
A Retiree Discovers an Elusive Math Proof (2017) - ForFreedom
https://www.wired.com/2017/04/elusive-math-proof-found-almost-lost
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marcelluspye
>“He had formulas that enabled him to pull off his magic,” Pitt said. “And I
didn’t have the formulas.”

The more I do pure mathematics, the more I realize just how important these
kinds of insights are. Very often, solving a theoretical problem involves two
key ingredients:

1\. Rewriting your problem in a particular way, so that it is amenable to a
certain suite of methods/looks like known results.

2\. Apply a key bit of knowledge gleaned from intuition. This is unrelated to
the formal way the problem was written down.

Sometimes, showing your intuition is true formally actually takes a lot of
work. And for some proofs, looking at the problem a particular way makes the
solution obvious on its own, with no need for a step 2. And other times, like
this, all the technical tools in the world are no match for just _knowing_ the
right piece of information.

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tangentspace
I think many highly productive mathematicians are very good at organizing
formulas and facts in such a way that they can be retrieved easily from memory
based on context. Maybe something analogous to a hash function from computer
science.

Some mathematicians seem to index facts based on geometric images, others seem
to be more inclined to symbolic or algebraic statements. Whatever the
representation, when confronted with a new mathematical situation they then
scan quickly for matches to various aspects of the problem at hand.

Maybe to some degree my observation here is obvious. But I thought a lot about
it while I was in grad school studying a book called Geometric Measure Theory
by Herbert Federer. That book is enormous, and full of highly intricate
technical proofs that require pulling together a large number of detailed
technical facts.

The book is also very highly structured, and that led me to conclude that the
text likely mirrored how Federer organized this information in his head. It
reads like code for a complex but cleanly architected software system, and
that's a big part of what led me from math to software development.

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mlevental
are you under the impression the people write books like that without
referring to sources themselves? because they don't. I doubt any one knows all
the proofs in a book like by heart or could reconstruct them without
references for key facts.

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n4r9
People of that calibre are quite rare but they do exist. I've seen final year
undergraduate courses pulled off without the lecturer once having to refer to
notes. All proofs were completed in exacting detail on the whiteboard.

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electricslpnsld
Sure, but those math profs have probably taught the same course 20+ times.
Going through material that many times will permanently burn it into your
brain.

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tangentspace
Absolutely. And in mathematics, advanced structures and theorems are built up
layers by layer upon more elementary material. A professor who has mastered
presentation of undergraduate material on a topic also likely teaches a
graduate course on it, and mentors students on it, and does research on it.

They can talk about their chosen topic at many levels to many different
audiences, from general audience (who may provide funding to them), high
school students (outreach and recruiting), university students, and peers.
This flexibility is an important part of being a very successful
mathematician, and you have to burn it into your brain to reach that level of
fluency.

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BlackFingolfin
This is from 2017, previous discussion here:
[https://news.ycombinator.com/item?id=13977554](https://news.ycombinator.com/item?id=13977554)

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harshreality
It would be nice if the title named the proof. Math is a giant field, and very
few HNers are mathematicians or interested in any particular area of
mathematics, so it would be helpful to know what the general topic is without
clicking on the link and reading a few paragraphs.

"A Retiree Discovers an Elusive Math Proof of the Gaussian Correlation
Inequality (2017)"

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jlarocco
I'm sorry to be mean, but this title is stupid and condescending. He didn't
use Word to solve the problem, he used Word to write the paper about the
solution. It really has nothing to do with how the problem was actually
solved. Might as well claim he "used Windows" to solve the problem.

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jwilk
For context, the submission title was "This 67-year-old retiree solved a math
problem–using Microsoft Word". Thankfully, it's been fixed.

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bbeonx
Ahh, thank you. I was very confused

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vladislav
It seems like a stretch to call this a big discovery in the math world. Even
if it had been published in a top journal etc, it would be unlikely to be
heralded as a major achievement.

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tangentspace
Is it being characterized as a major discovery somewhere in this article? I
see it described as an elusive problem, and it's claimed that the solution is
a major paper worthy of publication in Annals of Statistics, but mostly it
just comes across as an interesting story about how this proof came to be.

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jchw
(regarding the current title of this submission, in case it gets changed:)

>This 67-year-old retiree solved a math problem–using Microsoft Word

What does Microsoft Word have to do with this? The fact that the document was
typeset in Microsoft Word instead of LaTeX does not really sound remarkable.

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ars
> What does Microsoft Word have to do with this?

It's an indication that the person who solved it is an amateur, that's all.

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mnl
No, he's not an amateur but a retired statistian. And the fact that LaTeX is
the standard for DIY typesetting in academia nowadays has nothing to do with
your competence as a mathematician, or the rigour of a proof published as a
Word document. Likewise, it doesn't matter if you work with pen and paper or
with pencil and paper.

This title is absurd.

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ryanjmo
Well it got me to click on it. Which in the end I’m pretty happy about; it was
a very interesting article. Can clickbait be justifiable if the end product is
good?

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mnl
You're opening a can of worms there.

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stealthmodeclan
This is based on experience, i used to teach math. (~4000)

And i found it easier to teach math to people whoes father, grandfather, great
grandfather all had masters in math.

So, i wonder if mathematical abilities are in genes and gene function changes
when you bring a person with such genes into a math intense environment.

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Ultimatt
Not sure why you would even remotely assume genetics over just skills being
passed down..? Pre war if you look at careers in census everyone used to do
what their parents did. Its because its what they taught you!

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stealthmodeclan
> Not sure why you would even remotely assume genetics over just skills being
> passed down..?

There were also orphans who had never seen their parents or grandparents.

When genes are responsible for being lactose tolerate, why is it hard to
hypothesise that only some people benefit from being raised in a math intense
environment and not others?

