Left out, a more illustrative fact. In the late 1950s the most popular man in America was Jonas Salk.
And yet, there is one thing to say for the vaxxers. All those vaccines must have done brain damage, after all. Because we boomers are the most outrageously gullible, sanctimonious and dullard generation ever.... to fall for the imbecillic, anti-scientific and dismally ungrateful trips that are rampant across today's very-far-left and entire right.
Below, the 13 films. Just watching the trailers is rewarding. If you've never met a mathematician, these should give you a personal look into the very diverse worlds of some great modern mathematicians and to see the humanity behind the thinking. If you're a mathematician or love mathematics, these are inspiring.
 Counting from Infinity: Yitang Zhang & the Twin Prime Conjecture (2015)
The central challenge of the film was finding a way to depict Yitang Zhang's dedication to working in isolation. The qualities he embraces-solitude, quiet, concentration-are the opposites of those valued in the media. Fortunately, it is a conundrum Csicsery had faced before in other films about mathematicians. He had learned that contrary to the rules, it is okay to shoot long scenes of "the grass growing," or in this case, shots of "a person just sitting with pencil and paper and thinking. The longer the scene, the more you realize that you really can see someone thinking. The human face is very expressive. Give it time and it speaks volumes." - George Csicsery
 Porridge Pulleys & Pi: Two Mathematical Journeys (Hendrik Lenstra, Number Theory, Elliptic Curves & Cryptography) & (Vaughan Jones: Quantum Mechanics, Knot Theory, and DNA Protein Folding) (2004)
Trailer: http://www.imdb.com/video/wab/vi1773798425/ About: http://www.zalafilms.com/films/pppdirector.html
"There are several stereotypes and beliefs about mathematicians that Porridge pulleys and Pi aims to dispel. First, I wanted to show that there is no single type of person who can become a mathematician. ... given the right training, any child with the aptitude can turn into a mathematician. ... Jones and Lenstra are the opposites of the eccentric nerdy type who has come to characterize the popular conception of what mathematicians are like. Another cliche I hope to debunk is that of the tortured genius. This film contains clear evidence that mathematicians derive a great deal of pleasure from their work." - George Csiscery
 Taking the Long View: The Life of Shiing-shen Chern (one of the fathers of modern differential geometry) (2011)
View Short: http://zalafilms.com/takingthelongviewfilm/viewfilm.html
“There’s a quotation from Lao Tzu, an ancient Chinese philosopher, that could have been written about Chern. ‘The master does his job and then stops. He understands that the universe is forever out of control, and that trying to dominate events goes against the current of the Tao. Because he believes in himself, he doesn’t try to convince others. Because he is content with himself, he doesn’t need other’s approval. Because he accepts himself, the whole world accepts him.’” - Alan Weinstein, UC Berkeley
The true importance of Shiing-shen Chern’s role in the development of mathematics ... His influence with Chinese government leaders helped bring Western mathematicians to China and send Chinese students to study abroad. Today’s leaders in Chinese mathematics were all beneficiaries of Chern’s vision. His greatest contribution to the restoration of Chinese mathematics, however, is the establishment of the Nankai Institute of Mathematics, today known as the Chern Institute of Mathematics. The Chern Institute provided a base for these international interactions which often led to collaborations, reciprocal visits, and joint papers.
“He said, ‘my policy to operate this institute is very simple. Three words in Chinese. First, no meetings. Second, no plan. Third, do more.’ That means, just do your research work.”
Molin Ge, Theoretical Physicist, Chern Institute of Mathematics
 Invitation to Discover: An Introduction to the MSRI (Mathematical Sciences Research Institute) (2002)
 I Want to Be a Mathematician: A Conversation with Paul Halmos (2009)
"When an engineer knocks at your door with a mathematical question, you should not try to get rid of him or her as quickly as possible. You are likely to make a mistake I myself made for many years: to believe that the engineer wants you to solve his or her problem. This is a kind of over simplification for which mathematicians are notorious. Believe me, the engineer does not want you to solve his or her problem. Once I did so by mistake (actually I had read the solution in the library two hours previously, quite by accident) and he got quite furious, as if I were taking away his livelihood. What an engineer wants is to be treated with respect and consideration, like the human being he is, and most of all to be listened to with rapt attention. If you do this, he will be likely to hit upon a clever idea as he explains the problem to you, and you will get some of the credit. Listening to engineers and other scientists is our duty. You may learn some interesting mathematics while doing so." - Gian-Carlo Rota, Indiscreet Thoughts 1979
 Julia Robinson and Hilbert's 10th Problem (2008)
 Navajo Math Circles (in production)
"Open-ended questions are totally new to most of the kids. Usually you have to have an answer within 20 seconds, 30 seconds, that’s what math is. Math circles are the opposite. We start with some simple questions, and we ask more questions and more questions. We get some answers along the way. The answers actually don’t matter. The more and more questions… we’re opening whole research problems, and that is something totally new to the kids. And once they like it, it’s just amazing, it’s transformative." - Matthias Kawski, Arizona State University
 Hard Problems: The Road to World's Toughest Math Contest, covering the story of the 2006 US IMO team (2008)
 N is a Number: A Portrait of Paul Erdos (1993)
Trailer: https://www.simonsfoundation.org/multimedia/n-is-a-number-a-portrait-of-paul-erdos/ About: http://www.zalafilms.com/films/nisfilm.html
 Erdos 100 (2013)
 To Prove and Conjecture: Excerpts from Three Lectures by Paul Erdos (1993)
 The Right Spin: How to fly a broken space craft (Mir), the Story of a Dramatic Rescue in Space and the Mathematics Behind It (2005)
About: http://plus.maths.org/content/right-spin-how-fly-broken-space-craft http://archive.msri.org/specials/rightspin Alternate documentary: https://www.youtube.com/watch?v=tM7fTLLmgbk
 On Mathematical Grounds: A Refresh of an Introduction to the Mathematical Sciences Research Institute (MSRI) (2009)
[a] George Csicsery, Producer & Director, Zala Films, in his own words: http://zalafilms.com/takingthelongviewfilm/directors_statement.html
[b] The Films: http://www.zalafilms.com/films/index.html
[c] The story of George Csicsery: Math Films, Yes - But So Much More: http://cinesourcemagazine.com/index.php?/site/comments/csicsery_math_films_yes_but_so_much_more/
[d] Science Lives, Simon Foundation & Zala Films, videos of interviews with living mathematicians https://www.simonsfoundation.org/category/multimedia/science-lives/alphabetical-listing/
If you add up the first n numbers and square the result, this produces the same answer as adding the first n cubes. The picture gives a wordless proof of this result.
The picture shows the case n=5. In this case, the sum of the first 5 natural numbers is 1+2+3+4+5=15, which squares to 15x15=225. On the other hand, the sum of the first n cubes is (1x1x1)+(2x2x2)+(3x3x3)+(4x4x4)+(5x5x5)=1+8+27+64+125, which also adds up to 225. There is nothing special about the number 5 here: an analogous identity holds for any other positive integer, and it can be illustrated by a similar picture.
So how exactly does the picture illustrate the equation? Well, the big square is a grid whose area is 15x15=225, where our unit of length is the side length of the smallest box appearing in the picture. The vertical strip to the right of the square and the horizontal strip below the square are each 1+2+3+4+5=15 boxes long. It follows that the total number of boxes in the big square is (1+2+3+4+5)^2.
On the other hand, consider the area of the red part of the big square. There are 5 red squares, each of which measures 5x5. The total red area is thus 5x5x5=125, or 5 cubed. Something similar happens for the dark blue squares, provided that the two half-squares on the left edge and top edge are combined to form one big 4x4 square. We then have 4 dark blue squares, each of which measures 4x4, giving a total dark blue area of 4x4x4=64, or 4 cubed. Adding up the areas of each colour gives a total area of 1+8+27+64+125, which is the sum of the first five cubes.
We have counted the integer-valued area of the big square in two ways. Both methods must produce the same answer, from which it follows that the equation must hold. This technique of counting a quantity in two different ways and equating the two results is what mathematicians call a combinatorial proof. The “sum of cubes” identity can be proved in a fairly mechanical way using the standard technique of mathematical induction, but that proof does not give any intuition for why the result should be true. A combinatorial proof, such as the one in the picture, gives a better idea of why the result should be true, and is therefore more satisfying to a mathematician than the other proof.
One might expect, given that there are cubes of integers appearing on one side of the equation, that a combinatorial proof of the result would involve summing volumes, but remarkably, it reduces to summing areas.
Combinatorial proofs are also known as counting arguments. Here's another post by me in which I explain, using a counting argument, why it is not possible for everybody on Google+ to have more than 5,000 followers (https://plus.google.com/101584889282878921052/posts/YV7j9LRqKsX). That post provoked some surprisingly negative reactions.
The picture is based on a picture from Brian R. Sears' website (http://users.tru.eastlink.ca/~brsears/math/oldprob.htm#p32). I found the picture in a recent paper by Johann Cigler (http://arxiv.org/abs/1403.6609) which examines some generalizations of the sum of cubes result.
- Northern Arizona UniversityMathematics, 1995 - 1997
- University of Texas at DallasApplied Mathematics, 1988 - 1990
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