[HN Gopher] Ramanujan Surprises Again (2015)
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Ramanujan Surprises Again (2015)
Author : tmbsundar
Score : 213 points
Date : 2020-02-16 17:39 UTC (5 hours ago)
(HTM) web link (plus.maths.org)
(TXT) w3m dump (plus.maths.org)
| nneonneo wrote:
| An interesting coincidence: it was recently (2019) discovered
| that the fastest way to multiply two n-bit integers, in time O(n
| log n), involves 1729-dimensional Fourier transforms:
| https://hal.archives-ouvertes.fr/hal-02070778. It is quite
| surprising that the asymptotically best way to perform such an
| elementary operation should be tied to Ramanujan's famous taxicab
| number.
|
| (Technically, it works for any number of dimensions >= 1729, but
| the proof fails for dimensions less than that. Future work might
| bring the bound down, or better explain why that bound is
| necessary.)
| user2994cb wrote:
| In fact, there seems to be a lot of interesting things about
| 1729: https://en.wikipedia.org/wiki/1729_(number)
| nexuist wrote:
| Well, now I know why my Scheme class in uni was called CSE
| 1729.
| pixelpoet wrote:
| I love how the article starts with the most boring facts
| about 1729:
|
| > 1729 is the natural number following 1728 and preceding
| 1730.
| russellbeattie wrote:
| Heh. I've been reading HN for long enough to never be
| surprised by the capability of incredibly pedantic people
| to be incredibly pedantic.
| skunkworker wrote:
| Interesting read, The title should have 2015 in it though.
| dang wrote:
| Added. Thanks!
| dannykwells wrote:
| The taxi cab story is easily a top-5 math story, and is
| quintessential Ramanujan.
|
| Has there been a genius of his kind since? Maybe Terry Tao, but
| his work also lacks the ease and lack of machinery that Ramanujan
| had. Truly amazing.
| pmoriarty wrote:
| What are the other 4 top math stories?
|
| For me one of them has to be of Evariste Galois[1], who, legend
| has it, hastily wrote fragments of his last mathematical
| discoveries on his shirt sleeves before fighting the duel that
| would end his life.
|
| [1] - https://en.wikipedia.org/wiki/%C3%89variste_Galois
| QuesnayJr wrote:
| There have been lots. Twenty? Thirty? A hundred? It was a good
| century plus for mathematical genius.
| rq1 wrote:
| Yes definitely: Alexandre Grothendieck. And Terrence Tao can't
| sit at his table (yet?).
|
| But honestly it's kind of a silly game to rank mathematicians
| this way.
| mindcrime wrote:
| _Has there been a genius of his kind since? Maybe Terry Tao,
| but his work also lacks the ease and lack of machinery that
| Ramanujan had. Truly amazing._
|
| It's hard to compare mathematicians, but I suppose Erdos[1]
| would be in the conversation.
|
| [1]: https://en.wikipedia.org/wiki/Paul_Erd%C5%91s
| rkhacker wrote:
| Don't we think that the credit for the number 1729 should belong
| to Hardy, for he took the cab and mentioned that number to
| Ramanujan. Of course, Ramanujan could see beauty in every number
| and would have produced something equally beautiful for some
| other number Hardy could utter.
| Vinceo wrote:
| He credited his work to his family goddess. From wikipedia:
|
| "A deeply religious Hindu, Ramanujan credited his substantial
| mathematical capacities to divinity, and said the mathematical
| knowledge he displayed was revealed to him by his family goddess.
| "An equation for me has no meaning," he once said, "unless it
| expresses a thought of God.""
| dr_dshiv wrote:
| Mathematics are the best expression of the transcendental
| divine. Pythagoras and Plato had the same perspective.
| unlinked_dll wrote:
| Funny to use the word transcendental there, since the
| Pythagoreans held ratios to be divine but couldn't figure out
| irrational numbers, like pi. They had trouble squaring that
| circle.
| dr_dshiv wrote:
| That's why I think Pythagoras refused to write down his
| doctrines. He knew there was more to be empirically
| discovered -- and he was wary of how text could become
| dogma. The divine he uncovered was based on a mathematical,
| harmonious cosmos; but he recognized it was beyond
| understanding in a lifetime. That's why Pythagorean
| mysticism is compatible with modern science -- he didn't
| write anything down!
|
| 2000 years later, Kepler had faith in a harmonious cosmos,
| and charged his model of harmony so it could fit the
| evidence. He elipsed the circles, instead of squaring them.
|
| Fun fact #1: it is impossible to square a circle [1]
|
| Fun fact #2: the Pythagoreans conducted the first attested
| scientific experiment in Western history (according to a
| recent PhD thesis at UMich [2])
|
| [1] https://en.m.wikipedia.org/wiki/Squaring_the_circle
|
| [2] https://deepblue.lib.umich.edu/handle/2027.42/150050
| psychoslave wrote:
| Yes, it looks like for many mathematicians, the confusion
| between stable conceptual foundation and eternal objective
| reality is too seductive to not fall in the illusion of
| identity of things locally indistinguishables.
| jackconnor wrote:
| Fantastic article that explains the math (and physics) very
| clearly.
| dang wrote:
| Discussed at the time:
| https://news.ycombinator.com/item?id=10518452
| v64 wrote:
| Great read! When you first hear the taxicab number story, your
| initial impression is to be struck by Ramanujan's innate
| calculating capability. It's interesting to find out that the
| real coincidence here is that Hardy rode in a taxicab whose
| number had happened to show up in Ramanujan's investigations of
| Fermat's last theorem.
| zamadatix wrote:
| I'm not sure I'd call it coincidence rather "being struck by
| the vast amount of time and passion Ramanujan put into
| mathematics". I'd be absolutely amazed if he couldn't have
| recalled a similarly obscure fact for most numbers below
| 10,000.
| hnews_account_1 wrote:
| A lot of genius stories are like this. I was also under the
| illusion that these guys could just do things that fast, but at
| some point, I read Feynman's biography where he explicitly
| talks about how he used to solve homework problems or something
| beforehand and then he used to pretend that he found the
| solution while solving it if his classmates asked.
|
| That threw me for a loop and I started believing shit like no
| one's smarter than I was etc. Then I just ... grew up, I guess.
| And I remembered this story by Feynman and I realised that
| despite his absolutely undoubtable genius, he'd have appeared
| godlike to me if I was his classmate back in the day.
|
| Ramanujan's brain worked even faster by most accounts. He
| dreamed in math, I think. So there are multiple stories where
| people ask him a puzzle and he'll answer with an equation that
| solves it for the entire family of problems that the puzzle
| could come from.
| Psyladine wrote:
| Feynman was undoubtedly a genius, but he also suffered from a
| need to be admired. The safecracking episodes at Los Alamos
| are a perfect example - giving the impression he was an
| expert safe cracker when his real methodology was guesswork
| and sometimes subterfuge (birthdays, anniversaries, or even
| subtlety observing someone inputting their combination).
| dorchadas wrote:
| What was the quote about Feynman? That he loved to cultivate
| anecdotes about himself or something similar? Makes a lot of
| his stories make a lot more sense, too.
| OldGuyInTheClub wrote:
| From Murray Gell-Mann:
| https://www.youtube.com/watch?v=rnMsgxIIQEE
|
| Several clips from Gell-Mann's Web of Stories interview
| (late 1990s) pertain to his on-again off-again
| collaboration with Feynman.
|
| https://www.youtube.com/watch?v=o2sEW4ggVlA&list=PLVV0r6CmE
| s...
| avip wrote:
| It's a rant by fellow Physicist Gell-Mann.
| Quekid5 wrote:
| I think it's pretty plausible that he was a raging
| egomaniac (narcissist, perhaps?).
|
| Undoubtedly a great thinker and genius, but that doesn't
| say very much about personality traits.
| [deleted]
| user2994cb wrote:
| Feynman even has his own 1729 anecdote:
| https://www.ee.ryerson.ca/~elf/abacus/feynman.html
| hnews_account_1 wrote:
| I think the part that makes it genuine is that he was
| comically self aware of himself and his craziness. Even
| when he was pushing the boundaries just for the sake of it
| and to make a caricature / character out of himself, he did
| it in a way that made me think that he didn't really
| pretend to not be doing it for his ego.
|
| It's like 4 levels of thinking somehow merged in his
| actions: 1) be normal and look at the crazy people, 2) be a
| crazy person, 3) be a crazy person and be aware of your
| craziness, 4) be a crazy person, be aware of it and let
| others know that you're aware of it. It feels like one of
| those thought spirals I go into if I have weed. It's right
| on the boundary of crazy but probably also (in his case)
| inside the realm of genius.
| gameswithgo wrote:
| i recall him explaining several shortcuts one can use to
| solve problems in seemingly impossible speeds by drawing on
| a breadth of experience from similar problems that you have
| memorized or are easy to compute and interpolating.
|
| its still genius but not in the sense of actually being
| able to do huge calculations in ones head the way a
| computer would.
| [deleted]
| wenc wrote:
| I think most of us are impressed by computational parlor
| tricks (and indeed computational intelligence in general --
| being able to process information and compute quickly and
| accurately), but for me, genius goes beyond that.
|
| Genius is about having rare and useful insights that the rest
| of us are incapable of, and that a computer is unable to
| easily replicate.
|
| For instance, there was a thing on Twitter recently about all
| percentages being reversible (7% of 50 is equal to 50% of 7,
| but the latter is easier to mentally calculate). Most of us
| are aware that multiplication is commutative, but it takes
| genius to recognize and frame that insight in a useful way.
| karmakaze wrote:
| This reminds me of the von Neumann fly puzzle story:
|
| https://en.wikipedia.org/wiki/John_von_Neumann#Cognitive_abi.
| ..
| eesmith wrote:
| Or swallow, if you think Wigner's account is more accurate
| than Halmos'.
| HenryKissinger wrote:
| Only neckbeards care about Ramanujan.
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