
A math problem stumped experts for 50 years. This grad student solved it in days - tysone
https://www.bostonglobe.com/2020/08/20/magazine/math-problem-stumped-experts-50-years-this-grad-student-maine-solved-it-days/
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merricksb
Discussed 3 months ago:

[https://news.ycombinator.com/item?id=23236599](https://news.ycombinator.com/item?id=23236599)

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eganist
They buried the _how_ extremely deep in the article. Fished it out for y'all.

> The day after hearing about the Conway knot problem, Piccirillo, then 27,
> sat down at her desk and began looking for a solution. Because much of her
> graduate work involved building pairs of knots that were different but
> shared some 4-D properties, she already knew that any two knots that share
> the same 4-D space also share sliceness — they’re either both slice or both
> not slice. Since her goal was to prove that the Conway knot wasn’t slice,
> her first step was come up with an entirely different knot with the same
> four-dimensional space, she explains. “Then I’ll try to show that the other
> knot isn’t slice.”

> She spent spare time over the next several days hand-sketching and
> manipulating configurations of the 4-D space occupied by the Conway knot. “I
> didn’t allow myself to work on it during the day,” she told Quanta Magazine
> earlier this year, “because I didn’t consider it to be real math. I thought
> it was, like, my homework.”

> The next step was to try to prove that the knot she drew was not slice.
> “There are lots of tools already in the literature for doing that,” she
> says. She would feed the knot iterations into a computer, “and based on the
> data of the knot, maybe based on how its crossings look or other data that
> you can pull from the knot, the algorithm spits out an integer.” In less
> than a week, Piccirillo had created a knot that hit the sweet spot: It had
> the same 4-D properties as the Conway knot, and it was found by the
> algorithm to be not slice.

> She had suddenly succeeded where countless mathematicians had failed for
> five decades. She had solved the Conway knot problem.

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the_solenoid
"The principle of generating small amounts of finite improbability by simply
hooking the logic circuits of a Bambleweeny 57 Sub-Meson Brain to an atomic
vector plotter suspended in a strong Brownian Motion producer (say a nice hot
cup of tea) were well understood. It is said, by the Guide, that such
generators were often used to break the ice at parties by making all the
molecules in the hostess's undergarments leap simultaneously one foot to the
left, in accordance with the theory of indeterminacy.

Many respectable physicists said that they weren't going to stand for this,
partly because it was a debasement of science, but mostly because they didn't
get invited to those sorts of parties.

The physicists encountered repeated failures while trying to construct a
machine which could generate the infinite improbability field needed to flip a
spaceship across the mind-paralyzing distances between the farthest stars.
They eventually announced that such a machine was virtually impossible.

Then, one day, a student who had been left to sweep up after a particularly
unsuccessful party found himself reasoning in this way: If he thought to
himself, such a machine is a virtual impossibility, it must have finite
improbability. So all I have to do in order to make one is to work out how
exactly improbable it is, feed that figure into the finite improbability
generator, give it a fresh cup of really hot tea... and turn it on!

He did this and managed to create the long sought after golden Infinite
Improbability generator out of thin air. Unfortunately, after he was awarded
the Galactic Institute's Prize for Extreme Cleverness he was lynched by a
rampaging mob of respectable physicists who couldn't stand him being "a smart
arse."

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NonEUCitizen
Boston Globe article was behind paywall for me, but was able to access these
other articles:

[https://www.quantamagazine.org/graduate-student-solves-
decad...](https://www.quantamagazine.org/graduate-student-solves-decades-old-
conway-knot-problem-20200519/)

[https://www.smithsonianmag.com/smart-news/graduate-
student-u...](https://www.smithsonianmag.com/smart-news/graduate-student-
untangles-decades-old-math-problem-180974978/)

