ,
Uncertainty, Contradiction. AI engineers today are mining
meaning from noise.
What counts as “structure” is often just the best
pragmatic/effective description available at that moment.
Bye
Mild Shock schrieb:
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.
Hi,
I am trying to verify my hypothesis that Rocq is a dead horse. Dead
horses can come in different forms,
you do need a theory of terms, and a specific one
Hi,
Ok I have to correct "Rational Term" was less
common, what was more in use "Rational Trees",
but they might have also talked about finitely
represented infinite tree. Rational trees itself
probably an echo from Dmitry Mirimanoffs
(1861–1945) “extraordinaire” sets.
Dmitry Semionovitch Mirimanoff (Russian:
Дми́трий Семёнович Мирима́нов; 13 September 1861, Pereslavl-Zalessky, Russia – 5 January 1945, Geneva,
Switzerland) was a member of the Moscow Mathematical
Society in 1897.[1] And later became a doctor of
mathematical sciences in 1900, in Geneva, and
taught at the universities of Geneva and Lausanne. https://en.wikipedia.org/wiki/Dmitry_Mirimanoff
This year we can again celebrate another researcher,
who died in 2023, Peter Aczel R.I.P., who made
as well some thoughtful deviance from orthodoxy.
Peter Aczel Memorial Conference on 10th September 2025.
Logic Colloquium will take place at the University
of Manchester (UK) from 11th to 12th September 2025 https://sites.google.com/view/blc2025/home
Have Fun!
Bye
Mild Shock schrieb:
Hi,
An example of human intelligence, is of course the
name "Rational Term" for cyclic terms set forth by
Alain Colmerauer. Since it plays with "Rational Numbers".
A subset of cyclic terms can indeed represent
rational numbers, and they give a nice counter
example to transitivity:
?- problem(X,Y,Z).
X = _S1-7-9-1, % where
_S1 = _S1-6-8-0-6-2-8,
Y = _S2-1-6-1-5-4-6-1, % where
_S2 = _S2-0-9-2,
Z = _S3-3-0, % where
_S3 = _S3-8-1
The Fuzzer 2 from 2025 does just what I did in 2023,
expanding rational numbers into rational terms:
% fuzzy(-Term)
fuzzy(X) :-
random_between(1,100,A),
random_between(1,100,B),
random_between(1,10,M),
fuzzy_chunk(M,A,B,C,X,Y),
random_between(1,10,L),
fuzzy_chunk(L,C,B,_,Y,Z),
Z = Y.
% fuzzy_chunk(+Integer,+Integer,+Integer,-Integer,+Term,-Term)
fuzzy_chunk(0, A, _, A, X, X) :- !.
fuzzy_chunk(N, A, B, C, Y-D, X) :-
M is N-1,
D is A // B,
H is 10*(A - B*D),
fuzzy_chunk(M, H, B, C, Y, X).
Bye
Mild Shock schrieb:
Hi,
Rota often celebrated symbolic, analogical, and
conceptual understanding over brute calculation.
This philosophy has come full circle in modern AI:
- Large Language Models (LLMs) like GPT-4 don't
just store facts — they recognize patterns,
make analogies, and generate new structures
from old ones.
- Rota’s work in combinatorics, symbolic logic, and
operator theory is essentially pattern-based
manipulation — exactly the kind of reasoning LLMs
aim to emulate at scale.
Rota had a clear aesthetic. He valued clean formalisms,
symbolic beauty, and well-defined structures. Rota wanted
mathematics to mean something — to be not just correct,
but intelligible and expressive.
In contrast, modern AI (especially LLMs like GPT) thrives
on the messy, including: Noisy data , Inconsistency ,
Uncertainty, Contradiction. AI engineers today are mining
meaning from noise.
What counts as “structure” is often just the best
pragmatic/effective description available at that moment.
Bye
Mild Shock schrieb:
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.
| Sysop: | Keyop |
|---|---|
| Location: | Huddersfield, West Yorkshire, UK |
| Users: | 546 |
| Nodes: | 16 (2 / 14) |
| Uptime: | 14:04:28 |
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| Messages: | 6,416,893 |