Re: Log i = 0

On 05/25/2025 07:22 PM, sobriquet wrote:

Op 25/05/2025 om 20:41 schreef efji:

Le 25/05/2025 à 19:17, sobriquet a écrit :

Humans are fallible creatures. Math communities consist of humans.
Conclusion, there is no certainty in math. Though of course it's
extremely unlikely for something to turn out to be false if its proof
has been verified and accepted by the entire community of
mathematicians and has stood the test of time. But there are also
other factors involved. For instance the proof could consist of
terabytes of data, so in that case we might increase our confidence
level if we formalize the
proof so it gets checked independently by a computer.

>
It seems that your level in mathematics may not be very advanced, and
you appear to be repeating, somewhat awkwardly, what you’ve read in
mainstream media.
>
No, proofs of theorems generally do not involve "terabytes of data" :)
>
ChatGPT gives the following rough evaluations:
>
* 3 to 5 millions of theorems proved since the beginning of humanity,
some of them with multiple proofs (e.g. Pythagorean Theorem: more than
400 independent proofs).
>
* 250000 to 350000 theorems published last year (between 100000 and
120000 maths publications in peer reviews).
>
Among these millions of theorems, only a few involve a computer to
help the proof. The first one was the "4 colors Theorem" in 1976 that
used a computer to check 1936 identified configurations, too long to
check manually.
>
Each year, a few theorems use computers to be proved, either using
"proof assistants" that formalize and check the logic of hundreds of
pages of inductions, or, like in the case of the 4 colors Theorem,
check a finite number of remaining cases (possibly big) while the main
human proof says something like "for n>N, blablabla".
>
But although the mainstream media talk a lot about them, they are
totally marginal in the crowd of new theorems.
>
>

>
I'm just interested in math and science at an abstract level from a
historical perspective and how technology (AI in particular) has the
potential to transform education and the dissemination/accessibility of
knowledge and understanding.
>
https://www.quantamagazine.org/mathematical-beauty-truth-and-proof-in-the-age-of-ai-20250430/
>
>
>

I suppose there are big differences between "collective intelligence"
and 'individualized intelligence" and "collective communication" and
"individualized communication".
Who's going to have any idea what the Claude-Claude-Claude-Claude-Claude
theorem is? I have some ideas of theorems of Calude, not so much of collude.
(A Calude is a researcher in type theory, also a Calude is a researching
in Stirling numbers.)
"See theorem 64-bit hash lemma 32-bit hash, arithmetic coding scheme
time-of-day."
What about Mizar and Metamath and all sorts usual notions of knowledge
representation and knowledge inference formats?
Everyone in a school should get the same worksheets and same problems.
And cheat off, or lean on, their friends: not their phone.
I don't much go to Quanta Magazine. It's like "Simon says" and
it's like "I don't necessarily care nor observe what Simon says"
and it's like "Simon didn't say" and it's like "go to hell Simon".