‘Outsiders’ Crack 50-Year-Old Math Problem (2015)
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‘Outsiders’ Crack 50-Year-Old Math Problem (2015)
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Re: ‘Outsiders’ Crack 50-Year-Old Math Problem (2015)
#2"He guessed that the problem might take him a few weeks. Instead, it took him five years"
Perhaps the key to their success was typically programming work estimations ;)
More seriously, I think that if you think something is easy for you, or that you are almost there, you may be more willing to put in the necessary time, than if you knew it would take 5 years from the outset.
"Spielman realized that he himself might be in the perfect position to solve it. “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.’”"
Re: ‘Outsiders’ Crack 50-Year-Old Math Problem (2015)
#3Quick note that the article is from 2015, and the MSS result dates back to 2013.
There's a blog post by Nikhil here that explains the proof of the discrepancy result that implies Kadison-Singer: https://windowsontheory.org/2013/07/11/discrepancy-graphs-an...
The main result is a theorem that replaces a Chernoff bound (saying here that a random partition has discrepancy logarithmic in the number of vectors with high probability) with a bound that says achieves a better bound on the discrepancy, independent of the number of vectors, at the cost of replacing the "with high probability" with "there exists".
The proof uses some really beautiful techniques from the geometry of polynomial roots to prove this and is a pretty fun read: https://arxiv.org/abs/1306.3969
Re: ‘Outsiders’ Crack 50-Year-Old Math Problem (2015)
#4Great story that reminds me of something I've had. There's just so much knowledge out there - and growing - that researchers have to be increasingly specialized. Isn't it inevitable that 4 years of undergrad + 1-2 yrs of grad school classes won't prepare you sufficiently to do novel research? Imagine when people have to be in school for something like 10 years before they know enough to do "real" work! And people will necessarily have to become more and more specialized, making situations like the one in the article even rarer.
Just a thought.
Re: ‘Outsiders’ Crack 50-Year-Old Math Problem (2015)
#5Great story that reminds me of something I've had. There's just so much knowledge out there - and growing - that researchers have to be increasingly specialized. Isn't it inevitable that 4 years of undergrad + 1-2 yrs of grad school classes won't prepare you sufficiently to do novel research? Imagine when people have to be in school for something like 10 years before they know enough to do "real" work! And people wil…
I have also wondered about that. It seems to me that as we better understand an area we are able to develop more powerful abstractions that allow people to reach the limits of current knowledge faster.
Re: ‘Outsiders’ Crack 50-Year-Old Math Problem (2015)
#6Great story that reminds me of something I've had. There's just so much knowledge out there - and growing - that researchers have to be increasingly specialized. Isn't it inevitable that 4 years of undergrad + 1-2 yrs of grad school classes won't prepare you sufficiently to do novel research? Imagine when people have to be in school for something like 10 years before they know enough to do "real" work! And people wil…
This is a real phenomenon by the name of credential creep:
https://en.wikipedia.org/wiki/Credentialism_and_educational_...
Re: ‘Outsiders’ Crack 50-Year-Old Math Problem (2015)
#7Great story that reminds me of something I've had. There's just so much knowledge out there - and growing - that researchers have to be increasingly specialized. Isn't it inevitable that 4 years of undergrad + 1-2 yrs of grad school classes won't prepare you sufficiently to do novel research? Imagine when people have to be in school for something like 10 years before they know enough to do "real" work! And people wil…
I think, like many things, this varies a lot by field. In computer science, which is still comparatively "new", it is not that uncommon (at top 5 schools, it may even be common) for grad students to publish real research in good venues in their first or second year of grad school (what is nominally coursework time). Even in areas like theory where you're not really hacking away at experiments or building stuff.
Contrast this with say pure math, where (I believe) most students even at the strongest schools do not publish or even produce publishable research in their first few years.
Re: ‘Outsiders’ Crack 50-Year-Old Math Problem (2015)
#8Great story that reminds me of something I've had. There's just so much knowledge out there - and growing - that researchers have to be increasingly specialized. Isn't it inevitable that 4 years of undergrad + 1-2 yrs of grad school classes won't prepare you sufficiently to do novel research? Imagine when people have to be in school for something like 10 years before they know enough to do "real" work! And people wil…
This is a real phenomenon by the name of credential creep: https://en.wikipedia.org/wiki/Credentialism_and_educational_...
It has very little to do with credential creep. The problem is that, in order to do work at the frontier of a field, you first have to get to the frontier - you have to learn what's going on there, which means that you have to learn all the stuff you have to learn in order to actually understand what's going on there. The learning to actually understand enough to get to the frontier is taking longer and longer. That's not credential creep, that's creep in how far away the frontier is from the foundations.
Re: ‘Outsiders’ Crack 50-Year-Old Math Problem (2015)
#9Great story that reminds me of something I've had. There's just so much knowledge out there - and growing - that researchers have to be increasingly specialized. Isn't it inevitable that 4 years of undergrad + 1-2 yrs of grad school classes won't prepare you sufficiently to do novel research? Imagine when people have to be in school for something like 10 years before they know enough to do "real" work! And people wil…
This is a real phenomenon by the name of credential creep: https://en.wikipedia.org/wiki/Credentialism_and_educational_...
This is the opposite of credential creep ... the mathematicians with the credentials were really open minded and excited that someone from the "outside" had a solution! They didn't give a rip about the math pedigree.
Re: ‘Outsiders’ Crack 50-Year-Old Math Problem (2015)
#10"He guessed that the problem might take him a few weeks. Instead, it took him five years" Perhaps the key to their success was typically programming work estimations ;) More seriously, I think that if you think something is easy for you, or that you are almost there, you may be more willing to put in the necessary time, than if you knew it would take 5 years from the outset. "Spielman realized that he himself might b…
Related but different advice: build the habit of learning things by trying to figure it out yourself. Richard Feynman did this when learning quantum mechanics, and invented the Feynman diagram as a result. While not a different model or theory per se, the diagram made apparent the connection to functional integrals and a different method for solving that made previously intractable problems (relatively) simple.
Funny story is he “invented” this technique in his school days and only found out that it wasn’t standard during he Manhattan project when a colleague complained a problem was t tractable and Feynman went to the black board to illustrate the “obvious” solution.
Sometimes optimal solutions aren’t found because nobody bothered to look, assuming if they think about it at all that any remaining work must be more complex than the already known suboptimal solution.