Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

A Retiree Discovers an Elusive Math Proof (2017)

wired.com

Post reply on HN
Print view View original

31–40 of 47 posts

Re: A Retiree Discovers an Elusive Math Proof (2017)

#31

Post by tangentspace »

spiderPig wrote: post #29
loeber wrote: post #24

Earlier quoted context omitted.

A similar realization is that most algorithms/data structures problems posed in software engineering interviews are all about imposing the right mathematical formalisms. If you correctly infer the _structure_ of the problem, then you're going to have an easy time solving it. If not, you'll use a great lot of time hunting for a fruitful angle of attack.

Oh please let’s not glorify those simple trick questions to be anywhere near as hard or require the degree of intuition that OP or theoretical mathematicians work on. 75% of interview questions can be solved with some form of BFS/DFS and they’re largely a hazing ritual these days. I’m saying this as someone who recently got offers from 4 of the big 5 companies

I've worked through various exams and research problems leading to a math PhD, and I see the similarity. I fail to see how someone articulating an observation about that "glorifies" the interview questions.

I've heard students complain that graduate qualifying exams are a form of hazing for people hoping to become pure mathematicians, and although I don't entirely agree with that sentiment, they do play a similar role in weeding out people based on preparation rather than ability to generate deep, novel insights.

Re: A Retiree Discovers an Elusive Math Proof (2017)

#32

Post by tangentspace »

vladislav wrote: post #26

It seems like a stretch to call this a big discovery in the math world. Even if it had been published in a top journal etc, it would be unlikely to be heralded as a major achievement.

Is it being characterized as a major discovery somewhere in this article? I see it described as an elusive problem, and it's claimed that the solution is a major paper worthy of publication in Annals of Statistics, but mostly it just comes across as an interesting story about how this proof came to be.

Re: A Retiree Discovers an Elusive Math Proof (2017)

#33

Post by tangentspace »

marcelluspye wrote: post #9

>“He had formulas that enabled him to pull off his magic,” Pitt said. “And I didn’t have the formulas.” The more I do pure mathematics, the more I realize just how important these kinds of insights are. Very often, solving a theoretical problem involves two key ingredients: 1. Rewriting your problem in a particular way, so that it is amenable to a certain suite of methods/looks like known results. 2. Apply a key bit…

I think many highly productive mathematicians are very good at organizing formulas and facts in such a way that they can be retrieved easily from memory based on context. Maybe something analogous to a hash function from computer science.

Some mathematicians seem to index facts based on geometric images, others seem to be more inclined to symbolic or algebraic statements. Whatever the representation, when confronted with a new mathematical situation they then scan quickly for matches to various aspects of the problem at hand.

Maybe to some degree my observation here is obvious. But I thought a lot about it while I was in grad school studying a book called Geometric Measure Theory by Herbert Federer. That book is enormous, and full of highly intricate technical proofs that require pulling together a large number of detailed technical facts.

The book is also very highly structured, and that led me to conclude that the text likely mirrored how Federer organized this information in his head. It reads like code for a complex but cleanly architected software system, and that's a big part of what led me from math to software development.

Re: A Retiree Discovers an Elusive Math Proof (2017)

#34

Post by mlevental »

tangentspace wrote: post #33
marcelluspye wrote: post #9

>“He had formulas that enabled him to pull off his magic,” Pitt said. “And I didn’t have the formulas.” The more I do pure mathematics, the more I realize just how important these kinds of insights are. Very often, solving a theoretical problem involves two key ingredients: 1. Rewriting your problem in a particular way, so that it is amenable to a certain suite of methods/looks like known results. 2. Apply a key bit…

I think many highly productive mathematicians are very good at organizing formulas and facts in such a way that they can be retrieved easily from memory based on context. Maybe something analogous to a hash function from computer science. Some mathematicians seem to index facts based on geometric images, others seem to be more inclined to symbolic or algebraic statements. Whatever the representation, when confronted…

are you under the impression the people write books like that without referring to sources themselves? because they don't. I doubt any one knows all the proofs in a book like by heart or could reconstruct them without references for key facts.

Re: A Retiree Discovers an Elusive Math Proof (2017)

#35

Post by n4r9 »

mlevental wrote: post #34
tangentspace wrote: post #33

Earlier quoted context omitted.

I think many highly productive mathematicians are very good at organizing formulas and facts in such a way that they can be retrieved easily from memory based on context. Maybe something analogous to a hash function from computer science. Some mathematicians seem to index facts based on geometric images, others seem to be more inclined to symbolic or algebraic statements. Whatever the representation, when confronted…

are you under the impression the people write books like that without referring to sources themselves? because they don't. I doubt any one knows all the proofs in a book like by heart or could reconstruct them without references for key facts.

People of that calibre are quite rare but they do exist. I've seen final year undergraduate courses pulled off without the lecturer once having to refer to notes. All proofs were completed in exacting detail on the whiteboard.

Re: A Retiree Discovers an Elusive Math Proof (2017)

#36

Post by stealthmodeclan »

This is based on experience, i used to teach math. (~4000)

And i found it easier to teach math to people whoes father, grandfather, great grandfather all had masters in math.

So, i wonder if mathematical abilities are in genes and gene function changes when you bring a person with such genes into a math intense environment.

Re: A Retiree Discovers an Elusive Math Proof (2017)

#37

Post by full_pint »

stealthmodeclan wrote: post #36

This is based on experience, i used to teach math. (~4000) And i found it easier to teach math to people whoes father, grandfather, great grandfather all had masters in math. So, i wonder if mathematical abilities are in genes and gene function changes when you bring a person with such genes into a math intense environment.

Could it just possibly be the fact they've been raised in environment that encourages the thought processes necessary to understand more "abstract" math?

Phrased differently, they've been given somewhat "institutional" tools necessary to accomplish these types of goals?

Re: A Retiree Discovers an Elusive Math Proof (2017)

#38

Post by bbeonx »

jwilk wrote: post #23
jlarocco wrote: post #17

I'm sorry to be mean, but this title is stupid and condescending. He didn't use Word to solve the problem, he used Word to write the paper about the solution. It really has nothing to do with how the problem was actually solved. Might as well claim he "used Windows" to solve the problem.

For context, the submission title was "This 67-year-old retiree solved a math problem–using Microsoft Word". Thankfully, it's been fixed.

Ahh, thank you. I was very confused

Re: A Retiree Discovers an Elusive Math Proof (2017)

#39

Post by electricslpnsld »

n4r9 wrote: post #35
mlevental wrote: post #34

Earlier quoted context omitted.

are you under the impression the people write books like that without referring to sources themselves? because they don't. I doubt any one knows all the proofs in a book like by heart or could reconstruct them without references for key facts.

People of that calibre are quite rare but they do exist. I've seen final year undergraduate courses pulled off without the lecturer once having to refer to notes. All proofs were completed in exacting detail on the whiteboard.

Sure, but those math profs have probably taught the same course 20+ times. Going through material that many times will permanently burn it into your brain.

Re: A Retiree Discovers an Elusive Math Proof (2017)

#40

Post by tangentspace »

mlevental wrote: post #34
tangentspace wrote: post #33

Earlier quoted context omitted.

I think many highly productive mathematicians are very good at organizing formulas and facts in such a way that they can be retrieved easily from memory based on context. Maybe something analogous to a hash function from computer science. Some mathematicians seem to index facts based on geometric images, others seem to be more inclined to symbolic or algebraic statements. Whatever the representation, when confronted…

are you under the impression the people write books like that without referring to sources themselves? because they don't. I doubt any one knows all the proofs in a book like by heart or could reconstruct them without references for key facts.

No, I was never under that impression. I once had a discussion about the creation of the book with one of Federer's students who had also helped proofread it. The book was essentially an outgrowth of his personal and course notes, since of course he couldn't keep all this in his head.

What he likely did have in his head was an index into the contents, that's the crux of my observation. If I am very good at organizing my workshop, I can quickly grab the tools and materials needed for a particular task without breaking my flow of thought. Same basic principle applies to mathematicians and other intellectual workers, just as it does with physical trades.

Post reply on HN