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From: Mild Shock <janburse@fastmail.fm>
Newsgroups: sci.math
Subject: Re: Ask Marilyn , the female WM?
Date: Wed, 2 Oct 2024 20:19:12 +0200
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WM the male Marilyn, neiter WM nor Marilyn
have any substance. At least ChatGPT disagrees:

- Elliptic curves are not "hyperbolic," and
Wiles’ proof does not make improper use of
hyperbolic geometry. If vos Savant mentioned
hyperbolic geometry in her critique, it
likely reflects a misunderstanding of the
mathematical concepts involved.

- The Grothendieck axiom in question (e.g.,
Grothendieck universes) is a large cardinal-like
assumption, but Wiles' proof did not require
such axioms for its validity.

Who is right?

See also:
https://chatgpt.com/share/66fd8d7c-3c4c-8013-8afe-b5bfdff7b8ee

Ross Finlayson schrieb:
> On 10/02/2024 08:10 AM, Mild Shock wrote:
>> I admit an interesting person.
>> I wonder what happened here:
>>
>> A few months after Andrew Wiles said he had proved Fermat's Last
>> Theorem, Savant published the book The World's Most Famous Math Problem
>> (October 1993),[27] which surveys the history of Fermat's Last Theorem
>> as well as other mathematical problems.
>>
>> Especially contested was Savant's statement that Wiles' proof should be
>> rejected for its use of non-Euclidean geometry. Savant stated that
>> because "the chain of proof is based in hyperbolic (Lobachevskian)
>> geometry",
>>
>> and because squaring the circle is seen as a "famous impossibility"
>> despite being possible in hyperbolic geometry, then "if we reject a
>> hyperbolic method of squaring the circle, we should also reject a
>> hyperbolic proof of Fermat's last theorem."
>> https://en.wikipedia.org/wiki/Marilyn_vos_Savant#Fermat's_Last_Theorem
>>
>> Ross Finlayson schrieb:
>>> On 10/01/2024 03:29 PM, Mild Shock wrote:
>>>> Holy shit, what would Cantor say?
>>>>
>>>> Q: Dear Marilyn:
>>>> Which is the biggest, an infinite line,
>>>> an infinite circle, or an infinite plane?
>>>>
>>>> A: Dear Reader:
>>>> I'd say an infinite plane. When comparing
>>>> only a line and a circle, no matter how
>>>> large they grow, the circle would have the
>>>> greater number of points. (For example, a
>>>> one-mile-wide circular line "straightened
>>>> out" would be over three miles long.) If
>>>> the circle were "filled in" as well, it
>>>> would have an even greater number of points
>>>> an its surface. An unbounded plane surface,
>>>> however, would have even more because it
>>>> could be said to consist of an infinite
>>>> number of infinite lines, laid side by side.
>>>> However bad it would be to mow along an
>>>> infinite sidewalk, it would be worse to
>>>> mow the entire lawn it bordered.
>>>>
>>>> https://archive.org/details/paradesaskmarily00mari/page/184/mode/2up
>>>
>>> There's Katz' OUTPACING,
>>> I imagine Cantor wouldn't say
>>> much as he's been six feet deep
>>> about a hundred years.
>>>
>>>
>>> Then when that columnist "greatest IQ
>>> in the world" gets into either of the
>>> "material implication" or "Monty Haul",
>>> now either of those are _wrong_, and
>>> here it looks to be an intentional aggravation,
>>> anyways that's not funny on sci.math
>>> and many might wonder whether it's just plain fake.
>>>
>>>
>>> Anyways Katz' OUTPACING simply enough makes for
>>> a size relation that's "proper superset is bigger",
>>> then with some naive "points" comprising the things,
>>> all only one set of them, in "the space".
>>>
>>> Mostly though you'd get "I was in either New Math I or
>>> New Math II and my thusly modern mathematics has that
>>> according to cardinals, those all have the same cardinal
>>> as point-sets, while for example in size relations of
>>> how they relate inversely matters of perspective and
>>> projective, I can definitely see how a simple sort of
>>> logical geometry can result that what relations exist,
>>> in cardinality, according to functional relations,
>>> make for furthermore simple size relations based on
>>> 'logical geometry' and cardinality, so that the fact
>>> that I was taught transfinite cardinals before I ever
>>> learned calculus, isn't so embarrassing when it's
>>> got no applicability".
>>>
>>>
>>> Anyways you can just futz a 'logical geometry' where
>>> some matters of relations of those as then invariant
>>> makes a simple hierarchy of those that happen to relate
>>> as whatever's a transitive inequality in infinite sets,
>>> transfinite cardinality.
>>>
>>>
>>> Anyways that's stupid probably and that's merely bait.
>>>
>>>
>>
> 
> 
> There are many open conjectures in standard number theory
> that will always be so, because, a) they're independent
> standard number theory, b) there's no standard model of
> integers, c) there are variously fragments and extensions
> where they are/aren't so.
> 
> The Wiles Shaniyama/Timura up out of Bourbaki Groethendieck
> about elliptic curves, some have as one of these examples,
> to give elliptic curve cryptography a veneer of validity,
> when it's not so.
> 
> 
> Anyways if you add an Archimedean spiral to edge and compass,
> then circle-squaring is classical with the third tool.
> 
> 
> 
> So, many proposed theorems of what are open conjectures in
> number theory, like Fermat, Goldbach, Szmeredi, and so on,
> are foolish and only reflect unstated assumptions.
> 
> 
>