5 ms·

>Even when researchers do want their work shared widely, why don’t we read more about the fuel that makes math grow? “The physicists tell exciting stories,” Vog

by jasode 9y ago

>Even when researchers do want their work shared widely, why don’t we read more about the fuel that makes math grow? “The physicists tell exciting stories,” Vogan said. “In some ways, this is a failure of mathematicians to tell exciting stories.” The physicists also have better names. Black hole and God particle quicken the pulse somewhat more than “irreducible unitary representation.” Mathematics also has some cute names such as Monstrous Moonshine[1] and Hairy Ball Theorem[2]. I don't understand Monstrous Moonshine but the name had enough poetry to cause stickiness in the brain for later recall. A math problem closer to layman's experience with a cute name might be the "Secretary Problem".[3] Leaving aside the naming and surveying the "importance" of open math problems... I would guess the P!=NP proof would be an example. Unfortunately, it doesn't have any easy description that the average person would understand. The same goes for all the other Clay[4] Millenium problems. [1] https://en.wikipedia.org/wiki/Monstrous_moonshine https://en.wikipedia.org/wiki/Monstrous_moonshine [2] https://en.wikipedia.org/wiki/Hairy_ball_theorem https://en.wikipedia.org/wiki/Hairy_ball_theorem [3] https://en.wikipedia.org/wiki/Secretary_problem https://en.wikipedia.org/wiki/Secretary_problem [4] http://www.claymath.org/millennium-problems http://www.claymath.org/millennium-problems

empath75 9y ago
Monstrous moonshine is actually related to lie groups.
odonnellryan 9y ago
P versus NP isn't hard to explain if some of the problems are first familiar with the person you're explaining it to. "It's very easy to check if sudoku is correct, right? You just go line by line, box by box. But isn't it fairly hard to solve?" You'd have to go more in-depth than that, you're right: there's not a good one or two sentence explanation. But, explaining that "some things are really easy to check if they are correct, but really hard to solve: what does easy and hard mean? generally, it means it takes either a short time (easy) or a long time (hard)" isn't too bad.
- dgacmu 9y ago
  I can't do it in two sentences, but this is approximately the version I teach to first-year non-CS undergrads: A problem is called "NP" if I can give you a solution to it and you can easily verify that the solution is correct. For example, "find 3 different odd numbers that together add up to ten" (here's a possible solution: 3, 5, 7). What's awesome about this is that there are a lot of problems of that form where we don't know whether or not it's possible to find a solution to the problems before dying of old age -- or before the sun runs out of fuel, even though you could check the answer in a few minutes using pencil and paper. Nobody has ever figured out how to solve them fast, but it's a huge open question of whether they can be solved fast. The P = NP question is whether there exists a fast solution to any problem that you can verify easily if I give you a solution. And it's not just of theoretical interest: some those problems underlie everything from cryptography (communicating and storing information securely using encryption) to things like optimizing airline routes or the way UPS chooses where to route packages. Amazingly, there's a set of problems that if you find way to solve any one of them fast, you can solve all problems in NP fast. Which means the NSA and everyone else will try to kidnap you to find out the secret. Fortunately, most people who study it don't think that there's a solution. But it's one of the most famous and important problems in computing, and nobody -- of some of the smartest people in the field -- has ever managed to prove it either way. (Truth in advertising: We actually use subset sum as the example, and walk through it a little, but that's because we're trying to teach it in more detail than just telling the story. And have also taught a handwavy version of asymptotic analysis. If you want to show someone how hard it gets quickly, subset sum is a nice way to do it. The "talking" example above is, of course, an instance of subset sum, but it doesn't explain the general form of the problem.)
  - odonnellryan 9y ago
    Isn't it a little misleading to say a problem is NP "if I can give you a solution to it and you can easily verify that the solution is correct." Not all problems that fit that description fall into NP, right?
    - dgacmu 9y ago
wayn3 9y ago
there are a lot of very interesting math things with cool names. heres the problem. mathematicians dont build expensive shit. theres no math lhc that cost the equivalent of feeding bangladesh for a century that econ minded folks could whine about. theres no "mathematicians will create a black hole under geneva that will swallow us all". if the riemann conjecture is proven, precisely nothing happens. its not even possible that something happens in the tangible world, because of some result in mathematics. mathematics isnt irrelevant because it doesnt have cool names. its irrelevant because its impossible to make the news. a biologist can accidentally create a virus that kills us all. obviously science fiction, but its at least potentially possible. a chemist can invent some kind of explosive that isis could steal and make some building go boom. physicists can totally make black holes appear and build warp drives and all this weird stuff that is more fiction than science, but spock talked about it and light sabers duh. mathematics just powers all those things. there are no lasers without math, either, but they arent attributed to mathematics. they are physics stuff. when the first fusion reactor finally runs profitably, mathematics will have contributed a lot of necessities. but its the billionaire douche who funded the thing who gets to talk about how the engineers built an impressive machine. mathematics doesnt get any kind of fame outside the scientific world, because its invisible. but the scientists who use all the math stuff know that without mathematics, they'd be almost useless.
- ggambetta 9y ago
  Interesting point. I guess encryption (and indirectly, blockchains) are some of the few closer to "pure" applications of math. But even then, they're treated as black boxes to some extent - not sure math gets all the credit it deserves there, for the average user.
  - wayn3 9y ago
    muricans dont even admit that "computer science" is a sub-field of mathematics. but thats ok. mathematics is way too powerful to care about mainstream fame.
- badosu 9y ago
  > if the riemann conjecture is proven, precisely nothing happens. its not even possible that something happens in the tangible world, because of some result in mathematics. Unless I'm mistaken, if proved the Riemann Conjecture could provide insights on the distribution of prime numbers or a polynomial-time algorithm for prime factorization, which would enable attacks on ciphers that rely on the difficulty of this problem (e.g. RSA). This is not assured by the yes/no answer of the conjecture, but the underlying work to reach that.
chestervonwinch 9y ago
There's also a surprising number of math/science related theorems/problem named after food. This came up on HN a couple years ago: http://notmatthancock.github.io/2015/08/21/math-and-food.html http://notmatthancock.github.io/2015/08/21/math-and-food.htm...
jlg23 9y ago
> I would guess the P!=NP proof would be an example. Unfortunately, it doesn't have any easy description that the average person would understand. "Hard. Really hard. Don't be ridiculous.". Now backtrack 2 small examples on paper. Oh, look, the number of steps here grow, but these grow even faster! Especially mathematics when explained to a layperson so much depends on the language used. If one manages to keep the rest of the complexity zoo[1] out of the explanation and invests time into very basic examples, a lot things can be explained that otherwise the average person would not understand. [1] https://complexityzoo.uwaterloo.ca/Complexity_Zoo#All_Classes https://complexityzoo.uwaterloo.ca/Complexity_Zoo#All_Classe... EDIT: Looking for a video I stumbled upon last week that had a very nice, short explanation of P vs NP (which I did not find again), I found this one: Not lay-person simple, but very funny and also provides a cursory glance at what lies beyond P vs NP, i.e. the complexity zoo: https://www.youtube.com/watch?v=YX40hbAHx3s https://www.youtube.com/watch?v=YX40hbAHx3s (10 min)
noobermin 9y ago
P!=NP is a hint at one great application of mathematics, computer science. CS is closer to math in my opinion than any of the physical scientists. Proofs in information theory have profound effects on IT security, for example.

by jasode 9y ago

empath75 9y ago

Monstrous moonshine is actually related to lie groups.

odonnellryan 9y ago

P versus NP isn't hard to explain if some of the problems are first familiar with the person you're explaining it to. "It's very easy to check if sudoku is correct, right? You just go line by line, box by box. But isn't it fairly hard to solve?" You'd have to go more in-depth than that, you're right: there's not a good one or two sentence explanation. But, explaining that "some things are really easy to check if they are correct, but really hard to solve: what does easy and hard mean? generally, it means it takes either a short time (easy) or a long time (hard)" isn't too bad.

dgacmu 9y ago
I can't do it in two sentences, but this is approximately the version I teach to first-year non-CS undergrads: A problem is called "NP" if I can give you a solution to it and you can easily verify that the solution is correct. For example, "find 3 different odd numbers that together add up to ten" (here's a possible solution: 3, 5, 7). What's awesome about this is that there are a lot of problems of that form where we don't know whether or not it's possible to find a solution to the problems before dying of old age -- or before the sun runs out of fuel, even though you could check the answer in a few minutes using pencil and paper. Nobody has ever figured out how to solve them fast, but it's a huge open question of whether they can be solved fast. The P = NP question is whether there exists a fast solution to any problem that you can verify easily if I give you a solution. And it's not just of theoretical interest: some those problems underlie everything from cryptography (communicating and storing information securely using encryption) to things like optimizing airline routes or the way UPS chooses where to route packages. Amazingly, there's a set of problems that if you find way to solve any one of them fast, you can solve all problems in NP fast. Which means the NSA and everyone else will try to kidnap you to find out the secret. Fortunately, most people who study it don't think that there's a solution. But it's one of the most famous and important problems in computing, and nobody -- of some of the smartest people in the field -- has ever managed to prove it either way. (Truth in advertising: We actually use subset sum as the example, and walk through it a little, but that's because we're trying to teach it in more detail than just telling the story. And have also taught a handwavy version of asymptotic analysis. If you want to show someone how hard it gets quickly, subset sum is a nice way to do it. The "talking" example above is, of course, an instance of subset sum, but it doesn't explain the general form of the problem.)
- odonnellryan 9y ago
  Isn't it a little misleading to say a problem is NP "if I can give you a solution to it and you can easily verify that the solution is correct." Not all problems that fit that description fall into NP, right?
  - dgacmu 9y ago

wayn3 9y ago

there are a lot of very interesting math things with cool names. heres the problem. mathematicians dont build expensive shit. theres no math lhc that cost the equivalent of feeding bangladesh for a century that econ minded folks could whine about. theres no "mathematicians will create a black hole under geneva that will swallow us all". if the riemann conjecture is proven, precisely nothing happens. its not even possible that something happens in the tangible world, because of some result in mathematics. mathematics isnt irrelevant because it doesnt have cool names. its irrelevant because its impossible to make the news. a biologist can accidentally create a virus that kills us all. obviously science fiction, but its at least potentially possible. a chemist can invent some kind of explosive that isis could steal and make some building go boom. physicists can totally make black holes appear and build warp drives and all this weird stuff that is more fiction than science, but spock talked about it and light sabers duh. mathematics just powers all those things. there are no lasers without math, either, but they arent attributed to mathematics. they are physics stuff. when the first fusion reactor finally runs profitably, mathematics will have contributed a lot of necessities. but its the billionaire douche who funded the thing who gets to talk about how the engineers built an impressive machine. mathematics doesnt get any kind of fame outside the scientific world, because its invisible. but the scientists who use all the math stuff know that without mathematics, they'd be almost useless.

ggambetta 9y ago
Interesting point. I guess encryption (and indirectly, blockchains) are some of the few closer to "pure" applications of math. But even then, they're treated as black boxes to some extent - not sure math gets all the credit it deserves there, for the average user.
- wayn3 9y ago
  muricans dont even admit that "computer science" is a sub-field of mathematics. but thats ok. mathematics is way too powerful to care about mainstream fame.
badosu 9y ago
> if the riemann conjecture is proven, precisely nothing happens. its not even possible that something happens in the tangible world, because of some result in mathematics. Unless I'm mistaken, if proved the Riemann Conjecture could provide insights on the distribution of prime numbers or a polynomial-time algorithm for prime factorization, which would enable attacks on ciphers that rely on the difficulty of this problem (e.g. RSA). This is not assured by the yes/no answer of the conjecture, but the underlying work to reach that.

chestervonwinch 9y ago

There's also a surprising number of math/science related theorems/problem named after food. This came up on HN a couple years ago: http://notmatthancock.github.io/2015/08/21/math-and-food.html http://notmatthancock.github.io/2015/08/21/math-and-food.htm...

jlg23 9y ago

> I would guess the P!=NP proof would be an example. Unfortunately, it doesn't have any easy description that the average person would understand. "Hard. Really hard. Don't be ridiculous.". Now backtrack 2 small examples on paper. Oh, look, the number of steps here grow, but these grow even faster! Especially mathematics when explained to a layperson so much depends on the language used. If one manages to keep the rest of the complexity zoo[1] out of the explanation and invests time into very basic examples, a lot things can be explained that otherwise the average person would not understand. [1] https://complexityzoo.uwaterloo.ca/Complexity_Zoo#All_Classes https://complexityzoo.uwaterloo.ca/Complexity_Zoo#All_Classe... EDIT: Looking for a video I stumbled upon last week that had a very nice, short explanation of P vs NP (which I did not find again), I found this one: Not lay-person simple, but very funny and also provides a cursory glance at what lies beyond P vs NP, i.e. the complexity zoo: https://www.youtube.com/watch?v=YX40hbAHx3s https://www.youtube.com/watch?v=YX40hbAHx3s (10 min)

noobermin 9y ago

P!=NP is a hint at one great application of mathematics, computer science. CS is closer to math in my opinion than any of the physical scientists. Proofs in information theory have profound effects on IT security, for example.