
Math Invariants Helped Lisa Piccirillo Solve Conway Knot Problem - rbanffy
https://www.quantamagazine.org/math-invariants-helped-lisa-piccirillo-solve-conway-knot-problem-20200602/
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analog31
I don't know if it's precisely the same thing, but invariants in the form of
conservation laws are quite handy in physics too. They let you take problems
with complicated details and turn them into accounting problems. One of my
favorites is the optical invariant, which relates the area and divergence of a
light beam. It provides a way to work through problems very quickly, say,
during a meeting or when considering design options.

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bonzini
Invariants are always useful! They were a major software engineering
innovation in the 80s with languages such as Eiffel, and Lamport for example
suggests teaching concurrency in terms of invariants (for example, conditions
that must be respected at the end of all mutual exclusive sections).

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yesenadam
Might be better to link to this, which gives a lot more context and explains
how she did it & shows the knot she created to solve the problem.

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

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coolgeek
That was linked 19 days ago, 479 points

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

This is new/different

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frandroid
"Lisa Piccirillo used math invariants to solve Conway Knot problem"

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shoo
( this reminded me of the sadly topical
[https://www.mcsweeneys.net/articles/an-interactive-guide-
to-...](https://www.mcsweeneys.net/articles/an-interactive-guide-to-ambiguous-
grammar) )

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auggierose
Interesting introductory talk from her about topology:
[https://vimeo.com/66928168](https://vimeo.com/66928168)

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lurkmurk
Can anyone share how big a deal is this proof? I remember seeing one post
already about it on quanta.

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boothby
I'm not sure about the severity of its impact, but I toyed with the problem
when I was learning knot theory. It's a spot where probably hundreds of
mathematicians have tried to itch. Advances have been made in attempts to
solve it, but didn't quite do the job. Piccirillo's approach is really quite
beautiful, and... sorry, this is where mathematics gets weird: the statement
of the theorem is what lay-people consume; the method of proof (not even the
actual proof, but the ludicrously high-level abstract algorithm that the proof
is a concrete instance of) is what mathematicians consume. In that regard,
this seems quite buzzworthy.

But if you're a fan of mathematics but still consider yourself a lay person:
this stumped John Conway!

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fhssn1
> ... this stumped John Conway!

Do you have a source for this? Thanks

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solveit
I don't know about a source, but Conway had been compiling knot tables since
high school, and as a knot with only 11 crossings, the Conway knot is certain
to have been on his radar. It's just such a simple knot, and sliceness such a
fundamental property that Conway is sure to have tried to figure it out.

