11 ms·

The asymmetry in storytelling between math and the other sciences

191 points by digital55 9y ago

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.
Jun8 9y ago
The second chapter of the book The Mathematical Experience has a hilarious interview between a hypothetical pure mathematician working on "non-Rimenan hypersquares" and a reporter who wants to do a piece on his work (pdf link, starts on page 39: http://www.springer.com/cda/content/document/cda_downloaddocument/9780817682941-c1.pdf http://www.springer.com/cda/content/document/cda_downloaddoc...). It demonstrates this exact issue.
- mturmon 9y ago
  It is an extraordinary book. I've read and re-read it. Just a chunk from the part you mentioned: "He finds it difficult to establish meaningful conversation with that large portion of humanity that has never heard of a non-Riemannian hypersquare. This creates grave difficulties for him; there are two colleagues in his department who know something about non-Riemannian hypersquares, but one of them is on sabbatical, and the other is much more interested in non-Eulerian semirings."
rspeer 9y ago
I recognize a piece of background that the article is leaving unstated. A decade ago, the mathematical group E_8 was the subject of a unified theory of physics by an outsider, Antony Lisi, who called it "An Exceptionally Simple Theory of Everything". [1] This theory never got published (it was supposedly the most downloaded paper on arXiV for a while, though). Peer review was not favorable to it. But the popular press ran with it, especially because of the story they could tell about how a surfer dude was maybe the next Einstein. I assume that the echoes of this are why a mathematician writing down facts about E_8 got caught up in an explosion of weird publicity about God Particles. [1] https://en.wikipedia.org/wiki/An_Exceptionally_Simple_Theory_of_Everything https://en.wikipedia.org/wiki/An_Exceptionally_Simple_Theory...
- kbenson 9y ago
  I remember that. IIRC, the draw of the "surfer dude" wasn't just that he was a surfer, but that he lived out of his van, was a mathematician or physicist, and basically just traveled around surfing and doing theoretical math when he wasn't surfing. It's fairly easy for a lot of people to romanticize that. I don't recall whether I read about him, or watched a Ted talk, or both, but a good portion of the time when I read "unified theory" some recollection of that story comes back. I'm sure it helped that a very dumbed down version could be understood almost purely through visual aids with pretty colors and symmetry. ;)
  - Certhas 9y ago
    I met Lisi back in the day. It also helped that he was actually not a crack pot. Certainly not in the classical sense. He understood the math at a level typical of a theoretical physicist in the field, and he engaged the scientific community about his ideas in a deep proper way. The rebuttals and criticism he drew also showed his work was at least taken somewhat seriously and considered. At the end of the day his theory remained to incomplete. Chirality problems were hand-waved away unconvincingly. It's more a mathematical curiosity than a proper proposal for unification.
  - eastWestMath 9y ago
    You'd be surprised at how many mathematicians are avid hikers. I've heard stories of people flying to Calgary, disappearing in the Rockies, then showing up at UBC for a conference over a month later.
deleted 9y ago
[deleted]
redthrowaway 9y ago
By far the best math teacher I ever had, Fred Irani, taught math in a way no teacher I'd had before or since did. We didn't use the textbook, and we didn't have homework. We just worked through the problems in class, the way the people who originally figured them out did: by working from what we already knew and making logical inferences. Learning calculus from him was as much history as it was math, but the math stuck. I really wish more math teachers taught that way.
- ianai 9y ago
  My favorite math professor would ensure he taught to and beyond the homework. He always had the toughest homework - but he managed to keep it accessible. Then the tests were based on the same sort of questions and material - but easier. Somehow most of my professors at that college got that mixture wrong. They would seemingly get bored with the topics and decide to throw out curveballs everywhere.
  - redthrowaway 9y ago
    I've had profs like that. What really struck me about Irani is that even without the homework, even with only weekly quizzes, it still stuck. It wasn't an AP class, but he encouraged us to write the AP exam at the end of the year and nearly everyone got a 4 or a 5. I do agree with the notion that profs are more effective when the homework is harder than the exam, however. I had the exact opposite for a fourth-year crypto class. For homework, we'd work through some basic cryptanalysis with lots of hints. Then the test would come around, and two or three of the ten questions would involve breaking a cypher, from scratch. I got about 25% on the first test, which ended up being 65% after he scaled it. Brutal class.
    - ianai 9y ago
      It's a huge disservice to just destroy people's academic careers like that.
- abandonliberty 9y ago
  >working from what we already knew and making logical inferences. The hardest & most valid exam I ever wrote used the same technique. Every single question on the exam was novel. I flipped through each page looking for something familiar, got to the end. The class required about 30 hours of homework per week, but we were told we could do it while walking, showering, etc.
Futurebot 9y ago
Relatedly, "Mathematics for the non-mathematician" is a great book that talks about the stories of math: history of how certain ideas, techniques, and discoveries happened. Recommended to anyone that wants to learn / review math in a more story-oriented way.
jcranberry 9y ago
>"There is a general feeling in the pure math community that popularizing mathematics is betraying mathematics,” I don't think this is true at all. My experience with math professors is that they either would welcome more popularity in the field, or they simply don't care. I DO think that they would be very dissatisfied with the kind of farcical representation of physics that sometimes goes on (looking at you Michio Kaku). I also think it's very misleading to say mathematics has nothing to do with the real world. The obvious contradiction would be physics, since it's applied math, but I think the quoted person was talking about mathematical research, which is a much fairer point. While it's true that a lot, if not most, of mathematical research has little to offer in terms of applications, but a lot of times "useless" math can still describe real world phenomena, sometimes very beautifully.
- vorotato 9y ago
  You and the author are conflating two different things. The pure math community probably DOES feel that popularizing only applied mathematics is betraying pure mathematics, and they're probably right. We don't really teach proofs outside of highschool geometric proofs and maybe a single class in university. However there's no good reason why we can't popularize both applied AND pure mathematics.
  - thanatropism 9y ago
    There's this joke in applied math departments that the best way to spook a pure mathematician is to whisper in his ear "We've found an use for your theorem..."
    - nonbel 9y ago
      "We've found an use for your theorem..." I'd think that would be more likely to spook the English department.
      - dredmorbius 9y ago
        Rhetoric.
mathgenius 9y ago
The paper is here [1]. It begins with: """ The purpose of this paper is to give a finite algorithm for computing the set of irreducible unitary representations of a real reductive Lie group G. Before explaining the nature of the algorithm, it is worth recalling why this is an interesting question. A serious historical survey would go back at least to the work of Fourier (which can be understood in terms of the irreducible unitary representations of the circle). """ This work is also related to the "Langlands program", which is perhaps the mathematician's version of a grand unified theory of mathematics. [1] "Unitary representations of real reductive groups" https://arxiv.org/abs/1212.2192 https://arxiv.org/abs/1212.2192
quantum_state 9y ago
Given the very structural nature of the Lie algebra, wonder if the work, or part of it, can be automated and done by computers ... Enlightenment from any experts would be appreciated.
dkarapetyan 9y ago
Even basic biological research has this problem. Anyone remember CRISPR? The press ran with all sorts of analogies about laser-like precision to reprogram genomes. Turns out it's not as laser-like as the press made it out to be. Really the problem is writers and journalists who are not domain experts trying to explain this stuff to laypeople. There is no requirement for story writers to have been mathematicians or biologists when it comes to popularizing so you end up with half-truths and outright lies.
panic 9y ago
The Atlas project itself has some interesting stuff, including a custom programming language (http://www.liegroups.org/software/documentation/atlasofliegroups-docs/library/axis.html http://www.liegroups.org/software/documentation/atlasofliegr...) with parts written in literate C++ (e.g. https://github.com/jeffreyadams/atlasofliegroups/blob/master/sources/interpreter/axis-types.w https://github.com/jeffreyadams/atlasofliegroups/blob/master...)!
peter303 9y ago
Math's 'god particle' may be prime numbers. Though on the surface the concept of prime numbers involves just integers and you can explain it to 8-year olds, there are major unproven conjectures and deep allied mathematics. And now the worlds digital banking system and private messages depends on special properties of prime numbers [factorization].
- popcorncolonel 9y ago
  That's just because we know very little about them. It very well could be the case that factoring semiprimes might be ridiculously easy, but we are just too dumb right now to figure out how to do it quickly (even if P != NP -- we haven't even shown that factorization is NP complete).

191 points by digital55 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.

Jun8 9y ago

The second chapter of the book The Mathematical Experience has a hilarious interview between a hypothetical pure mathematician working on "non-Rimenan hypersquares" and a reporter who wants to do a piece on his work (pdf link, starts on page 39: http://www.springer.com/cda/content/document/cda_downloaddocument/9780817682941-c1.pdf http://www.springer.com/cda/content/document/cda_downloaddoc...). It demonstrates this exact issue.

mturmon 9y ago
It is an extraordinary book. I've read and re-read it. Just a chunk from the part you mentioned: "He finds it difficult to establish meaningful conversation with that large portion of humanity that has never heard of a non-Riemannian hypersquare. This creates grave difficulties for him; there are two colleagues in his department who know something about non-Riemannian hypersquares, but one of them is on sabbatical, and the other is much more interested in non-Eulerian semirings."

rspeer 9y ago

I recognize a piece of background that the article is leaving unstated. A decade ago, the mathematical group E_8 was the subject of a unified theory of physics by an outsider, Antony Lisi, who called it "An Exceptionally Simple Theory of Everything". [1] This theory never got published (it was supposedly the most downloaded paper on arXiV for a while, though). Peer review was not favorable to it. But the popular press ran with it, especially because of the story they could tell about how a surfer dude was maybe the next Einstein. I assume that the echoes of this are why a mathematician writing down facts about E_8 got caught up in an explosion of weird publicity about God Particles. [1] https://en.wikipedia.org/wiki/An_Exceptionally_Simple_Theory_of_Everything https://en.wikipedia.org/wiki/An_Exceptionally_Simple_Theory...

kbenson 9y ago
I remember that. IIRC, the draw of the "surfer dude" wasn't just that he was a surfer, but that he lived out of his van, was a mathematician or physicist, and basically just traveled around surfing and doing theoretical math when he wasn't surfing. It's fairly easy for a lot of people to romanticize that. I don't recall whether I read about him, or watched a Ted talk, or both, but a good portion of the time when I read "unified theory" some recollection of that story comes back. I'm sure it helped that a very dumbed down version could be understood almost purely through visual aids with pretty colors and symmetry. ;)
- Certhas 9y ago
  I met Lisi back in the day. It also helped that he was actually not a crack pot. Certainly not in the classical sense. He understood the math at a level typical of a theoretical physicist in the field, and he engaged the scientific community about his ideas in a deep proper way. The rebuttals and criticism he drew also showed his work was at least taken somewhat seriously and considered. At the end of the day his theory remained to incomplete. Chirality problems were hand-waved away unconvincingly. It's more a mathematical curiosity than a proper proposal for unification.
- eastWestMath 9y ago
  You'd be surprised at how many mathematicians are avid hikers. I've heard stories of people flying to Calgary, disappearing in the Rockies, then showing up at UBC for a conference over a month later.

deleted 9y ago

[deleted]

redthrowaway 9y ago

By far the best math teacher I ever had, Fred Irani, taught math in a way no teacher I'd had before or since did. We didn't use the textbook, and we didn't have homework. We just worked through the problems in class, the way the people who originally figured them out did: by working from what we already knew and making logical inferences. Learning calculus from him was as much history as it was math, but the math stuck. I really wish more math teachers taught that way.

ianai 9y ago
My favorite math professor would ensure he taught to and beyond the homework. He always had the toughest homework - but he managed to keep it accessible. Then the tests were based on the same sort of questions and material - but easier. Somehow most of my professors at that college got that mixture wrong. They would seemingly get bored with the topics and decide to throw out curveballs everywhere.
- redthrowaway 9y ago
  I've had profs like that. What really struck me about Irani is that even without the homework, even with only weekly quizzes, it still stuck. It wasn't an AP class, but he encouraged us to write the AP exam at the end of the year and nearly everyone got a 4 or a 5. I do agree with the notion that profs are more effective when the homework is harder than the exam, however. I had the exact opposite for a fourth-year crypto class. For homework, we'd work through some basic cryptanalysis with lots of hints. Then the test would come around, and two or three of the ten questions would involve breaking a cypher, from scratch. I got about 25% on the first test, which ended up being 65% after he scaled it. Brutal class.
  - ianai 9y ago
    It's a huge disservice to just destroy people's academic careers like that.
abandonliberty 9y ago
>working from what we already knew and making logical inferences. The hardest & most valid exam I ever wrote used the same technique. Every single question on the exam was novel. I flipped through each page looking for something familiar, got to the end. The class required about 30 hours of homework per week, but we were told we could do it while walking, showering, etc.

Futurebot 9y ago

Relatedly, "Mathematics for the non-mathematician" is a great book that talks about the stories of math: history of how certain ideas, techniques, and discoveries happened. Recommended to anyone that wants to learn / review math in a more story-oriented way.

jcranberry 9y ago

>"There is a general feeling in the pure math community that popularizing mathematics is betraying mathematics,” I don't think this is true at all. My experience with math professors is that they either would welcome more popularity in the field, or they simply don't care. I DO think that they would be very dissatisfied with the kind of farcical representation of physics that sometimes goes on (looking at you Michio Kaku). I also think it's very misleading to say mathematics has nothing to do with the real world. The obvious contradiction would be physics, since it's applied math, but I think the quoted person was talking about mathematical research, which is a much fairer point. While it's true that a lot, if not most, of mathematical research has little to offer in terms of applications, but a lot of times "useless" math can still describe real world phenomena, sometimes very beautifully.

vorotato 9y ago
You and the author are conflating two different things. The pure math community probably DOES feel that popularizing only applied mathematics is betraying pure mathematics, and they're probably right. We don't really teach proofs outside of highschool geometric proofs and maybe a single class in university. However there's no good reason why we can't popularize both applied AND pure mathematics.
- thanatropism 9y ago
  There's this joke in applied math departments that the best way to spook a pure mathematician is to whisper in his ear "We've found an use for your theorem..."
  - nonbel 9y ago
    "We've found an use for your theorem..." I'd think that would be more likely to spook the English department.
    - dredmorbius 9y ago
      Rhetoric.

mathgenius 9y ago

The paper is here [1]. It begins with: """ The purpose of this paper is to give a finite algorithm for computing the set of irreducible unitary representations of a real reductive Lie group G. Before explaining the nature of the algorithm, it is worth recalling why this is an interesting question. A serious historical survey would go back at least to the work of Fourier (which can be understood in terms of the irreducible unitary representations of the circle). """ This work is also related to the "Langlands program", which is perhaps the mathematician's version of a grand unified theory of mathematics. [1] "Unitary representations of real reductive groups" https://arxiv.org/abs/1212.2192 https://arxiv.org/abs/1212.2192

quantum_state 9y ago

Given the very structural nature of the Lie algebra, wonder if the work, or part of it, can be automated and done by computers ... Enlightenment from any experts would be appreciated.

dkarapetyan 9y ago

Even basic biological research has this problem. Anyone remember CRISPR? The press ran with all sorts of analogies about laser-like precision to reprogram genomes. Turns out it's not as laser-like as the press made it out to be. Really the problem is writers and journalists who are not domain experts trying to explain this stuff to laypeople. There is no requirement for story writers to have been mathematicians or biologists when it comes to popularizing so you end up with half-truths and outright lies.

panic 9y ago

The Atlas project itself has some interesting stuff, including a custom programming language (http://www.liegroups.org/software/documentation/atlasofliegroups-docs/library/axis.html http://www.liegroups.org/software/documentation/atlasofliegr...) with parts written in literate C++ (e.g. https://github.com/jeffreyadams/atlasofliegroups/blob/master/sources/interpreter/axis-types.w https://github.com/jeffreyadams/atlasofliegroups/blob/master...)!

peter303 9y ago

Math's 'god particle' may be prime numbers. Though on the surface the concept of prime numbers involves just integers and you can explain it to 8-year olds, there are major unproven conjectures and deep allied mathematics. And now the worlds digital banking system and private messages depends on special properties of prime numbers [factorization].

popcorncolonel 9y ago
That's just because we know very little about them. It very well could be the case that factoring semiprimes might be ridiculously easy, but we are just too dumb right now to figure out how to do it quickly (even if P != NP -- we haven't even shown that factorization is NP complete).