A mathematician blogs.
This Tuesday evening, September 4, MSRI is hosting a public lecture Alan Turing: A Centenary Celebration. Andrew Hodges, author of Alan Turing: The Enigma 
And for those of you like me who don’t have cars, it’s at Berkeley City College! Right near BART! No need to trek up into the hills.
I’m looking for a job, in the SF Bay Area. See my linkedin profile.
Einstein, The cause of the formation of meanders in the coursers of rivers and of the so-called Baer’s law. via metafilter
The BBC looks at mathematical knitting.
James Tanton has a sequence of videos on things counted by Fibonacci numbers: part one, two, three. (This is a bit old – April 2012 – but I’m going through a backlog of links.)
Peter Norvig of Google speaks about mathematical models for language, at the Museum of Mathematics.
MIT’s 2011 Simons Lectures by Steven Strogatz: Coupled oscillators that synchronize themselves, Social networks that balance themselves, Blogging about math for the New York Times.
An interview with Grigori Perelman (and a description of the stakeout that led to it).
I found this somewhat by accident, while looking for something else: Andrew Ranicki’s page of topological baked goods (and some other novelties).
Jesus was a descendant of David, says the Bible, but so was everyone else alive at that time.
From Grantland, some new-school NFL statistics.
Norm Matloff has written a textbook, freely available online, From Algorithms to Z-Scores: Probabilistic and Statistical Modeling in Computer Science.
From Steven Strogatz on twitter, a couple links to good chaos resources: Michael Cross’s Caltech lecture notes and Chaos: Classical and Quantum by P. Cvitanovic, R. Artuso, R. Mainieri, G. Tanner and G. Vattay.
I’m looking for a job, in the SF Bay Area. See my linkedin profile.
I said yesterday that the mathematician Jerry Nelson died. Wondering who Jerry Nelson is? He’s the muppeteer of the Count on Sesame Street. Here are some videos:
Cookie monster and Count cooperate
Slate cuts together the Count counting a bunch of things.
From More or Less: at 25:29 in this podcast, an interview with the Count.
The first is William Thurston. I’m not a geometer, so I’ll just do a roundup of some interesting things I’ve seen:
John Horgan, How William Thurston (RIP) Helped Bring About “The Death of Proof”.
Edward Tenner in The Atlantic.
Terry Tao briefly summarizes some of Thurston’s work.
New York Times obituary (Leslie Kaufman). The headling here is “William P. Thurston, Theoretical Mathematician, Dies at 65; I’ve seen some people say that the word “theoretical” is superfluous here.
Daina Taimina‘s pictures and remembrances.
A couple videos:
And a couple bits of metamathematics:
Thurston, On Proof and Progress in Mathematics
Thurston’s answer to the MathOverflow question What’s a mathematician to do? (to contribute to mathematics). “The product of mathematics is clarity and understanding.”
The second, somewhat closer to my background as a combinatorialist, is Jerry Nelson.
The rise and fall of scoring in baseball, a visualization from Smithsonian. (Could this have something to do with the recent surfeit of perfect games?)
Joseph Gallian, in the Notices of the AMS, writes that undergraduate research in mathematics has come of age. (He’s the one behind the Duluth REU.)
Rod Carvalho has reposted, with some cleanup a Google Buzz post by Terence Tao on classical deduction and Bayesian probability. Short version: “one can view classical logic as the qualitative projection of Bayesian probability, or equivalently, one can view Bayesian probability as a quantitative refinement of classical logic.” (How’d I miss this the first time around? Oh, right, I was in the crucnh time on my dissertation.)
How to build a teleportation machine: intro to qubits. (On a related note I’ve been enjoying Umesh Vazirani’s Coursera course Quantum mechanics and quantum computation.
Friendship networks and social status, by Brian Ball and M. E. J. Newman. Quick version: observe which friendships go unreciprocated in high schools. Assume that if A lists B as a friend but not vice versa, then B likely has higher “social status” than A. This gives a ranking by social status.
Vector Racer is an online implementation of the game of Racetrack. (Via Metafilter.)
In the fall of 2001 Jim Propp (then visiting Harvard from Madison, currently at UMass Lowell) taught a course on algebraic combinatorics for undergrads with the explicit goal to “bring [undergraduate!] students to the point of being able to conduct original research in low-dimensional combinatorics, using algebraic and bijective techniques.” Why am I mentioning an eleven-year-old course? Because the videos are available online (see link above). (You’ll need RealPlayer.)
A traveling salesman variant from Twelve Mile Circle: what’s the shortest (in mileage) driving route that hits all of the 48 contiguous states?
Anand Rajaraman and Jeff Ullman’s book Mining of Massive Datasets is downloadable online from the authors. There’s also a hardcopy.
Montgomery County [Maryland] Math Team elevates math to competitive sport, from the Washington Post Magazine.
A mathematician goes to the beach, from Gregory Buck, at the New Yorker culture desk.
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So earlier today I was walking along, listening to the Math/Maths Podcast. They mentioned Erdös numbers, as math people are wont to do occasionally. It occurred to me that nobody can get an Erdös number of 1 now — of course — and that at some point in the future, all of Erdös’s collaborators will have died, so it will be impossible to get an Erdös number of 2. So how old, I wondered, is the youngest of Erdös’s collaborators?
The latest birthdate I could find on the Internet for an Erdos collaborator was Csaba Sandor, May 10, 1972.
(This Christian Mauduit, born 6/9/75, is not the Erdos collaborator.) Information about dates of PhDs and such is easier to find, and yields two potential younger collaborators. Gergely Harcos is one: he started primary school in ’79, university in ’91, and got his PhD in ’03. Laszlo Koczy got his PhD in ’03; he’s an economist but has some discrete-math interests, so may be the Erdos collaborator. To find these people I took the list of Erdos collaborators by date of first collaboration and started googling names from the bottom until I got tired. This happened pretty quickly, so I can’t guarantee that I’ve found Erdös’s youngest collaborator.
Of course then I got home and came across a similar question for baseball players at sports nation divided. Here the nodes are baseball players, and two players are linked if they faced each other in Major League Baseball play, one as a batter and the other as a pitcher. It’s possible to get from the 19th century to the present day in six steps. This seems about right — twenty years is a rough upper bound for the length of an MLB career, and a regular batter/pitcher will face most pitchers/batters in their league in a given season, so it should be possible to do this in six steps.
Uncovering Ramanujan’s “Lost” Notebook: An Oral History, by Robert Schneider from interviews with George Andrews, Bruce Berndt, and Ken Ono.
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The Chaos Within Sudoku, by Maria Ercsey-Ravasz and Zoltan Toroczkai; from the Technology Review blog; this paper gives a means of algorithmically rating Sudoku puzzles’ hardness by mapping them onto dynamical systems. David Eppstein comments; he’s previously given this question some thought.
Jeremy Kun has an excellent blog entitled Math ∩ Programming.
Rubik’s Cube Twists Back Into Limelight (and the Times is on it!)
Nate Silver runs down a list of other presidential forecasting models.
Olympics: medals per capita, alternative medal table.
The little book of R for time series
Stanislas Dehaene and Steven Strogatz, How Math Comes to Mind: Intuition, Visualization, and Teaching, 79 minute public lecture given at Princeton in 2011. The story of how Strogatz almost got weeded out of math starts at 29:10. (Audio-only track is also available, and it should hold up that way; it’s just people talking.)
Square root laws for basketball.
I’m looking for a job, in the SF Bay Area. See my linkedin profile.
Which country wins the Olympics? Right now China is in the lead for most medals (73: 34 gold, 21 silver, 18 bronze) and most golds. The USA is second in both categories (71: 30 gold, 19 silver, 22 bronze). In 2008 there was some controversy about whether the ranking should be done by largest total number of medals or largest golds; here’s the table from Wikipedia. If I recall correctly (though it’s surprisingly hard to search for this) non-Americans were saying that the “right” way to do it is by golds, but Americans insisted on doing it by total medals. Not surprisingly the USA had the most total medalists in ’08 (110, to China’s 100) but not the most golds (36, to China’s 51).
But it hardly seems fair to expect, say, France to get as many medals as the USA, simply because they have about one-fifth the population. Shouldn’t their 41 medals in ’08 count for something? In fact they beat the US on a per-capita basis. In the current (2012) Olympics, as of two days ago Slovenia led the medal table per capita, says the New York Times. (This actually isn’t a case of a small country winning one medal; the Slovenes, at that point, had four medals for their two million people.) Medals per capita has up-to-the-minute data; as of this writing New Zealand (one medal per 443,262 people) has pulled ahead of Slovenia, and Grenada (110,821 people; one medal) is in the lead and is quite likely to stay there. Historical data is available as well; since 1984 it’s always been a very small country in the per-capita lead.
But per-capita counting is probably a little bit too aggressive in adjusting high-population countries downwards, because there are some events that have a limit in number of competitors per country. Team sports come to mind; there’s no way the USA will win more than two medals in basketball, despite its dominance. (Of course I’m trying to prop up the USA here! The site’s creator, Craig Nevill-Manning, is a New Zealander.) We could do regression to determine how many medals we’d expect a country of a given size to win, and then judge countries relative to that benchmark.
So here’s a way to put a partial order on countries: country A is “better” at the Olympics as country B at the Olympics if A wins more medals than B and has smaller population. We can plot the medal counts in a scatterplot — see below. The “winners” of the Olympics — and there are many — are all the maxima under this partial order, that is, all the countries for which no smaller country got more medals. Winners therefore include the lowest-population country to win a medal — in ’08, that was Iceland — and the country that won the most medals — that is, the USA. Intermediate between them, in 2008, were the Bahamas, Jamaica, Belarus, Cuba, Australia, Great Britain, and Russia. On the scatter plot below, these are those countries for which, if you draw a vertical line and a horizontal line through the point representing them, there are no points in the upper left quadrant; I’ve drawn those lines for Australia.
So far in 2012 the leaders in this category are China, the USA, Great Britain, Australia, Romania, Hungary, Slovenia, Estonia, and Grenada. (But don’t read too much into the differences between these lists, especially at the small-country end; during the Olympics such a list will be biased towards countries that happen to be good in events that happen early on.) I’ll put out the final results once the Olympics end.
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Edited to add, 12:29 pm: in this 2012 New York Review of Books article on the pursuit of medals, I found a link to this 2008 Wall Street Journal article on differing schemes of ranking countries, namely the gold-versus-total-medals debate.
If I type “mathematicians are” into Google and let it auto-suggest completions, I get “mathematicians are people too”, “mathematicians are like frenchmen”, “mathematicians are people too pdf”, and “mathematicians are weird”.
The first and third are references to a book Mathematicians Are People, Too: Stories from the Lives of Great Mathematicians
which appears to be a book of stories from the lives of mathematicians, intended for young children.
The second refers to a quote of Goethe: Die Mathematiker sind eine Art Franzosen; redet man mit ihnen, so übersetzen sie es in ihre Sprache, und dann ist es alsobald ganz etwas anderes. (Mathematicians are [like] a sort of Frenchmen; if you talk to them, they translate it into their own language, and then it is immediately something quite different.)
The fourth doesn’t seem to be a reference to anything in particular, but turns up some interesting Google results on how people perceive mathematicians; I’ll let you do your own Googling.
Possible completions for “statisticians are” are: “statisticians are liars”, “statisticians are many lovers”, “statisticians dc area”, “are statisticians scientists”. Apparently the quip about lies, damned lies, and statistics has been rephrased as “liars, damned liars, and statisticians”; “statisticians are many lovers” might be a distortion of “statisticians are mean lovers”. I’m not touching the question of whether statisticians are scientists before coffee.
I’m looking for a job, in the SF Bay Area. See my linkedin profile.
Maximizing the probability of getting a medal in diving.
The most mathematical flag, from Numberphile. (The pictures you’ll want to see are here.)
John D. Barrow asks: How fast can Usain Bolt run? PDF, one-hour lecture on more general topics including this.
The optimal angle of release in shot put, by Alexander Lenz and Florian Rappl: paper at the arxiv, Technology Review blog (It’s not 45 degrees.)
Cosmos: A Three-Movement Choral Suite, by Kenley Kristofferson. (Yeah, I know, it’s not math. Deal with it.)
God plays dice 