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Ramanujan Surprises Again (2015)
- skunkworker 7y agoInteresting read, The title should have 2015 in it though.
- dang 7y agoAdded. Thanks!
- dannykwells 7y agoThe 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.
- rq1 7y agoYes 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.
- solveit 7y agoGrothendieck and lack of machinery do not belong in the same sentence. But yes, it is kind of silly.
- JadeNB 7y ago> Grothendieck and lack of machinery do not belong in the same sentence. They most certainly do! Grothendieck’s work is heavy on definitions, but the essence of his work is that the right definitions obviate (and are seen to be right because they obviate) the need for heavy machinery. See the famous quote, taken from Wikipedia (https://en.wikiquote.org/wiki/Alexander_Grothendieck#Quotes_by_Grothendieck https://en.wikiquote.org/wiki/Alexander_Grothendieck#Quotes_...) because that’s the first place I found it: > I can illustrate the ... approach with the ... image of a nut to be opened. The first analogy that came to my mind is of immersing the nut in some softening liquid, and why not simply water? From time to time you rub so the liquid penetrates better, and otherwise you let time pass. The shell becomes more flexible through weeks and months — when the time is ripe, hand pressure is enough, the shell opens like a perfectly ripened avocado! A different image came to me a few weeks ago. The unknown thing to be known appeared to me as some stretch of earth or hard marl, resisting penetration ... the sea advances insensibly in silence, nothing seems to happen, nothing moves, the water is so far off you hardly hear it ... yet finally it surrounds the resistant substance.
- solveit 7y agoI mean, we're arguing semantics at this point, but these definitions we're talking about are things like schemes, which pretty much everybody would call heavy machinery.
- QuesnayJr 7y agoThere have been lots. Twenty? Thirty? A hundred? It was a good century plus for mathematical genius.
- mindcrime 7y agoHas 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 Erdős[1] would be in the conversation. [1]: https://en.wikipedia.org/wiki/Paul_Erd%C5%91s https://en.wikipedia.org/wiki/Paul_Erd%C5%91s
- pmoriarty 7y agoWhat are the other 4 top math stories? For me one of them has to be of Évariste 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 https://en.wikipedia.org/wiki/%C3%89variste_Galois
- dboreham 7y agoFun mathematical tourism stop: go up to the top of the Tour Montparnasse. Look straight down. Galois is buried in the cemetery below. Nobody knows where, but he's down there somewhere.
- madcaptenor 7y agoMy understanding is that this legend has been debunked, but ironically I can't find a source. (My instinct is to blame E. T. Bell.)
- amrx431 7y agoI am surprised no one in including Gauss.
- mindcrime 7y agoDidn't Gauss live and die before Ramanujan was born?
- lvncelot 7y agoJohn von Neumann is someone that often comes up in this context - there are numerous anecdotes on how he was perceived as frightingly clever; also his body of work is beyond impressive.
- Vinceo 7y agoHe 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 7y agoMathematics are the best expression of the transcendental divine. Pythagoras and Plato had the same perspective.
- psychoslave 7y agoYes, 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.
- unlinked_dll 7y agoFunny 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 7y agoThat'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 https://en.m.wikipedia.org/wiki/Squaring_the_circle [2] https://deepblue.lib.umich.edu/handle/2027.42/150050 https://deepblue.lib.umich.edu/handle/2027.42/150050
- dang 7y agoDiscussed at the time: https://news.ycombinator.com/item?id=10518452 https://news.ycombinator.com/item?id=10518452
- v64 7y agoGreat 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.
- hnews_account_1 7y agoA 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.
- dorchadas 7y agoWhat 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.
- nneonneo 7y agoAn 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 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 7y agoIn fact, there seems to be a lot of interesting things about 1729: https://en.wikipedia.org/wiki/1729_(number) https://en.wikipedia.org/wiki/1729_(number)
- nexuist 7y agoWell, now I know why my Scheme class in uni was called CSE 1729.
- pixelpoet 7y agoI love how the article starts with the most boring facts about 1729: > 1729 is the natural number following 1728 and preceding 1730.
- russellbeattie 7y agoHeh. I've been reading HN for long enough to never be surprised by the capability of incredibly pedantic people to be incredibly pedantic.
- JoeAltmaier 7y agoWe had to have a home somewhere :) And this is it.
- wwweston 7y ago
- jackconnor 7y agoFantastic article that explains the math (and physics) very clearly.
- rkhacker 7y agoDon'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.
- HenryKissinger 7y agoOnly neckbeards care about Ramanujan.
- foo101 7y agoRamanujan also claimed 1 + 2 + 3 + ... = -1/12. How does that work? Who can explain this to me?
- adenadel 7y agoHere's a Numberphile video on this https://www.youtube.com/watch?v=w-I6XTVZXww https://www.youtube.com/watch?v=w-I6XTVZXww
- asfarley 7y agoI think this is basically a “shock value” interpretation of a more subtle statement. Obviously adding strictly-positive numbers does not result in a negative number under normal arithmetic. Check the numberphile video and you may be simultaneously irritated and disappointed.
- stan_rogers 7y agoBurkard Polster's (Mathologer) videos on the subject are probably going to be more useful than Numberphile. Numberphile merely presents a trick; Mathologer points out both that it's patent nonsense [0] and that it's useful patent nonsense [1]. [0] https://www.youtube.com/watch?v=YuIIjLr6vUA https://www.youtube.com/watch?v=YuIIjLr6vUA [1] https://www.youtube.com/watch?v=jcKRGpMiVTw https://www.youtube.com/watch?v=jcKRGpMiVTw
- perseusprime11 7y agoI always found Ramanujan very intriguing. He operates on a dimension that is unknown to most of us. Makes me wonder if he is a great yogi or a time traveler.