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Mathematician Solves Sensitivity Conjecture in Two Pages (2019)

quantamagazine.org

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Re: Mathematician Solves Sensitivity Conjecture in Two Pages (2019)

#31

Post by angry_octet »

wenc wrote: post #16

I remember this article from 2019. I remember the writing style struck me then as being a little strange. My first thought was "who's the mathematician"? But the article doesn't actually mention the author's name until a few paragraphs down, electing instead to put the spotlight on Scott Aaronson and other commentators. I felt then as I do now that it was a little lacking in respect.

I agree, it's extremely distasteful. I feel the author has cut their teeth writing clickbait headlines to make information extraction harder, the way a supermarket puts the milk at the far corner of the store. I want a link/cite to the original paper in the first para.

Re: Mathematician Solves Sensitivity Conjecture in Two Pages (2019)

#32

Post by alberto_ol »

anchpop wrote: post #23
scythmic_waves wrote: post #5

From Scott Aaronson's blog (linked in the article): > Another Update: In the comments section, my former student Shalev Ben-David points out a simplification [1] of Huang’s argument, which no longer uses Cauchy’s interlacing theorem. I thought there was no way this proof could possibly be made any simpler, and I was wrong! [1] https://www.scottaaronson.com/blog/?p=4229#comment-1813084

Kind of makes this seem funny in retrospect: > Aaronson and O’Donnell both called Huang’s paper the “book” proof of the sensitivity conjecture, referring to Paul Erdős’ notion of a celestial book in which God writes the perfect proof of every theorem. “I find it hard to imagine that even God knows how to prove the Sensitivity Conjecture in any simpler way than this,” Aaronson wrote.

A few comments below a guy called Don Knuth claims to have shortened the proof to one page https://www.scottaaronson.com/blog/?p=4229#comment-1815290

Re: Mathematician Solves Sensitivity Conjecture in Two Pages (2019)

#33

Post by sethc2 »

adamnemecek wrote: post #3

“ I find it hard to imagine that even God knows how to prove the Sensitivity Conjecture in any simpler way than this.” Why is there a tendency to invoke God in math?

I think it’s because God is often seen as the infinite, or uncreated, or all that can be known. The something that exists apart from any material existence.

Mathematical relationships and patterns have this quality.

Really what I wonder is why can’t we all just believe in god again?

Even if it was just to recognize the fact that there are things that exist in an immaterial way. That there are things that are good and true and beautiful whose goodness truth and beauty is not quantifiable or reduced to some set of atoms. We might disagree on what things are better physical manifestations of the immaterial things, but we don’t need to disagree on their existence.

Though I think it is because so many people have said “god is like this” and then posit some religious thing that affirms their often heinous actions, that people have chosen to say yeah I don’t believe in that.

But it seems sad that we can’t just talk about god in the sense of there are things bigger than ourself, even if we don’t know them because they are unknowable.

Even if we just acknowledged “God” as the first cause or the existence of things not material (like 2+2=4 is true even if there was no material thing to represent it), I feel like we could go a long way to finding that us humans, usually have more in common than we have not in common. That the things that divide us are actually smaller than the thing that unites us.

(I don’t see why your question was downvoted by the way)

Re: Mathematician Solves Sensitivity Conjecture in Two Pages (2019)

#34

Post by AlanYx »

adamnemecek wrote: post #28
erdevs wrote: post #11

Earlier quoted context omitted.

Mathematics often deal in abstractions, and "God" may be used as a linguistic abstraction for ideal or perfect knowledge. It's a shorthand in writing casually about the most elegant mathematical insights. Its use is also a tradition via Erdos with "The Book", which Aaronson and many mathematicians pay homage to.

I understand what it means, but I still don't like it.

If it's any consolation, Erdős himself said in one famous lecture that the "God" part is irrelevant: "You don't have to believe in God, but you should believe in The Book."

Re: Mathematician Solves Sensitivity Conjecture in Two Pages (2019)

#35

Post by TheRealPomax »

When of course, in reality rather than clickbaity titles, they only wrote up the final, concise proof using two pages _after_ thinking about, and working on, the problem for seven years, building on decades of specific research combined with seven years of learning new mathematics (new to Huang, not necessarily new to the world) that might offer ways into cracking this problem.

Re: Mathematician Solves Sensitivity Conjecture in Two Pages (2019)

#36

Post by [deleted] »

wenc wrote: post #16

I remember this article from 2019. I remember the writing style struck me then as being a little strange. My first thought was "who's the mathematician"? But the article doesn't actually mention the author's name until a few paragraphs down, electing instead to put the spotlight on Scott Aaronson and other commentators. I felt then as I do now that it was a little lacking in respect.

[deleted]

Re: Mathematician Solves Sensitivity Conjecture in Two Pages (2019)

#37

Post by uniqueid »

angry_octet wrote: post #31
wenc wrote: post #16

I remember this article from 2019. I remember the writing style struck me then as being a little strange. My first thought was "who's the mathematician"? But the article doesn't actually mention the author's name until a few paragraphs down, electing instead to put the spotlight on Scott Aaronson and other commentators. I felt then as I do now that it was a little lacking in respect.

I agree, it's extremely distasteful. I feel the author has cut their teeth writing clickbait headlines to make information extraction harder, the way a supermarket puts the milk at the far corner of the store. I want a link/cite to the original paper in the first para.

It reminds me of that interview a few years back 'Ms Bacall, what was it like working with a screen legend like Nicole Kidman?'

Re: Mathematician Solves Sensitivity Conjecture in Two Pages (2019)

#38

Post by GuB-42 »

adamnemecek wrote: post #3

“ I find it hard to imagine that even God knows how to prove the Sensitivity Conjecture in any simpler way than this.” Why is there a tendency to invoke God in math?

In most religions, God is an omnipotent, omniscient, and generally perfect being.

Mathematicians simply borrowed that definition. For example, Rubik's cube "God's number" is 20. Because, of course, God, as an omniscient, omnipotent perfect being will solve the puzzle in the minimum possible amount of moves. And that number is 20 in the most complex case.

Computer science have a similar, more formal concept with oracles. An oracle is a machine that can quickly solve a problem. How it does it is not the question, it can be supernatural, but we simply assume that such a machine exists in order to study some theoretical problems.

Re: Mathematician Solves Sensitivity Conjecture in Two Pages (2019)

#39

Post by _rerr »

scythmic_waves wrote: post #5

From Scott Aaronson's blog (linked in the article): > Another Update: In the comments section, my former student Shalev Ben-David points out a simplification [1] of Huang’s argument, which no longer uses Cauchy’s interlacing theorem. I thought there was no way this proof could possibly be made any simpler, and I was wrong! [1] https://www.scottaaronson.com/blog/?p=4229#comment-1813084

I really enjoyed Ben-David (and Shalev-Schwartz)'s book "Understanding machine learning". It's essentially about theory though, not "learn all about machine learning in torchsorflow in 10 days".

Re: Mathematician Solves Sensitivity Conjecture in Two Pages (2019)

#40

Post by jessriedel »

TheRealPomax wrote: post #35

When of course, in reality rather than clickbaity titles, they only wrote up the final, concise proof using two pages _after_ thinking about, and working on, the problem for seven years, building on decades of specific research combined with seven years of learning new mathematics (new to Huang, not necessarily new to the world) that might offer ways into cracking this problem.

I suppose the title could be slightly more accurate by replacing "solves" with "proves", but I think it's fine. The fact that proof is only 2 pages long is highly notable. This is not a case of a headline making a typical event look more notable than it is.
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