‘Outsiders’ who cracked the 50-Year-Old Kadison-Singer Problem | Hacker News Reader

‘Outsiders’ who cracked the 50-Year-Old Kadison-Singer Problem

quantamagazine.org

108 pointsretupmoc0122 comments

> 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).

When will there be more info about YC Research??

The article headline is incorrect. Theoretical Computer Scientists are mathematicians as well...

> 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?

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

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

The title, and the biography of those that cracked it, does.

But I don't think it's false. The point is that this hyper-specialised; hyper-abstract field of mathematics, which nobody outside of had a grip on, rather suddenly came to be shown equivalent to many problems in many fields.

One such field & problem was (still mathematics, if you like, and) accessible to these computer scientists.

I particularly enjoyed:

    > “It seemed so natural, so central to the kinds of things 
    > I think about,” he said. “I thought, ‘I’ve got to be
    > able to prove that.’” He guessed that the problem might
    > take him a few weeks.
    > 
    > Instead, it took him five years.

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.

Theoretical computer science is mathematics

But it's not "discipline at the heart of the problem".

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.

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.

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.

Some of the first code I ever wrote outside of a classroom was in Mathematica to generate examples that would later fuel the results in a set of two papers (in pure mathematics).

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

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

Pftt. The guy measuring the capacitor has got his leads the wrong way round.

“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.

Can anyone link the research articles?

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)

The article's dated "November 24, 2015" tho.

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

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