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What is the most awesome anagram? Sujith Vijay , Up, up and a way with words. 273 upvotes by M.Arun Kumar , Vismay Parmar , Rakesh Muthyala , (more) In 1996, a man named Richard Wallace published a book titled Jack the Ripper, Lighthearted Friend with the central premise that Jack the Ripper, the unknown serial killer who murdered eleven East London prostitutes, was none other than Rev. Charles Dodgson, also known as Lewis Carroll. What proof did he have? Anagrams. Here is a representative sample of Wallace's handiwork. He considered the following sentence, from The Nursery Alice , an abridged version of Alice in Wonderland that Carroll wrote for very young readers. So she wandered away through the wood, carrying the ugly little thing with her. And a great job it was to keep hold of it, it wriggled about so. But at last she found out that the proper way was to keep tight hold of its foot and its right ear. Apparently, after dropping a few letters and switching a couple of vowels, this is an anagram of (drumroll): She wriggled about so! But at last Dodgson and Bayne found a way to keep hold of the fat little whore. I got a tight hold of her and slit her throat, left to right. It was tough, wet, disgusting, too. So weary of it, they threw up Jack the Ripper. The book did create a bit of a stir, because some people will believe anything a seriouslooking man in a seriouslooking suit told them. But then something wicked happened. Francis Heaney and Guy Jacobson decided to give Wallace a taste of his own medicine. Here are the first three sentences of his book. This is my story of Jack the Ripper, the man behind Britain's worst unsolved murders. It is a story that points to the unlikeliest of suspects: a man who wrote children's stories. That man is Charles Dodgson, better known as Lewis Carroll, author of such beloved books as Alice in Wonderland. And here is the anagram of those three sentences that Heaney and Jacobson came up with. No dropping letters, no changing vowels. As clean as anagrams get. The truth is this: I, Richard Wallace, stabbed and killed a muted Nicole Brown in cold blood, severing her throat with my trusty shiv's strokes. I set up Orenthal James Simpson,who is utterly innocent of this murder. P.S. I also wrote Shakespeare's sonnets, and a lot of Francis Bacon's works too. Epic win. Written 11 Apr . 8.9k views. What is the toughest problem ever asked in an IMO? Sujith Vijay , Combinatorial number theorist 164 upvotes by Alon Amit (PhD in Mathematics; Mathcircler.), Michal Forišek (Ph. D. in theoretical Computer Science), Anurag Bishnoi (Ph.D. student in Mathematics at Ghent University.), (more) I vote for Problem 6, IMO 1988 . Let and be positive integers such that . Show that must be a perfect square. Niven, Zuckerman and Montgomery, in their infinite wisdom, have added this problem a doublestarred exercise in Section 1.2 (Divisibility) of their textbook An Introduction to the Theory of Numbers . The problem has a chequered history, narrated among other places in Arthur Engel's ProblemSolving Strategies . This problem was submitted in 1988 by West Germany. None of the six members of the Australian problem committee could solve it. Two of the members were George and Esther Szekeres, both famous problem solvers and problem creators. Since it was a numbertheoretic problem, it was sent to the four most renowned Australian number theorists. They were asked to work on it for six hours. None of them could solve it in this time. The problem committee submitted it to the jury of the XXIX IMO marked with a double asterisk, which meant a superhard problem, possibly too hard to pose. After a long discussion, the jury finally had the courage to choose it as the last problem of the competition. Eleven students gave perfect solutions. Among the eleven contestants who answered the problem correctly were Fields Medallist Ngo Bao Chau and Putnam Fellow Ravi Vakil . Among the many who scored 1 point out of 7 were Fields Medallist Terence Tao (who was, after all, only 13 years old) and Putnam Fellow Jordan Ellenberg , who had perfect scores in 1987 and 1989. H.L. Mencken once said, " For every complex problem, there is a solution that is clear, simple and wrong. " If you try small cases, you will observe that the first few pairs the hypothesis of the statement are all of the form that satisfy or vice versa. We call these the trivial solutions, as the statement clearly holds for such pairs . If somehow it can be shown that the only solutions are the trivial ones, then we are done. But any such proof will be wrong. For example, is a nontrivial solution. The far more intricate approach that actually works builds on this, showing that every positive integer that is of the form is also of the form where is a trivial solution. Updated 3 May . 14k views. Why is the 90’s sitcom Friends so popular amongst Indian quora members? Sujith Vijay , Nerdenabler 155 upvotes by Arjun Ravichandran , Rohan Ramakrishna , Ankit Sethi , (more) The prerequisites for enjoying Friends are minimal; it is exactly the sort of "chewing gum for the eyes" that Frank Lloyd Wright was talking about when he described television in general. Appreciating Simpsons requires solid understanding of American pop culture. Appreciating Seinfeld requires firsthand experience of the New York brand of neuroticism. Appreciating Arrested Development requires benevolent tolerance of the boundaries of humour in the context of family ties. Friends is just the path of least resistance. It is the cotton candy of American comedy. Updated 19 Oct, 2014 . 5.3k views. What are some of the most ridiculous proofs in mathematics? Sujith Vijay , Combinatorial number theorist 93 upvotes by David Joyce (Professor of Mathematics at Clark University), Anurag Bishnoi (Ph.D. student in Mathematics at Ghent University.), Archit Sachdeva , (more) We will prove that for all . We say that a permutation of the set is exciting if each entry is the highest number so far, or the lowest number so far. For example, the permutation (2,1,3) is exciting because 2 is a new high, 1 is a new low, and 3 is a new high. However, the permutation (1,3,2) is not exciting because 2 is neither a new high nor a new low. How many permutations of the set are exciting? Well, the last entry of an exciting permutation has to be 1 or n. In the former case, the remaining numbers must form an exciting permutation of , and in the latter case, the remaining numbers must form an exciting permutation of . This gives the following recurrence relation. Let permutations of that there are denote the number of exciting . Then and exciting permutations of . It follows . So the number of permutations that are not exciting is . Since this is a nonnegative integer, it follows that for all . This is the long proof. The short proof is left as an exercise for the reader. Updated 13 Mar . 9.6k views. How can I factorize ? Sujith Vijay , Combinatorial number theorist 73 upvotes by Igor Markov (MA in Mathematics, PhD in CS), David Joyce (Professor of Mathematics at Clark University), Sushruth Muralidharan , (more) Put . You get . And that's decimal, not binary. Now how do you factorise that? Well, it is . Or . Aha! So it is a multiple of . . Of course, is really , and is really . Thus the factors are and Multiply the two, and you get . . At this point, the solution is as rigorous as any. Could be factorised further? Suppose where has degree and has degree . Then . Define and has at most real roots and . Since has at most real roots, it follows that . ● Any integer such that ● ● Any integer such that contributes to . is prime contributes to Now . . It follows that Don't try this at school. Updated 2 Jan . 4.1k views. cannot be factorised further. Srinivasa Ramanujan: Ramanujan got only 57% in Mathematics in his First Examination of the Arts (FA Exam). Yet he is still a genius in Mathematics. How is this possible? Sujith Vijay , Combinatorial number theorist 53 upvotes by David Joyce (Professor of Mathematics at Clark University), Anurag Bishnoi (Ph.D. student in Mathematics at Ghent University.), Daniel McLaury (Ph.D. Student in Mathematics at University of Illinois), (more) This may sound blasphemous, but evidence for the breadth of Ramanujan's mathematical acumen is tenuous at best. As Hardy himself said, " The limitations of his knowledge were as startling as its profundity. " In particular, his ideas of what constituted a proof were quite unorthodox, especially before he started working with Hardy and Littlewood. Here is the question paper of the FA Exam that Ramanujan took in 1907. http://www.math.uiuc.edu/~berndt... The geometry section (Page 10) looks formidable, especially if you're expected to do all that in 3 hours. Grade inflation is a fairly recent phenomeon; it is quite possible that 57% was among the highest scores in this paper. Updated 3 May . 6.5k views. Why do apparently intelligent people waste their time, and others’, by “proving” that the sum of all positive natural numbers equals 1/12, when simple logic dictates that their proof is wrong? Sujith Vijay , Numb and numberer. 26 upvotes by Anurag Bishnoi (Ph.D. student in Mathematics at Ghent University.), Paul Olaru , Phani Raj , (more) Think of it this way. We have a new notion — let us call it hypersum — that agrees with the conventional sum for finite sequences and convergent series, and assigns real values to divergent series in a manner that is far from arbitrary. It is a bit like extending logarithms to negative numbers. What does it mean to multiply by itself times and get as the answer? Physically, not much. But there will hardly be any complex analysis without Euler's formula. And complex analysis helps us count the number of primes up to in an asymptotic sense, which is as concrete as it gets. Most collegelevel undergraduates find modern physics far more exciting than modern mathematics because the former often challenges their intuition in bizarre ways. If a few young people get excited by the possibility of a method behind the madness of , I think it is a great thing. The soul of a good joke is often status inversion, and what could be a better example of status inversion than the sum of infinitely many positive integers turning out to be a negative fraction? Updated 21 Mar . 2.2k views. Physical Chemistry: If we can already make diamonds, why can’t we make gold yet? Is it just a matter of time? Sujith Vijay , Been there, done that. 26 upvotes by Phani Raj , Quora User, Shreyas Bhatevara , (more) When I was twelve, I wrapped a copper wire in a tin foil, placed it on a sheet of paper and set it on fire. Because, you know, atomic number of tin + atomic number of copper = atomic number of gold. It didn't work. I decided I would rather study mathematics than chemistry, because 50 + 29 was still equal to 79. No regrets. Written 19 Jan . 2.9k views. What are the most philosophical cartoons? Sujith Vijay , Philo Ed costs an arm and a chair. 25 upvotes by Phani Raj , Ashish Gupta , Indu Priya , (more) Saturday Morning Breakfast Cereal had a great one on Prisoner's Dilemma and the Tragedy of the Commons . Written 4 May . 1.2k views. What are some of the best Calvin and Hobbes cartoons? Sujith Vijay , Lives on comics and comestibles. 25 upvotes by Quora User, Quora User, Hari Kumar Jayan , (more) In which Tracer Bullet tracks down Mr. Billion. Written 6 Jan . 494 views. Are there any “deceptive” mathematical functions or algorithms? Sujith Vijay , Numb and numberer. 24 upvotes by Vivek Nagarajan , Sujit Menon , Phani Raj , (more) There is a nice example, first observed by Richard Guy, as far as I know. Let Here are the first ten values of OMG! The Fibonacci sequence! Right? Wrong. . Written 1 Dec . 1.4k views. What are the most common English grammatical errors made by people from India? Sujith Vijay , Nerdenabler 23 upvotes by Quora User, Venkateswar Jayanthy , Shivv Tiwari , (more) Several common howlers were compiled by Nissim Ezekiel in his famous poem Goodbye Party for Miss Pushpa T.S. Friends, Our dear sister is departing for foreign in two three days, and we are meeting today to wish her bon voyage. You are all knowing, friends, what sweetness is in Miss Pushpa. I don't mean only external sweetness but internal sweetness. Miss Pushpa is smiling and smiling even for no reason but simply because she is feeling. Miss Pushpa is coming from very high family. Her father was renowned advocate in Bulsar or Surat, I am not remembering now which place. Surat? Ah, yes, once only I stayed in Surat with family members of my uncle's very old friend, his wife was cooking nicely… that was long time ago. Coming back to Miss Pushpa she is most popular lady with men also and ladies also. Whenever I asked her to do anything, she was saying, 'just now only I will do it.' That is showing good spirit. I am always appreciating the good spirit. Pushpa Miss is never saying no. Whatever I or anybody is asking She is always saying yes, And today she is going to improve her prospect and we are wishing her bon voyage. Now I ask other speakers to speak and afterwards Miss Pushpa will do summing up. Updated 5 May . 3.5k views. What makes Kurt Vonnegut such an outstanding satirist? Sujith Vijay , in Soviet Russia, books read you. 22 upvotes by Phani Raj , Sayantan Sen , L. Lawliet , (more) Most satirists, from Jonathan Swift to Jerome Salinger and nearly everyone in between, have been misanthropes. Kurt Vonnegut, on the other hand, was a humanist who cared deeply about people. His writing was shaped and informed by his life as a soldier in the Second World War, as a graduate student in anthropology, and as an admirer of the great socialist politician Eugene Debs from his native Indiana. Here are three quotes from his books that may illustrate this point. I think about my education sometimes. I went to the University of Chicago for a while after the Second World War. I was a student in the Department of Anthropology. At that time they were teaching that there was absolutely no difference between anybody. They may be teaching that still. Another thing they taught was that no one was ridiculous or bad or disgusting. Shortly before my father died, he said to me, ‘You know – you never wrote a story with a villain in it.’ I told him that was one of the things I learned in college after the war. Slaughterhouse Five You might just learn something when you're in a mood to learn something. The only thing I ever learned was that some people are lucky and other people aren't and not even a graduate of the Harvard Business School can say why. The Sirens of Titan Then again, I am a monopolar depressive descended from monopolar depressives. That's how come I write so good. Timequake Updated 1 May . 2k views. Is “fortress” the feminine form of “fort” in some sense? Sujith Vijay , Up, up and a way with words. 22 upvotes by Quora User, Tim Hofstetter , Liam Donovan , (more) No, and neither is buttress. Written 12 Oct, 2014 . 758 views. Why do my math teachers get annoyed with me when I explain to them that I have OCD and will only write in base 13? Sujith Vijay , mathematician 21 upvotes by Anonymous, Milan Karia , Rahul Dewani , (more) Since 13 is prime, the O nly C ommon D ivisor of 13 and 10 is 1. And that will likely be your marks out of 10 if you insist on doing this your way. Written 5 May . 2.1k views. What are some of the most creative metaphors you’ve encountered in a novel? Sujith Vijay , Biblio Baggins 21 upvotes by Quora User, Amit Sharma , Quora User, (more) "No words had been exchanged between Upjohn and self on the journey out, but the glimpses I had caught of his face from the corner of his eye had told me that he was grim and resolute, his supply of the milk of human kindness plainly short by several gallons. " P. G. Wodehouse, Jeeves in the Offing Written 4 Feb . 2.3k views. Why do South Indians pronounce words starting with ‘h’ incorrectly? Sujith Vijay , Nerdenabler 20 upvotes by Quora User, Ganesh Prasadh Kidambi , Anonymous, (more) You'll be surprised how wide the web of the 'haitch' speakers extends. The fraction of South Indians who are haitchhikers may be higher than the corresponding fraction of North Indians, but these are relatively insignificant. The Great Battle of Haitch and Aitch is not fought along the corridors of the subcontinental dialect, but right at the altar of the Queen's English. The English have a view, naturally the Irish have the opposing view, and as usual the Scots and the Welsh have their opinions about the whole thing too. David McKie had written a delightful article on this in The Guardian a few years ago, appended below in full. The other day I rang a public library and asked if they had any files on a man called William Black. "Would that be William Haitch Black?" the librarian asked after due investigation. It might, and it might not, I was tempted to say; certainly he himself would have preferred William Aitch. But that would have been insufferably pedantic; so I meekly agreed. Later, on a train down from Scotland, the restaurant car, we kept being told, was located in "Carriage Haitch". And my granddaughter tells me that when she used "aitch" at school, one of her teachers insisted that the right way to say it was "haitch". All the dictionaries in my house agree that aitch is correct. One authority, bearing the mighty imprimaturs of both Oxford University and the BBC, concedes that haitch is standard practice in Ireland but rules it out on this side of the water. Yet it seems to me, after listening closely over the past month or two, that haitch is on the march and aitch is on the retreat. Just as the pushy aggressive grey squirrel has almost extirpated the timorous red one, so muscular abrasive haitch may have done for poor gentle aitch before long. Does that matter? Pronunciation, like all departments of language, evolves, and nowhere more so than when you deal with the letter H. In his excellent book The Adventure of English, Melvyn Bragg says there was once a primer called Poor Little H Its Use and Abuse, which ran to 40 editions. There was a time when sounding the H at the start of some word like Hackney or Hammermith was taken to be the hallmark of education, while dropping it was the 'allmark of the unschooled. Yet even among those who prided themselves on knowing how to talk proper, the correct use of H was debatable. It's customary still to drop the H at the start of words such as honour and hour, and to prefix them with an "an"; a precious few still do the same with hotel. But standard versions of the Bible preface a whole range of words, from habitation, half and hand to husband, hymn and hypocrite, with "an" rather than "a", suggesting that the dropping of H once habitually happened too. For centuries most people spoke as they pleased. The 18th century, lusting for standardisation, put a stop to all that. Among the first to lay down rules of what should and should not be done were two Scots, James Buchanan and William Johnston, and the playwright Sheridan, who was Irish. It was standard then to leave the L silent in words such as falter and vault, while failing to sound the R in a word such as lord or the H in a word such as while was reprehensible. One authority contended that only the Irish would rhyme great with state rather than seat, while another ordained with equal vehemence that only the Irish would rhyme it with seat. So would the supplanting of "aitch" by "haitch" really matter? In general, I'm against those who seek to steamroller diversity out of the language, but oddly enough I think it might. The way a word begins helps define the image of what it portrays. That's why so many words of abuse begin with a B, and why a word such as spit sounds so repelling as in Auden's threat to those who might be tempted to trespass into his private domain: "I have no gun, but I can spit." Aitch suggests something amenable, affable, amicable, where haitch is harder, harsher, more hostile. Aitch P Sauce, I think, may be expected to seep more gently and cooperatively out of the bottle than the possibly balky and truculent Haitch P Sauce. Haitch G Wells sounds to me a more aggressive man, and writer, than Aitch G Wells. An Aitch R Aitch might be expected to proffer a limp regal handshake, where Haitch R Haitch sounds more apt for trouble in nightclubs and service in Iraq. Likewise I'd expect a more compassionate welcome from the N Aitch S than I would from the N Haitch S a form that sounds the more unsettling because it also suggests the word "hitch". It's notable, though, that even aggressive haitchers will still use the gentler form when it's a middle initial. A former nurse, from Wiltshire, not Ireland, to whom I was talking this week, though in all other senses a committed haitcher, referred throughout to the N Aitch S or rather, as we all tend to do, to the N A Chess. Long may this reassuring practice continue. Updated 2 May . 1.7k views. What is the expected number of coin flips until you get two heads in a row? Sujith Vijay , Ramsey theorist 19 upvotes by Sayantan Sen , Phani Raj , Maruti Sridhar , (more) Let be the expected number of coin flips until you get heads in a row. In the world of Micawber, where happiness is just around the corner, In the world of Murphy, where anything that can go wrong will go wrong, (If that line bothers you, try deriving from it. ) In the world of Mathematics, where God plays dice with Micawber and Murphy, Simplifying, . Since . In particular, , it follows that and . Written 3 Apr . 2.8k views. Can you identify this game from the picture? What are its rules? Sujith Vijay , Nerdenabler 19 upvotes by Quora User, Shashank Sharma , Virang Trivedi , (more) The name of the game is Peg Solitaire. It used to be marketed in India as Brainvita, presumably a jocular reference to Bournvita, who were the sponsors of the most prestigious high school quiz contest at the time. The wellknown gametheorist John Beasley wrote a famous book on this game and its variants titled The Ins and Outs of Peg Solitaire , widely considered one of the classics in the field . The game begins with 32 of the 33 slots occupied, and the centre unoccupied. In each move, a marble is moved to an empty position two units horizontally or vertically away from the current position, provided there is a marble between the starting and ending positions. The marble in the middle is then removed from the game. So if x is an occupied slot and o is an empty slot, each move changes the local configuration from xxo to oox. The game ends when no more moves can be made. The game ends with fist pumps and great rejoicing when only one marble is left in the central slot, as this is how the player wins. Like many other things, mathematicians have taken this game way too seriously. See, for example: http://home.comcast.net/~gibell/... Updated 17 Oct, 2014 . 1.4k views. What are the best / most humorous Dilbert cartoons? Sujith Vijay , Lives on comics and comestibles. 18 upvotes by Gilles Reynaud , Paul deHolczer , Viola Yee , (more) The technology may be obsolete but the joke is funny as ever. Updated 4 May . 599 views. What is the most profound yet short/brief sentence, phrase, motto, nugget of wisdom, aphorism, epigram, quote you’ve ever heard or read? And why? Sujith Vijay , Nerdenabler 18 upvotes by Quora User, Waqar Hamza , Tijana Koljozova , (more) " One machine can do the work of fifty ordinary men. No machine can do the work of one extraordinary man. " Elbert Hubbard Updated 1 May, 2015 . 1.1k views. What are some mathematical or scientific proofs that were introduced in the last twenty years that hold a great significance, like the Pythagoras theorem or the NavierStokes equation did when they were introduced? Sujith Vijay , Combinatorial number theorist 16 upvotes by Anurag Bishnoi (Ph.D. student in Mathematics at Ghent University.), Phani Raj , Sushruth Muralidharan , (more) I am tempted to extend the domain from 20 years to 40 years, which would allow such gems as the Szemeredi regularity lemma , Khachiyan's ellipsoid algorithm for linear programming and the PCP theorem , but I presume the formulation was deliberately designed to eschew the granddaddy of them all, namely the proof of Fermat's Last Theorem by Wiles and Taylor. So let me not do that. Having said that, Irit Dinur's new and much more accessible proof of the PCP theorem is indeed within the last 20 years, so here is a link to what the theorem is all about. http://courses.cs.washington.edu... One of the holy grails of computational number theory and theoretical computer science was a deterministic polynomialtime algorithm for testing whether an integer is prime. Manindra Agarwal, Neeraj Kayal and Nitin Saxena of IIT Kanpur devised such an algorithm in 2002, winning the Godel Prize and the Fulkerson Prize, among others. In terms of technique, one of the most revolutionary results in recent memory is due to Daniel Goldston, Janos Pintz and Cem Yildirim . They showed that, for every infinitely many n such that , there exist where denotes the prime. There is an interesting story behind this, very similar to Fermat's Last Theorem. The original result was announced by Goldston and Yildirim in 2003 and had to be retracted due to "a bug in the remainder term". But techniques in this nonpaper were good enough for Ben Green and Terence Tao to show that there are arbitrarily long arithmetic progressions in the sequence of primes, settling a question that was open for more than two centuries. (Indeed, it is the sort of question even Euclid could have asked, except there is no record that he did.) Goldston and Yildirim, along with Pintz, were able to patch the proof by 2005, and this formed the backbone of the sensational result by Yitang Zhang in 2013 that there are infinitely many pairs of primes that differ by 70 million or less. (Thanks to the Polymath Army, the 70 million has now come down to 246.) And this is just number theory and complexity theory. There are many other groundbreaking results in other branches of mathematics, most notably Grisha Perelman's proof of the Poincare conjecture . Written 30 Jan . 1.2k views. Asked to answer by Sushruth Muralidharan . What is the dark side of being intelligent? Sujith Vijay , no spit, Hemlock 16 upvotes by Patrick Diamond , Phani Raj , Sayantan Sen , (more) As Adrian Monk would say, it is a gift and a curse. Voltaire has addressed this in his Story of the Good Brahmin. Appended is a paraphrase, as quoted by Will Durant in The Story of Philosophy. "I wish I had never been born!" the Brahmin remarked. "Why so?" said I. "Because," he replied, "I have been studying these forty years, and I find that it has been so much time lost... I believe that I am composed of matter, but I have never been able to satisfy myself what it is that produces thought. I am even ignorant whether my understanding is a simple faculty like that of walking or digesting, or if I think with my head in the same manner as I take hold of a thing with my hands... I talk a great deal, and when I have done speaking I remain confounded and ashamed of what I have said." The same day I had a conversation with an old woman, his neighbor. I asked her if she had ever been unhappy for not understanding how her soul was made. She did not even comprehend my question. She had not, for the briefest moment in her life, had a thought about these subjects with which the good Brahmin had so tormented himself. She believed in the bottom of her heart in the metamorphoses of Vishnu, and provided she could get some of the sacred water of the Ganges in which to make her ablutions, she thought herself the happiest of women. Struck with the happiness of this poor creature, I returned to my philosopher, whom I thus addressed: "Are you not ashamed to be thus miserable when, not fifty yards from you, there is an old automaton who thinks of nothing and lives contented?" "You are right," he replied. "I have said to myself a thousand times that I should be happy if I were but as ignorant as my old neighbor; and yet it is a happiness which I do not desire." This reply of the Brahmin made a greater impression on me than anything that had passed. Updated Apr 15, 2015 . 2.1k views. How many times do I have to roll a die to roll the same number six times in a row? Sujith Vijay , Combinatorial number theorist 15 upvotes by Fernando Montes , Sayantan Sen , Victoria Grace , (more) Let be the expected number of rolls until you get the same number On the roll after you get the same number with probability times in a row. times in a row, you either get or start over with probability in a row . Rearranging, . Since . In particular, , it follows that . Written 3 Apr . 1.4k views. What are some interesting facts about India? Sujith Vijay , MHA critic; MEA crusader. 15 upvotes by Krishna Vijay , Monika Mundhara , Kushal Shrinivas , (more) The number of Indian quora users named Amit Kumar is larger than the population of Christmas Island. Updated 10 Apr . 980 views. What are some of the most mindblowing facts? Sujith Vijay , Nerdenabler 15 upvotes by Ashwini Anvekar , Quora User, Paul Fraynt , (more) John Adams and Thomas Jefferson, the second and third presidents of the United States and also the first two vicepresidents, both died on 4th July, 1826, the fiftieth anniversary of American independence. Adams was unaware that Jefferson had died earlier that day, and his last words were "Thomas Jefferson still survives." Written 2 Jan . 884 views. What is the most beautiful theorem proof and why? Sujith Vijay , Combinatorial number theorist 15 upvotes by Anurag Bishnoi (Ph.D. student in Mathematics at Ghent University.), Paul Olaru , Bassam Karzeddin , (more) I nominate the following proof of Ramsey's theorem from the celebrated essay The Two Cultures of Mathematics by Fields Medallist Timothy Gowers . Theorem : If the edges of the complete graph on then there must be Proof : Let ordered. Let vertices such that all edges joining them have the same colour. be a graph with vertices, and let us suppose that the vertices are totally be the first vertex. Then by the pigeonhole principle, there is a set of vertices of size at least Now let vertices are coloured either red or blue, such that every edge from be the least vertex of to has the same colour. . By the pigeonhole principle again there is a set of size at least such that every edge from colour. Continuing this process, we obtain a sequence sequence edge from for every , and every has the same colour. It follows that the colour of the edge joining depends only on a subset has the same of vertices and a of sets such that to to of to . By the pigeonhole principle again, we can therefore find of size at least same, so that all edges joining vertices in such that this colour is always the have the same colour. Fame, fortune and a Fulkerson Prize awaits anyone who can replace by . Updated 15 Apr . 3.5k views. What are some things that mathematics students know that others don’t? Sujith Vijay , Combinatorial number theorist 15 upvotes by Anurag Bishnoi (Ph.D. student in Mathematics at Ghent University.), Raksha Partha , Abhishek Sharma , (more) ● ● ● There are infinitely many primes ending in . Let A, B, C, D and E be any five points in the plane. It is impossible to join all ten pairs of these points using lines or curves, without at least two of them crossing each other. And now for something completely different: ● ● The smallest prime ending in is . Let A, B, C, D, E, F and G be any seven points on the surface of a doughnut. It is possible to join all 21 pairs of these points using curves, without any of them crossing each other. ● Updated 15 Mar . 2.3k views. Talent: What are some examples of people who possess extraordinary human abilities? Sujith Vijay , Nerdenabler 15 upvotes by Quora User, Quora User, Ismail Sunni , (more) I nominate tenyearold Truman Henry Safford. “Multiply in your head," ordered the compassionate Dr. Adams 365,365,365,365,365,365 by 365,365,365,365,365,365 ". He (tenyearold Truman Henry Safford) flew around the room like a top, pulled his pantaloons over the tops of his boots, bit his hands, rolled his eyes in their sockets, sometimes smiling and talking, and then seeming to be in an agony, until, in not more than one minute, said he, 133,491,850,208,566,925,016,658,299,941,583,225 . An electronic computer might do the job a little faster but it wouldn't be as much fun to watch. James R. Newman, The World of Mathematics Written 5 May . 1.7k views. What are the most timeless xkcd comics? Sujith Vijay , Lives on comics and comestibles. 15 upvotes by Quora User, Varun Subramanian , Neeraj Mangalanandan , (more) For a choir performance, check out: https://www.youtube.com/watch?v=seGpYa8UO0E Written 30 Sep, 2014 . 1.9k views. Is “Bros before Hoes” offensive? Sujith Vijay , Nerdenabler 14 upvotes by Shitij Chadha , Quora User, Quora User, (more) There is much misunderstanding about the origins of this phrase. Captain Lemuel Gulliver, after his famous voyage to the islands of Lilliput and Blefuscu, was looking for new lands and new people to befriend and comprehend. Options were numerous Laputa, Balnibarbi, Luggnagg, Glubbdubdrib and Japan, among others. But there were two cultures that stood out to him the tall, athletic Brobdingnagians with a penchant for rhyme; and the calm, serene Houyhnhnms with a refreshingly novel worldview despite some anatomical differences. Gulliver could not decide which of these to visit first. He thought about it for a while and said, with a shrug, "Oh what the hell. Bros before Hos." Written 5 Nov, 2014 . 1.1k views. What are some of the best quiz questions you’ve seen? Sujith Vijay , Nerdenabler 14 upvotes by Aditya Pappula , Shubham Dixit , Pranshu Bhatnagar , (more) Many of my favourite questions have turned out to be urban legends, like Heisenberg's epitaph and Joseph Meister's confrontation with the Nazis. But here are a few I remember from my college days at IIT Delhi. Some of these are folklore now and may have been folklore then, so I hesitate to give attributions. The last one is entirely my fault, and elicited a " You may be a highly respected senior quizzer, but if you ask another one of those, we are going to pick you up and give you bumps right here, right now!" response from an otherwise peaceful guy. 1. A Treatise on the Binomial Theorem and The Dynamics of an Asteroid are the works of which English mathematician? http://www.wolframalpha.com/inpu... 2. Who is the only bowler in the history of first class cricket to take ten wickets in an innings, all cleanbowled? http://www.wolframalpha.com/inpu... 3. One of the earliest legends in the history of rock and roll, his name has now become synonymous with futility. He has been immortalised in the title of a work by Albert Camus. Who are we talking about? http://www.wolframalpha.com/inpu... Written 26 Dec . 3.2k views. Asked to answer by Sushruth Muralidharan . Are there organizations that do research in Mathematics like CERN in physics? Sujith Vijay , Nerdenabler 14 upvotes by Anurag Bishnoi (Ph.D. student in Mathematics at Ghent University.), Wesam Adel , Quora User, (more) Yes, plenty of them. Some of the most wellknown names are the Institute for Advanced Study , Princeton that has housed such giants as Kurt Godel, John von Neumann, Harish Chandra and Enrico Bombieri; the Isaac Newton Institute , Cambridge where Andrew Wiles announced his proof of Fermat's Last Theorem; and the Institut des Hautes Etudes Scientifique , Paris that gained a little notoriety when they lost Alexander Grothendieck after accepting funding from military sources. I should also mention the Pacific Institute for the Mathematical Sciences , Canada and Mathematisches Forschungsinstitut , Oberwolfach (Germany) that organise several workshops bringing mathematicians together for collaborative projects. In addition, there are 22 research institutes under the umbrella of the European Research Consortium for Informatics and Mathematics (most notably INRIA, CWI and SZTAKI), as well as nonprofit and corporatesponsored research institutes like Clay Mathematics Institute , Microsoft Research and IBM Research . The erstwhile Bell Labs and the Rand Corporation also did some fantastic work in combinatorics, theoretical computer science and mathematical economics back in the day. Written 5 Apr . 1.3k views. Asked to answer by Anurag Bishnoi . What are the best chess quotes? Sujith Vijay , quote, an = opposite quote. 14 upvotes by Nisarg Bhatt , Rohit Shinde , Raja Sampath , (more) Here is an excerpt from the autobiography of the immortal Mikhail Tal on what goes inside his stupendous mind in the middle of a game: "I will never forget my game with GM Vasiukov in one of the USSR Championships. We reached a very complicated position where I was intending to sacrifice a knight. The sacrifice was not obvious; there was a large number of possible variations; but when I began to study hard and work through them, I found to my horror that nothing would come of it. Ideas piled up one after another. I would transport a subtle reply by my opponent, which worked in one case, to another situation where it would naturally prove to be quite useless. As a result my head became filled with a completely chaotic pile of all sorts of moves, and the infamous "tree of variations", from which the chess trainers recommend that you cut off the small branches, which in this case spread with unbelievable rapidity. And then suddenly, for some reason, I remembered the classic couplet by Korney Ivanovich Chukovsky: "Oh, what a difficult job it was To drag out of the marsh the hippopotamus". I do not know from what associations the hippopotamus got into the chess board, but although the spectators were convinced that I was continuing to study the position, I, despite my humanitarian education, was trying at this time to work out: just how would y ou drag a hippopotamus out of the marsh? I remember how jacks figured in my thoughts, as well as levers, helicopters, and even a rope ladder. After a lengthy consideration I admitted defeat as an engineer, and thought spitefully to myself: "Well, just let it drown!" And suddenly the hippopotamus disappeared. Went right off the chessboard just as he had come on ... of his own accord! And straightaway the position did not appear to be so complicated. Now I somehow realized that it was not possible to calculate all the variations, and that the knight sacrifice was, by its very nature, purely intuitive. And since it promised an interesting game, I could not refrain from making it. And the following day, it was with pleasure that I read in the paper how Mikhail Tal, after carefully thinking over the position for 40 minutes, made an accurately calculated piece sacrifice." Written 16 Nov . 1.2k views. What are some of the best satirical scientific papers published in peerreviewed journals? Sujith Vijay , Been there, done that. 14 upvotes by George Savva , Quora User, Robert Kaspar , (more) A classic instance is the paper by G. Beck, H. Bethe and W. Riezler that appeared in Naturwissenschaften in 1931. In the 1920s, many scientists believed that the value of the fine structure constant (the ratio of the speed of an electron in the first Bohr orbit to the speed of a photon) was exactly 1/136. (It is now known that the value is more like 1/137.036). The revered physicist Sir Arthur Eddington promptly came up with an explanation as to where the 136 came from. His insight was that to specify the entries of a 16x16 symmetric matrix, you had 16+15+...+1=136 degrees of freedom. So far so good. But soon more accurate data came in, and people started thinking it should be 1/137 and not 1/136. That is when Eddington jumped the shark and came up with a crazy workaround of his original model that essentially allowed him to add 1. This didn't go very well, even with his fans. So to poke fun at Eddington, these three great men came up with a derivation of why the absolute zero temperature was 273 degree Celsius. They started from Eddington's 137, doubled it to account for a neutron being an electron plus a proton, and subtracted 1 as if it was the most natural thing in the world. Here is the paper in its entirety. Remark on the Quantum Theory of Zero Temperature We consider a hexagonal crystal lattice. The absolute zero of this is characterised by the condition that all degrees of freedom of the system freeze, that is all internal movements of the lattice cease. An exception to this is, of course, the motion of the electron in its Bohr orbit. According to Eddington each electron possesses degrees of freedom, where is the Sommerfeld fine structure constant. Besides electrons, our crystal contains only protons, and the number of degrees of freedom for them is the same since, according to Dirac, a proton can be regarded as a hole in the electron gas. Thus, since one degree of freedom remains because of the orbital motion, in order to attain absolute zero we must remove from a substance degrees of freedom per neutron ( = 1 electron + 1 proton; since our crystal has to be electrically neutral overall). We obtain therefore for the zero temperature degrees. Setting = 273° we obtain for the value 137, which, within limits of error, agrees completely with the value obtained in an independent way. One can easily convince oneself that our result is independent of the special choice of crystal structure. Cambridge. 10 December 1930 G Beck, H Bethe, W Riezler The joke soon got out of hand, when one of the authors was asked to present a seminar on the result. That was when Eddington decided enough was enough, and pretty soon the paper was withdrawn. The erratum read as follows: "The note by G. Beck, H.Bethe and W. Riezler published in the 9 January issue of this journal, was not meant to be taken seriously. It was intended to characterise a certain class of papers in theoretical physics of recent years which are purely speculative and based on spurious numerical arguments. In a letter received by the editors from these gentlemen they express regret that the formulation they gave this idea was suited to produce misunderstandings." A true "Charlie bit my finger again!" moment. Updated 28 Oct, 2014 . 941 views. What are some good math jokes? Sujith Vijay , Combinatorial number theorist 13 upvotes by David Joyce (Professor of Mathematics at Clark University), Jens Adler Nielsen , Vignesh Ramakrishnan , (more) From the 'truth is funnier than fiction' department: Enrico Bombieri, winner of the Fields Medal in 1974 and Roger Apery, who took the mathematical world by storm with his proof of the irrationality of (the sum of reciprocals of cubes of the positive integers) were having dinner at a conference in Canada. Bombieri suggested the following variation of Fermat's Last Theorem to Apery: To show that the equation has no nontrivial solutions for and . Bombieri was greeted next morning at the breakfast table by a beaming Apery who announced that was, in fact, a solution. Without batting an eyelid, Bombieri replied, "I said nontrivial." Written 7 Mar . 1.2k views. Does quantum mechanics say that I could be on Mars tomorrow if all of my electrons suddenly shifted? Sujith Vijay , Nerdenabler 13 upvotes by Christopher Reiss , Quora User, Danny Beissinger , (more) You are going to need the Infinite Improbability Generator , described in The Hitchhiker's Guide to the Galaxy by Douglas Adams. The principle of generating small amounts of finite improbability by simply hooking the logic circuits of a Bambleweeny 57 SubMeson Brain to an atomic vector plotter suspended in a strong Brownian Motion producer (say a nice hot cup of tea) were of course well understood and such generators were often used to break the ice at parties by making all the molecules in the hostess's undergarments leap simultaneously one foot to the left, in accordance with the Theory of Indeterminacy. Many respectable physicists said that they weren't going to stand for this partly because it was a debasement of science, but mostly because they didn't get invited to those sort of parties. Another thing they couldn't stand was the perpetual failure they encountered in trying to construct a machine which could generate the infinite improbability field needed to flip a spaceship across the mindparalysing distances between the furthest stars, and in the end they grumpily announced that such a machine was virtually impossible. Then, one day, a student who had been left to sweep up the lab after a particularly unsuccessful party found himself reasoning this way: If, he thought to himself, such a machine is a virtual impossibility, then it must logically be a finite improbability. So all I have to do in order to make one is to work out exactly how improbable it is, feed that figure into the finite improbability generator, give it a fresh cup of really hot tea ... and turn it on! He did this, and was rather startled to discover that he had managed to create the long sought after golden Infinite Improbability generator out of thin air. It startled him even more when just after he was awarded the Galactic Institute's Prize for Extreme Cleverness he got lynched by a rampaging mob of respectable physicists who had finally realized that the one thing they really couldn't stand was a smartass. Updated 9 Apr . 841 views. What is the truth about vaccinations? Sujith Vijay , Nerdenabler 12 upvotes by John Z Zitzelberger , Mike Barnard , Miguel Valdespino , (more) The most common adverse effect of vaccination is anaphylaxis (serious allergic reaction). The frequency of incidence varies with the type of vaccine (HPV/MMR/Chickenpox/Influenza) but is less than 1 in 38,000 in all cases. Additionally, the chickenpox vaccine has been implicated in vaccine strain viral reactivation, but the incidence of serious adverse events (e.g: meningitis) is less than 1 in 34,000. Studies show that the swine flu vaccination of 2009 in the United States caused GuillainBarre syndrome at the rate of 1 in 600,000 cases. A good summary of the current scientific consensus on what illnesses could be caused and not caused by vaccines can be found here. http://www.hrsa.gov/vaccinecompe... According to the National Oceanic and Atmospheric Administration (NOAA), the lifetime odds of a person living in the United States getting struck by lightning is 1 in 12,000. http://www.lightningsafety.noaa.... This is the sort of risk one just has to live with. Written Feb 5, 2015 . 1.2k views. Is Mathematics an absolute truth? Sujith Vijay , no spit, Hemlock 11 upvotes by Terry Drinkwater , Suzanne Baran , Peter Flom , (more) Here are three great quotes by three great mathematicians. 317 is a prime, not because we think so, or because our minds are shaped in one way rather than another, but because it is, because mathematical reality is built that way. G. H. Hardy Young man, in mathematics you don't understand things. You just get used to them. John von Neumann God exists because mathematics is consistent, and devil exists because we can't prove it. Andre Weil Updated 24 Mar . 1.7k views. What are some unsolved problems in math which seem easy at first glance? Sujith Vijay , Numb and numberer. 11 upvotes by Aidan Rocke , Arka Karmakar , Sannidhya Sandheer , (more) Let denote the fractional part of and so on. . Thus , , There is absolutely no reason to believe that has a limit as approaches infinity. Yet no one has been able to disprove the existence of a limit , and people have tried since the days of Littlewood. Of course, if is replaced by the golden ratio, then the limit exists and is equal to zero. Indeed, large powers of the golden ratio are very close to Lucas numbers. But the golden ratio is an algebraic number, whereas is transcendental. That should make all the difference, but so far nobody has succeeded in putting that fact to good work. Written 3 May . 2.4k views. What are some long unproved mathematical conjectures that were finally proven in 2013? Sujith Vijay , Combinatorial number theorist 11 upvotes by Anurag Bishnoi (Ph.D. student in Mathematics at Ghent University.), Alon Amit (PhD in Mathematics; Mathcircler.), Obinna Okechukwu , (more) Related to their work on the KadisonSinger conjecture, but of independent interest, is the construction of an infinite family of dregular Ramanujan graphs for all d > 2 by Adam Marcus, Daniel Spielman and Nikhil Srivastava, proving a conjecture of Bilu and Linial. This won a best paper award at FOCS. http://www.cs.yale.edu/homes/spi... But yes, Yitang Zhang's big step towards the resolution of the twin prime conjecture takes the cake. Natural barriers for this line of attack for gaps less than 16 notwithstanding, it is arguably the most exciting result in number theory since the GreenTao theorem. And what a Cinderella story! Written 26 Dec . 933 views. Asked to answer by Sushruth Muralidharan . Are all Nobel Prize winner books sad? Sujith Vijay , in Soviet Russia, books read you. 11 upvotes by Amir All , L. Lawliet , John James Morton , (more) The Nobel Prize for Literature in 1907 was not exactly awarded to How The Camel Got His Hump , but the Swedish Academy did give it to the author of that delightful tale, an Englishman by the name of Rudyard Kipling. Many Nobel Prize winners have written funny stuff. Sample this from Elmer Gantry by Sinclair Lewis, who won the 1930 Nobel. The Maker of the universe with stars a hundred thousand lightyears apart was interested, furious, and very personal about it if a small boy played baseball on Sunday afternoon. Or this poem from Old Possum's Book of Practical Cats by T.S. Eliot, who won the 1948 Nobel. The Naming of Cats is a difficult matter, It isn't just one of your holiday games; You may think at first I'm as mad as a hatter When I tell you, a cat must have THREE DIFFERENT NAMES. First of all, there's the name that the family use daily, Such as Peter, Augustus, Alonzo or James, Such as Victor or Jonathan, George or Bill Bailey All of them sensible everyday names. There are fancier names if you think they sound sweeter, Some for the gentlemen, some for the dames: Such as Plato, Admetus, Electra, Demeter But all of them sensible everyday names. But I tell you, a cat needs a name that's particular, A name that's peculiar, and more dignified, Else how can he keep up his tail perpendicular, Or spread out his whiskers, or cherish his pride? Of names of this kind, I can give you a quorum, Such as Munkustrap, Quaxo, or Coricopat, Such as Bombalurina, or else Jellylorum Names that never belong to more than one cat. But above and beyond there's still one name left over, And that is the name that you never will guess; The name that no human research can discover But THE CAT HIMSELF KNOWS, and will never confess. When you notice a cat in profound meditation, The reason, I tell you, is always the same: His mind is engaged in a rapt contemplation Of the thought, of the thought, of the thought of his name: His ineffable effable Effanineffable Deep and inscrutable singular Name. More recently, acerbic satirists Dario Fo and Jose Saramago won backtoback Nobel Prizes in 1997 and 1998. Other names that come to mind are Bernard Shaw (1925) and Harold Pinter (2005). Written 19 Apr . 1.4k views. How do mathematicians come up with these challenging problems in mathematical olympiads (like IMO)? Sujith Vijay , UIUC Putnam Coach (20082009) 11 upvotes by Alon Amit (PhD in Mathematics; Mathcircler.), Phani Raj , Ryan Alweiss , (more) One of my favourite articles on this topic is Some Thoughts on Writing for the Putnam by Professor Bruce Reznick, who has been involved in a whopping 14 Putnam Exams in various capacities participant, member of the winning team, coach, grader, Problem Subcommittee Member and Problem Subcommittee Chair. http://www.math.uiuc.edu/~reznic... It's fairly long, but well worth the read. If you're pressed for time, just read the last section. Written 17 Nov . 1.2k views. William Golding, the author of the novel “Lord of the Flies” is the most unworthy to win the Nobel Prize for Literature in the year 1983. Do you agree? Sujith Vijay , in Soviet Russia, books read you. 11 upvotes by Quora User, L. Lawliet , Prem Neeralgimath , (more) Yes, the solitary element of a singleton set is trivially the maximum as well as the minimum. But if you're asking who the least deserving Nobel Laureate for Literature is, in my opinion it is Winston Churchill by a distance, with Bertrand Russell coming second. Churchill winning the Literature Nobel wasn't too far from Nero winning the Olympic gold. Written 30 Apr . 1.3k views. Is it possible to make 10000 out of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 using only the sum operator and using all the digits exactly once? Sujith Vijay , Nerdenabler 11 upvotes by Phani Raj , Mahesh Rao , Prathyush Kumar , (more) 2 49 +7568+31+0=10000. Written Nov 24, 2014 . 1k views. What is the maximum number of sides a polygon can have before it can be considered a circle? Sujith Vijay , Numb and numberer. 11 upvotes by Ajay Sharma , Anurag Sethi , Sasha Kowalchuk , (more) Gauss was so proud of his discovery of constructible regular polygons that he wanted a 17sided regular polygon on his tombstone. But the engraver objected, saying it would be indistinguishable from a circle. That's one culturally significant data point for you. Updated 5 Dec . 2.6k views. Why are complex numbers considered to be numbers? Sujith Vijay , mathematician 10 upvotes by David Joyce (Professor of Mathematics at Clark University), Trym Bruset , Esteban Madrigal , (more) People like closure, algebraically and otherwise. If you allow complex numbers, you don't have to be apologetic about the domain of definition of useful functions. Square root of 1? Bring it on. Logarithm of 2? Bring it on. Arc cosine of 3? Bring. It. On. Written 1 Oct, 2014 . 865 views. What is the most beautiful short passage you have read ever? Sujith Vijay , in Soviet Russia, books read you. 10 upvotes by Anant Kajle 'avdhoot' , Ashwini Jnanendra , Jayesh Jain , (more) What a lousy earth! How many winners were losers, successes failures, rich men poor men? How many wise guys were stupid? How many happy endings were unhappy endings? How many honest men were liars, brave men cowards, loyal men traitors, how many sainted men were corrupt, how many people in positions of trust had sold their souls to blackguards for petty cash, how many had never had souls? How many straightandnarrow paths were crooked paths? How many best families were worst families and how many good people were bad people? When you added them all up and then subtracted, you might be left with only the children, and perhaps with an Albert Einstein and an old violinist or sculptor somewhere. Joseph Heller, Catch22 Written 16 Oct, 2014 . 1.3k views. What are some examples of interesting literary characters that are inanimate objects? Sujith Vijay , in Soviet Russia, books read you. 10 upvotes by George Healy , Quora User, Ilana Halupovich , (more) The Hitchhiker's series has at least three memorable computers Deep Thought, Eddie and Hactar. Indeed, Douglas Adams has created plenty of other interesting inanimate characters as well. For example, the bowl of petunias that said, "Oh no, not again!" and Zem the mattress of Squornshellous Zeta that globbered, flolloped and vollued to Marvin. But my favourite inanimate literary character is not from the Hitchhiker's series. It is the flower from The Little Prince. Updated 3 Dec . 999 views. Why do you like the book 'To Kill a Mockingbird'? Sujith Vijay , in Soviet Russia, books read you. 10 upvotes by Lakshmi Geethakrishnan , Quora User, Raktim Mittra , (more) In one of my favourite scenes from the TV Series Monk , the protagonist Adrian Monk tries to explain to twoyearold Tommy Graser exactly what he does. Monk : Hello. My name is Adrian Monk. Tommy : Munch! Monk : That's right. I'm working with the police department as a consultant. Do you understand "consultant"? Natalie : Mr. Monk, he's not gonna get that. Monk : Um, an adviser. Sort of an adjunct. Stottlemeyer : Monk, I don't know what an adjunct is. Tommy : Much Monk! Yet this impossible task is what To Kill A Mockingbird accomplishes with such ease. Themes that are considered inappropriate even today to discuss in the presence of young children dominate the book, and are narrated in the voice of a precocious child. Not once does Atticus talk down to his children; not once does Harper Lee dumb down her narration. Everybody knows that children have feelings; when you read Mockingbird it hits you that they also have thoughts, and fairly sophisticated thoughts at that. Most people think of Mockingbird as a book about growing up. It is certainly that, but to me, it is also a book about parenting. Atticus Finch is an allround mensch , but his most striking attribute is that he is a sterling example of a great parent. It is no coincidence that the book ends with the sentence, " He would be there all night, and he would be there when Jem waked up in the morning. " Also intentional is the use of the ungrammatical waked to remind the reader that the entire gutwrenching story has unfolded before the eyes of an eightyearold child. Great literature is all about making brilliant mistakes, and Mockingbird makes all the right ones. But if it is action that you seek, I recommend How To Kill A Mockingbird. https://www.youtube.com/watch?v=fo45o69HaKI Updated 2 May, 2015 . 1.9k views. What are some mathematical questions that are fairly easy to state but very difficult to prove? Sujith Vijay , Combinatorial number theorist 10 upvotes by Daniel McLaury (Ph.D. Student in Mathematics at University of Illinois at Chicago), Anurag Bishnoi (Ph.D. student in Mathematics at Ghent University.), Bhargav Ram , (more) Here is a problem attributed to Paul Erdos. Find a polynomial p ( x ) such that the sums p ( x )+ p ( y ) are distinct for all pairs of positive integers x , y with x < y . p ( x )= x doesn't work. 1+4=5=2+3 . 2 2 2 p ( x )= x2 doesn't work. 12 +8 =65=4 +7 . 3 3 3 p ( x )= x3 doesn't work. 13 +12 =1729=9 +10 . 4 4 4 4 p ( x )= x4 doesn't work. 133 +134 =635318657=59 +158 . p ( x )= x5 almost certainly works. Good luck proving that! Updated Apr 7, 2015 . 1.3k views. What novels have the best opening lines or opening paragraphs? Sujith Vijay , in Soviet Russia, books read you. 10 upvotes by Chris Lo , Ilana Halupovich , Gagan Gupta , (more) It can hardly be a coincidence that no language on Earth has ever produced the expression "as pretty as an airport". Airports are ugly. Some are very ugly. Some attain a degree of ugliness that can only be the result of a special effort. This ugliness arises because airports are full of people who are tired, cross and have just discovered that their luggage has landed in Murmansk (Murmansk airport is the only exception of this otherwise infallible rule), and architects have on the whole tried to reflect this in their designs. Douglas Adams, The Long Dark Teatime of the Soul Written Mar 21, 2015 . 1.8k views. What are some of the best Peanuts cartoons? Sujith Vijay , Lives on comics and comestibles. 10 upvotes by Divya Acharya , Vinati Singh , Madhav Pola , (more) Here are three of my favourites. Written Mar 2, 2015 . 1k views. Can you summarize the plot of your favorite book with one pithy sentence? Sujith Vijay , in Soviet Russia, books read you. 10 upvotes by Ann Litz , Aditya Vivek , Marcus Ford , (more) Darkness at Noon : "You cannot build paradise with concrete." (This is a quote from the book itself, and is a perfect summary of why communism should work, but doesn't.) Written Jan 16, 2015 . 834 views.
