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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
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.
Nothing clickbaity about the title. It says two pages without describing how much effort went into those two pages. Two pages does not imply it's easy. It implies it's elegant, which probably requires a fair amount of effort.
I would have written a shorter letter, but I did not have the time.
https://www.npr.org/sections/13.7/2014/02/03/270680304/this-...
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.
"Simple != easy." --Rich Hickey The closest I get in my career is striving for the simplest approach to building something in software, which is not all the easy path. The easy path always leads to complexity -- just look at any enterprise software project that's more than a year to two old. I find the process of striving for simplicity gratifying and reading this article about similar -- but much longer process -- p…
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".
Good to hear! I only made it partway through (up through the kernel trick I think) but I keep meaning to come back to finish it.
> torchsorflow
Lol
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
Knuth reduced it to half a page in the comments
https://www.reddit.com/r/math/comments/cl20l6/knuth_has_writ...
For the interested. Here is an online lecture from the author of the paper: https://www.youtube.com/watch?v=EJoe4qH6kLs
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.
Nothing clickbaity about the title. It says two pages without describing how much effort went into those two pages. Two pages does not imply it's easy. It implies it's elegant, which probably requires a fair amount of effort.
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.
Earlier quoted context omitted.
Nothing clickbaity about the title. It says two pages without describing how much effort went into those two pages. Two pages does not imply it's easy. It implies it's elegant, which probably requires a fair amount of effort.
It's been interesting to watch the rapid degradation of the term clickbait, we've quickly gone from the original targets of the term ("Local mother discovers one small trick", "He did X, you WON'T believe what happened next"), to it now being used in probably a third of HN's comment sections to describe any title which is even mildly editorialised and not a longwinded statement of plain facts.
Personally I feel that the mathematician should have used smaller font. Could have gotten it down to one page.
“ 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?
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.