
‘Outsiders’ who cracked the 50-Year-Old Kadison-Singer Problem - retupmoc01
https://www.quantamagazine.org/20151124-kadison-singer-math-problem/
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mathgenius
> The fact that he, Srivastava and Spielman were able to solve it “says
> something about what I hope will be the future of mathematics,” he said.
> When mathematicians import ideas across fields, “that’s when I think these
> really interesting jumps in knowledge happen.”

So much yes.

Academia is hyper-focused, over specializing everywhere. There is little
incentive to spending time making one's work understandable to a wider
audience. I would argue that this is actually dis-incentivised as the downside
to "making it look easy" is very bad indeed. But it's worse than this: the
typical academic seems to have little ability to even explain their work to
others within the same micro-field. Once again, the emphasis is on making it
look as complicated as possible, in the interests of securing prestige (and
funding).

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seventytwo
> There is little incentive to spending time making one's work understandable
> to a wider audience.

I wonder if there's a way to create incentive here? Or perhaps even a need to
fill for the academics who are poor at explaining their work? Maybe some kind
of layman's explanation service for technical papers with the authors' hope
that by better explaining their research, they might be able to gain a wider
audience or be more often referenced?

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noiseman
Computer scientists are hardly "outsiders" to math problems. The famous
computer scientists (Turing, Knuth, Dijkstra etc) were all mathematicians by
training.

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k2enemy
Absolutely nowhere in the article did it suggest that computer scientists are
outsiders to math problems.

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sp332
_Word spread quickly through the mathematics community that one of the
paramount problems in C_ * _-algebras and a host of other fields had been
solved by three outsiders — computer scientists who had barely a nodding
acquaintance with the disciplines at the heart of the problem._

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Ar-Curunir
Theoretical computer science _is_ mathematics

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seba_dos1
But it's _not_ "discipline at the heart of the problem".

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mherrmann
I think it's intriguing that they took an experimental approach to what is
originally a theoretical problem: Generate lots of examples with a computer
and see if you notice any patterns.

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AngrySkillzz
We do that all the time in mathematics though; generate some random examples
of the phenomena you're investigating to see if there are any "easy"
counterexamples. If not, try to visualize them and see if patterns emerge.
This is an easy way to build up intuition on a problem: seeing "how" something
behaves gives you clues about where to look when you go to prove it.

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Someone
Not only for the easy counterexamples, also to check whether the things you
are studying actually exist.

Once the stuff you think about is abstract enough, you may start thinking of
objects with properties P, Q, and R, showing all kinds of wonderful results
before somebody else shows that there are no objects having properties P, Q,
and R, or that there only are trivial ones.

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wrigby
Unrelated to the actual content, but am I the only one driven crazy by the way
that bridge rectifier is hooked up?

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amatus
Sometimes you need a diode and all you have in your parts bin is a bridge
rectifier with half the current capacity.

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bsder
“All of us were completely convinced it had a negative answer, so none of us
was actually trying to prove it”

The problem was preconceived bias, not ability to prove.

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IGetConfused
Can anyone link the research articles?

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OJFord
Could do with a "[2013]", just to be clear this is an editorial on the history
of the problem and solution, rather than "actual news" of a problem just
cracked.

(Very interesting regardless though)

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dang
We edited the title so it wouldn't imply that the solution itself was news.

