Owen and other mathies -
Japanese mathematician Shinichi Mochizuki, the Yoda of math and the
ABC Conjecture proof: Won't explain will I!
http://projectwordsworth.com/the-paradox-of-the-proof/
Just for math folks, others please delete.
And also "only for MathHoles" who like this particular brand of Silly Talk:
Rather than try to scale "Inter-universal Teichmuller Theory I:
Construction of Hodge Theaters" in a full frontal assault, I decided to
try to flank it (or at least start acclimatizing to the elevation) by
reading Grigori Perleman's proof of the Poincare Conjecture. Before
even starting on it I was blown away that Perleman has declined the EMS
prize (1996), the Fields Medal (2006) and the Millenium Prize 2010
($US1M for his solution to the Poincare Conjecture)! He has held a
very high standard for ethics and has withdrawn from (professional?)
mathematics as a consequence of public behaviour of other mathematicians
who he feels are being dishonest and starting with the light shed on him
by the Fields (declined) medal, he claims he cannot remain in the
milieu. He is reported to being unemployed and living with his
mother. His mother dropped out of Grad School in Mathematics to raise
him, maybe they sit in the kitchen after dinner scribbling equations on
the refrigerator with recycled white-board markers (add a few drops of
vodka to the tips to get their juices flowing again).
From Wikipedia:
Originally conjectured by Henri Poincaré
<https://en.wikipedia.org/wiki/Henri_Poincar%C3%A9>, the theorem
concerns a space that locally looks like ordinary three-dimensional
space but is connected, finite in size, and lacks any boundary (a
closed <https://en.wikipedia.org/wiki/Closed_manifold> 3-manifold
<https://en.wikipedia.org/wiki/3-manifold>). The Poincaré conjecture
claims that if such a space has the additional property that each
loop <https://en.wikipedia.org/wiki/Path_%28topology%29> in the
space can be continuously tightened to a point, then it is
necessarily a three-dimensional sphere.
This whole business is rather subtle to my palate, but there are several
interesting things I encountered on my way to trying to shovel this
down. Hardly seems worth $US1M! First, it is quite interesting that
Perleman used (inspired by earlier work done by Richard Hamilton)
something called Ricci flow which appears to be somewhat like a
flood-fill or diffusion process modulated by the curvature of the
manifold, the way the descriptions read, it feels as if the discoverer
(Hamilton) of this was inspired *by* the idea of heat diffusion. This
seems like a good example of art (mathematics) imitating life
(physics). I wonder if this type of physicsOmorphising of mathematics
detracts from the elegance of the proof? It seems it might.
Wading through Ricci tensors was entertaining. While relativity was
the most interesting of the physics I studied a lifetime ago, it is the
one area I've really never stumbled into an application for, beyond
"metaphorical" ones, in particular for the properties of reimannian
geometry.
Anybody else wade into any of this yet?
- Steve
And now for some Silly Talk (rhyme's with the Monty Python Players
Silly Walk?):
I think this story relates well to the discussion earlier about
"Outsider Science" and the communal/consensual nature of Science.
While this is technically Mathematics, "merely" a branch of Philosophy
and/or a "tool" for doing Science, most if not all of the same
principles apply to this story since what is happening is that someone
(with credibility in the community) has laid down a challenge to his
peers in the form of a "proof" of a conjecture that would be a a
theorem. The fact that he is unwilling or unable (?) to engage with
others significantly to explain or defend his proof and that *others*
are unwilling to do the hard work to slog through it creates an
interesting conundrum.
As a matter of practicality, I understand how many would be unwilling,
and why some would claim that if "nobody bothers" then the "proof is
not a proof at all". On the other hand, if he has done his work and
the proof is there, despite requiring a long and arduous engagement
with (apparently) a lot of intermediate work he has done, then some
day it *will* be verified by another and will have been a "proof" all
along, even if it wasn't shared by a community larger than himself.
I believe it is proper to say that Fermat's Last Theorem (which
relates to the ABC conjecture at hand) was a Theorem all along, but
only once a proof was found (and shared and validated) could we
actually make that claim... until then it was a Conjecture which may
or may not have a known (only to now-dead Fermat?) proof...
I'm not really that plugged into the academic world, but I can't
imagine there isn't some young prodigy right now lining up to get HER
PhD by mining Mochizuki's work and not only verifying his work, but
also finding some other gems in the work he did to get there which
would provide the basis for some original research (harder and harder
to find these days?).
It also seems that there are enough practical uses for this type of
abstract math (generally in the domain of cryptography?) to attract
people to sorting through all this for possible financial gains?
I *LOVED* the mathematical circumlutory style of his opening statement
in his first paper:
"Inter-universal Teichmuller Theory I: Construction of Hodge Theaters,"
starts out by stating that the goal is "to establish an arithmetic
version of Teichmuller theory for number fields equipped with an
elliptic curve... by applying the theory of semi-graphs of anabelioids,
Frobenioids, the etale theta function, and log-shells."
It might be the case that some folks here (I'm thinking Frank Wimberly
in particular) already might know what a Frobenius Monoid would be
and how they might differ from an anabeloid] (Anabelle's Monoid?).
With a BS (stale 35 years) in Math and a lot of
lay/professional-interest over decades, I admit to still feeling lame
while trying to tread water in Mochikizu's puddle. I had the great
good fun of mucking around in Fiber/Vector Bundles 15 years ago which
suggests I might be able to continue on and figure out Frobenoids and
such, but seems likely not, which sounds like hardly even a start
toward understanding his proof.
I didn't follow your suggestion to delete, nor my good judgement to
not try to drill down into Teichmuller theory, Frobenoids, and etale
theta funcitons so I suppose I got what I deserved!
Quaquaversally yours,
- Steve
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Meets Fridays 9a-11:30 at cafe at St. John's College
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