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"The World's Most Beautiful Mathematical Equation"

  • 1.  "The World's Most Beautiful Mathematical Equation"

    Posted 04-16-2017 22:56

    That in the Subject above is the title of an article by Richard A. Friedman in today's [16 April 2017] NYTimes. (My guess is many in this community will guess Friedman's choice. Friedman refers to it as an "identity" but such is in error; it comes from an identity.)

    Here's a link to the article:

    https://www.nytimes.com/2017/04/15/opinion/sunday/the-worlds-most-beautiful-mathematical-equation.html?ref=opinion


    BTW, What should be considered the most beautiful equation/formula in Statistics??


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    David Bernklau

    (David Bee on Internet)

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  • 2.  RE: "The World's Most Beautiful Mathematical Equation"

    Posted 04-17-2017 06:06
    The ratio of standard deviation to the average, defining the coefficient of variation, is what I would include in the list of the candidates.

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    Tatiana Lyashenko
    Professor
    Odessa State Academy of Construction & Architecture
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    Original Message


  • 3.  RE: "The World's Most Beautiful Mathematical Equation"

    Posted 04-18-2017 07:15
    I love the Normal Equations in linear models. I feel they take all those ugly sums of squares formulas we learn and teach in lower level courses in ANOVA and regression and show their simplicity and beauty.

    I think Ron Christensen in "Plane Answers to a complex Questions " captures that beauty well.

    Laura Kapitula

    Sent from my iPad


    Original Message


  • 4.  RE: "The World's Most Beautiful Mathematical Equation"

    Posted 04-18-2017 09:39

    Here comes Bayes! We have seen it everywhere and on BBC.

     

    http://www.bbc.com/earth/story/20160120-the-most-beautiful-equation-is-bayes-theorem

     




    Original Message


  • 5.  RE: "The World's Most Beautiful Mathematical Equation"

    Posted 04-18-2017 20:56
    I am reminded of the Lao Tzu quote "the truth is not beautiful."

    While mathematics is an art concerned primarily with beauty, the primary considerations of the statistician who conceived of statistics as a science are truth and utility.

    To ask an applied statistician what statistical equation is most beautiful is a bit like asking a pure mathematician what mathematical equation is most useful. It not only doesn't engage the real professional interest, it somewhat misapprehends what the profession is about. There are many aspects that are beautiful, but this is somewhat incidental and often a distraction from the real focus.

    Sent from my iPhone


    Original Message


  • 6.  RE: "The World's Most Beautiful Mathematical Equation"

    Posted 04-19-2017 11:27

    Re: "While mathematics is an art concerned primarily with beauty, the primary considerations of the statistician who conceived of statistics as a science are truth and utility."

    Good point!

    Thus, with respect to all of this, namely beauty and "truth and utility", one would have to say the Normal Distribution, especially because of its primary truth-and-utility aspect, namely the CLT, which is truly a beautiful result!


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    David Bernklau
    (David Bee on Internet)
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    Original Message


  • 7.  RE: "The World's Most Beautiful Mathematical Equation"

    Posted 04-20-2017 11:22

    Here is a beautiful formula that prima facie looks like Bayes's but is unrelated to it, a result from 1934 whose truth and utility has been clear ever since. Such was first derived by Jerzy Neyman in his groundbreaking paper "On the Two Different Aspects of the Representative Method: The Method of Stratified Sampling and the Method of Purposive Selection".

    nh = (NhSh  / Σ(NiSi))n , h = 1, 2, ..., L strata

    This gives the optimum allocation for sample sizes in each stratum after stratification of the population, optimal in the sense that it minimizes the overall sampling variance. (Not surprisingly, this is known as "Neyman Allocation".)

    Furthermore, it is equivalent to something that decided Election 2016, namely to the optimal allocation of the seats for the 50 states for apportionment of the House of Representatives, which follows each decennial census.

    [For more on this, see "The Equivalence of Neyman Optimum Allocation for Sampling and Equal Proportions for Apportioning the U.S. House of Representatives" by Tommy Wright in the November 2012 issue of The American Statistician (Vol. 66, No. 4).]












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    David Bernklau
    (David Bee on Internet)
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    Original Message


  • 8.  RE: "The World's Most Beautiful Mathematical Equation"

    Posted 04-21-2017 12:32
    I would vote for e to the pi i = -1.

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    Malcolm Sherman
    S.U.N.Y.-Albany
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    Original Message


  • 9.  RE: "The World's Most Beautiful Mathematical Equation"

    Posted 04-24-2017 23:59

    I would vote for e to the pi i = -1 but written as e to the pi i + 1 = 0. This form uses what are arguably the 5 most important constants in mathematics




    Original Message


  • 10.  RE: "The World's Most Beautiful Mathematical Equation"

    Posted 04-24-2017 04:46
    Agree. I would name Standard Normal. What a beauty is the Normal curve next to Gauss portrait on 10 DM banknote.

    Tatiana Lyashenko

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    Tatiana Lyashenko
    Professor
    Odessa State Academy of Construction & Architecture
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    Original Message


  • 11.  RE: "The World's Most Beautiful Mathematical Equation"

    Posted 04-24-2017 13:03
    I vote for:

    ∫ex = ƒυη

     



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    James Lucas
    J M Lucas & Associates
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    Original Message


  • 12.  RE: "The World's Most Beautiful Mathematical Equation"

    Posted 04-19-2017 12:53
    Why is exp(i*pi)=-1 any more beautiful than exp(2*i*pi)=1?

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    Emil M Friedman, PhD
    emilfriedman@gmail.com
    http://www.statisticalconsulting.org
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    Original Message


  • 13.  RE: "The World's Most Beautiful Mathematical Equation"

    Posted 04-24-2017 09:50
    I vote for E = mC**2 as the most beautiful equation so far!  It has impact on all phases of our non-emotional life. 

    Ajit K. Thakur, Ph.D.
    Retired Statistician.

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    Ajit Thakur
    Associate Director
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    Original Message


  • 14.  RE: "The World's Most Beautiful Mathematical Equation"

    Posted 04-24-2017 09:56
    On second thought, since I did not read the original question in toto, I have to vote for the Normal equation as the simplest, yet the most beautiful equation in statistics.  Apologize for the previous link although if we tried, we probably could find the Einsteinian equation in statistics as well!

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    Ajit Thakur
    Associate Director
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    Original Message


  • 15.  RE: "The World's Most Beautiful Mathematical Equation"

    Posted 04-25-2017 07:36
    There are so many flowers, too many to choose a favorite. But I'm grateful I can live and work in such beautiful gardens (which apparently are in other people's backyards, says John Tukey!).

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    Sean Bradley
    Clarke University
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    Original Message


  • 16.  RE: "The World's Most Beautiful Mathematical Equation"

    Posted 04-25-2017 08:34
    Write e(i*pi)+1=0, and you have e, i, pi, 0, 1 all in the same equation. Uncanny.

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    Anthony Babinec
    AB Analytics
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    Original Message


  • 17.  RE: "The World's Most Beautiful Mathematical Equation"

    Posted 04-25-2017 11:22
    One of my favorites is Newton's algorithm for root finding:  X_{n+1} = X_n - f(X_n) / f'(X_n)

    There is a beautiful symmetry about it.  This equation revolutionized the field of numerical analysis and computation.

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    Ravi Varadhan
    Johns Hopkins University
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    Original Message


  • 18.  RE: "The World's Most Beautiful Mathematical Equation"

    Posted 04-26-2017 22:47
      |   view attached


    The attached - not because it is beautiful or elegant, but because it is amazing (to me).

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    Kenneth Burnham
    Colorado State University
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    Attachment(s)

    pdf
    Fibonacci.pdf   40 KB 1 version
    Original Message


  • 19.  RE: "The World's Most Beautiful Mathematical Equation"

    Posted 04-25-2017 11:49

    AT and Others:

    Do you mean the equation for the Bose-Einstein Distribution?:

    http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/disbe.html

    DB



    Original Message


  • 20.  RE: "The World's Most Beautiful Mathematical Equation"

    Posted 04-25-2017 11:44
    A fun game to play. If you go to the article and load Appendix 1, their list is quite nice. Aesthetics meets epistemology. As an applied statistician, I might try to identify some relevant dimensions: breadth (scope of stuff collected), depth (contingent nature of stuff collected), simplicity (with elegance and surprise as sub elements), and consequences. But then you run into the lack of a complete ordering on Rk, and advocacy begins. For probability theory, I would want to include the Law of the Iterated Logarithm. Good breadth, depth, and surprise. I'll concede the other axes. The Ergodic Theorem is lovely as well. For statistics, it is odd, because beauty is not what we strive for. Still, if I had to make a pitch for being on a list I would go with Wald's Fundamental Identiity. Sequential notions still get pretty short shrift in statistics and stopping times are worth thinking about.

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    Robert Hoekstra
    Mathematical statistician
    Centers for Disease Control and Prevention
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    Original Message


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