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Golden State and the Mathematical Magic of Seventy-Three (newyorker.com)

Posted by msmash on from the 73 dept.

Charles Bethea has written a fascinating piece on the number '73' for The New Yorker. Below are some tidbits from the story but I urge you to hit the New Yorker link and read the story in entirety there. Bethea writes: "I am aware of the Warriors's push for seventy-three wins," Ken Ono, a professor of mathematics at Emory University and the author of "The Web of Modularity: Arithmetic of the Coefficients of Modular Forms and q-series," said recently. [...] Professor Ono worked as a math consultant on a film called "The Man Who Knew Infinity," which stars Dev Patel and Jeremy Irons, and which screens this week at the Tribeca Film Festival, in New York. The movie centers on the friendship of the legendary Indian mathematician Srinivasa Ramanujan (Patel) and his Cambridge University colleague G. H. Hardy (Irons), and it depicts a famous story that Hardy once told about Ramanujan. "I remember once going to see him when he was ill at Putney," Hardy said. "I had ridden in taxicab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. "No," he replied. "It is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways." One cubed plus twelve cubed, and nine cubed plus ten cubed. This was the first of what came to be known as "taxicab numbers." [...] So what does Professor Ono think of seventy-three? "I really like the number seventy-three," he said. "It is the sixth 'emirp.'" An emirp, he explained, is a prime number that remains prime when its digits are reversed. (Emirp, of course, is 'prime' spelled backward.)

7 of 102 comments (clear)

  1. Re:Editing... by whipslash · · Score: 3, Interesting

    Fixed

  2. Base 10 by Iamthecheese · · Score: 4, Interesting

    What's so special about base 10? There are other primes in base 9 that are also prime when the digits are reversed. And base 8. Does it really provide any useful information?

    --
    If video games influenced behavior the Pac Man generation would be eating pills and running away from their problems.
    1. Re:Base 10 by ShanghaiBill · · Score: 5, Interesting

      Not to mention, at what point does a number being "interesting" stop being mathematics and start being numerology?

      There are no uninteresting numbers. Proof: Assume N is the smallest uninteresting number. That property in itself makes it interesting. Therefore there can be no smallest uninteresting number, so logically uninteresting numbers cannot exist. QED.

      I mean, are things like taxicab numbers and 'emirps' useful for anything?

      There is no requirement that mathematics be useful. Many fields of math, including non-Euclidian geometry, trans-infinite set theory, etc. were developed long before there were any applications. The Greeks and Romans had no use for zero. Some mathematicians consider it a badge of honor to work on a topic that is considered purely theoretical, and therefore useless.

    2. Re:Base 10 by BlackPignouf · · Score: 3, Interesting

      There are no uninteresting numbers. Proof: Assume N is the smallest uninteresting number. That property in itself makes it interesting. Therefore there can be no smallest uninteresting number, so logically uninteresting numbers cannot exist. QED.

      Your proof is flawed, because it cannot work recursively. What about the second smallest uninteresting number? Your argument only reduces the set of uninteresting numbers by one, and until proven otherwise, there are an infinity of uninteresting numbers.
      BTW, 12407 seems to be the smallest uninteresting number http://www.kevinhouston.net/bl..., which, as you mentioned, makes it interesting. The next smallest uninteresting number really is uninteresting, and I don't even know which one it is :)

  3. Simplest Ramanujan anecdote ... by 140Mandak262Jamuna · · Score: 4, Interesting
    The taxi cab numbers is the simplest anecdote from Ramanujan that could be told to general audience. Rest of his stuff are so far out, it is impossible to describe to even highly educated engineers. Really sad he died so young.

    But Ramanujan was never taught the process of writing down formal proofs, he self thought everything from a handbook of mathematical identities. Rediscovering several things others had already discovered and proved. He was utterly at a loss to explain how he was able to do math. He simply said, "I look at the equation or a problem. Then Goddess Namagiri Devi writes the answer in my tongue and I recite it". (not an accurate quote, paraphrased by me)

    I wish it was Lord Oppiliappan, the family deity of his dad, not Namagiri Devi the consort of the family deity of his mom. Because Lord Oppiliappan is my family deity too. Would have gotten me some bragging rights.

    --
    sed -e 's/Chuck Norris/Rajnikant/g' joke > fact
    1. Re:Simplest Ramanujan anecdote ... by shawn2772 · · Score: 5, Interesting

      The taxi cab numbers is the simplest anecdote from Ramanujan that could be told to general audience.

      It's recently been discovered that there is a specific reason that Ramanujan recognized the property of 1729... and it's even more mind-boggling than the idea that Ramanujan simply saw such obscure properties in random numbers.

      As it turns out, Ramanujan was thinking about Fermat's Last Theorem and had written the two sum-of-cubes decomposition of 1729 in some of his papers, as part of an exploration of FLT "near misses", numbers that are almost, but not quite, counterexamples to FLT. What's really incredible, though, was that careful study of his papers reveal that he was in the process of developing a theory of elliptic curves... moving exactly towards the technique that Andrew Wiles used to finally prove FLT in 1994/95, some 75 years after Ramanujan's death.

      Given Ramanujan's highly intuitive approach to mathematics, what this most likely means is that Ramanujan somehow just saw the structure of elliptic curve theory and its relation to FLT. Andrew Wiles is clearly one of the most brilliant mathematicians of our day, and he was only able to make and prove this connection with years of intense work and only by building upon a mass of thoroughly developed elliptic curve theory, including the Taniyama-Shimura conjecture which was proposed 35 years after Ramanujan's death, and not observed to be related to FLT until the another 30 or so years after that.

      So when Hardy mentioned 1729 to Ramanujan and was surprised at Ramanujan's observation of the number's properties, he thought that it was just evidence that Ramanujan saw odd patterns in numbers, but it was actually evidence of vastly deeper insight into the structure of number theory.

      https://plus.maths.org/content/ramanujan

      Really sad he died so young.

      Really, really sad.

      He was utterly at a loss to explain how he was able to do math. He simply said, "I look at the equation or a problem. Then Goddess Namagiri Devi writes the answer in my tongue and I recite it".

      That's not completely true. Yes, he did say that, but he was also capable of producing proofs of a sort. He tended to skip a lot of steps that were -- to him -- too obvious to bother stating, and which everyone else had to think very hard about[*], but he could and did produce work that was understandable with appropriate background and sufficient study. It seems likely that had he lived longer and obtained more formal mathematical education that he'd have developed his ability to produce formal proofs for publication.

      Ramanujan was a simply incredible mathematical intellect. I have no doubt that if he'd lived a full life he'd have done great work to advance mathematics.

      [*] Mathematicians' definition of "obvious" is rather vague. One of my favorite math jokes is about a professor lecturing to his class and saying "It's obvious that...". A student raised his hand and said "Is that obvious? I don't see it". The professor looked at the board for a long minute then walked out of class, went to his office, scribbled furiously for 20 minutes then returned to class and said "Yes, it is obvious." He then continued his lecture without further elaboration.

    2. Re:Simplest Ramanujan anecdote ... by Applehu+Akbar · · Score: 4, Interesting

      "But Ramanujan was never taught the process of writing down formal proofs, he self thought everything from a handbook of mathematical identities. Rediscovering several things others had already discovered and proved. He was utterly at a loss to explain how he was able to do math. He simply said, "I look at the equation or a problem. Then Goddess Namagiri Devi writes the answer in my tongue and I recite it". (not an accurate quote, paraphrased by me)"

      The other mathematician who was self-taught in the same way was Blaise Pascal. He even invented his own terminology for conventional geometric forms because his family kept him away from formal study.