Re: Ask Marilyn , the female WM?

On 10/02/2024 08:10 AM, Mild Shock wrote:

I admit an interesting person.
I wonder what happened here:
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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.
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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",
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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
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Ross Finlayson schrieb:

On 10/01/2024 03:29 PM, Mild Shock wrote:

Holy shit, what would Cantor say?
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Q: Dear Marilyn:
Which is the biggest, an infinite line,
an infinite circle, or an infinite plane?
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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.
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https://archive.org/details/paradesaskmarily00mari/page/184/mode/2up

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There's Katz' OUTPACING,
I imagine Cantor wouldn't say
much as he's been six feet deep
about a hundred years.
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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.
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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".
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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".
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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.
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Anyways that's stupid probably and that's merely bait.
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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.