Dana's Bio


News & Events





Here are three publications that have featured my articles: Starting our Careers, published in 1999 by the American Mathematical Society; Science, published weekly by the American Association for the Advancement of Science; Swarthmore College Bulletin, published by Swarthmore College.

I specialize in writing about mathematics and the physical sciences, although I am glad to write about other subjects when the opportunity presents itself. To find the articles I have written in the field of interest to you, click on one of the options below. This will take you to a (more or less) complete list of the articles I have written since 2000 in that field. Unfortunately, to actually read the articles you will, in most cases, need to have a subscription to the publication they appeared in. I have provided hyperlinks to all the ones I know of that are free.

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Number Theory

Primed for Success, Smithsonian Special Issue, Fall 2007, 74-75.

Terence Tao has made one of the most difficult of all transitions ¾ he is the rare prodigy who lives up to his early promise. At age 32, he has already won a MacArthur "genius grant" and the most prestigious prize in math, the Fields Medal, and has made major advances in several branches of mathematics. And he's still just beginning.

'Cranky' Proof Reveals Hidden Regularities, Science, 1 April 2005, 36-37.

The fallout from Andrew Wiles' 1994 proof of Fermat's Last Theorem will probably last for decades. A group of three mathematicians uses Wiles-like methods, together with an elementary "binning" procedure, to uncover some neat patterns in a classical function of number theory, the partition function.

Hardy's Prime Problem Solved, New Scientist, 8 May 2004, 13.

A prime progression is a sequence of prime numbers that are all equally spaced -- such as 5, 17, 29, 41, 53. Mathematicians have have never found one with more than 22 terms. Now, two young number theorists have proved that prime progressions of any length exist.

Prime Proof Helps Mathematicians Mind the Gaps, Science, 4 April 2003, 32.

Dan Goldston of the U.S. and Cem Yildirim of Turkey prove that prime numbers are like weeds -- they occur in clumps. Unfortunately, since this article was published a gap has appeared in their proof, so its current status is unclear. Come back to this page for updates. [July 2005 update: Goldston's work was finally vindicated a month or two ago, with an even simpler proof.]


A Singular Career, Swarthmore Alumni Bulletin, March 2007

Bob MacPherson's career as a mathematician has been "singular" in three different ways. He invented intersection homology; he helped rescue Russian mathematics in the economic crisis after the fall of the Soviet regime; and he and Mark Goresky (the Rogers and Hammerstein of mathematics) have become one of the most successful gay couples in mathematics. Too bad a lot of gays aren't aware of their accomplishments.

Mapping the 248-Fold Way, Science, 23 March 2007.

Mathematicians, with a huge help from computers, succeed in computing a representation table for E8, the most mysterious and exotic of all Lie (pronounced "lee") groups. This may be relevant to physical theories of the universe ¾ we probably won't know for a long time. For mathematicians interested in different kinds of symmetry, it is something like the scaling of Mt. Everest or the completion of the Human Genome Project.

The Poincaré Conjecture — PROVED, Science, 22 December 2006.

Science's editors picked Grigori Perelman's proof of the Poincaré Conjecture as the Breakthrough of the Year for 2006. I wrote the cover article about it. This gave me a chance to survey and put into context the events of the preceding four years. You'd think that mathematicians would be overjoyed at seeing one of their greatest unsolved problems conquered (and they are), but it has been a bittersweet harvest because of the personal rivalries that have been stirred up.

Perelman Declines Math's Top Prize; Three Others Honored in Madrid, Science, 25 August 2006.

Grigori Perelman created a huge stir when he declined the Fields Medal (the mathematical equivalent of a Nobel Prize). The reclusive Russian mathematician was the first person in history to do so. However, three other young mathematicians accepted their well-deserved medals from Spain's King Juan Carlos: Andrei Okounkov of Princeton University, Terence Tao of UCLA, and Wendelin Werner of Université de Paris-Sud.

Taming the Hyperbolic Jungle by Pruning its Unruly Edges, Science, 24 December 2004.

Are you a fan of fractals? Find out what the first fractals were invented for, back in the 1800s. Then learn how topologists are now using them to pin down the geometry of hyperbolic (negatively curved) 3-dimensional universes. Or if that is a little too mind-boggling, just look at the amazing  pictures.

Mathematics World Abuzz Over Possible Poincaré Proof, Science, 18 April 2003, 417.

A mathematician goes into relative seclusion for seven years and emerges with a claim that he can prove one of the most famous problems in mathematics. Sound familiar? It happened 10 years ago with Fermat's Last Theorem, and now it has happened again with the Poincaré Conjecture. But mathematicians, burned often in the past, are being verrry verrry cautious about this claim.

A Fine Mess, New Scientist, 25 May 2002, 32-35.

Packing oranges together is pretty simple in ordinary Euclidean space, but in hyperbolic space it gets seriously weird. Charles Radin of the University of Texas figures out how weird.

Applied Mathematics

All Stirred Up, New Scientist, 1 December 2007, 54-57.

Turbulently flowing fluids appear to be complex and unpredictable. But they aren't, if you can detect the "Lagrangian coherent structures" concealed in them, which direct where fluid particles go. Physicists can now do this in near-real time. Applications include pollution control, detection of clear-air turbulence by LIDAR, and detection of abnormal blood flow that leads to the formation of athereosclerotic plaques.

Mathematicians Confront Climate Change, SIAM News, June 2007, 1.

A symposium on climate change at the Mathematical Sciences Research Institute, in Berkeley, CA, asks what contributions mathematicians can make towards understanding the process of climate change and finding solutions to the problem of global warming.

Tilt!, Discover, July 2005, 36-37.

A mathematician thinks he knows why certain buildings topple over during earthquakes and others don't. The answer lies partly in an ancient book of Archimedes, and partly in modern catastrophe theory.

Topologists Take Scalpel to Brain Scans, SIAM News, September 2004, 1-11.

Computer-rendered 3-dimensional MRI images are a valuable tool to brain surgeons. Unfortunately, the scans often contain glitches that mess up the spherical topology of the image, and wreak havoc with automated brain-mapping programs. A group of mathematicians has now found and proved a simple algorithm for cleaning  the images up.

Ensemble Kalman Filters Bring Weather Models Up to Date, SIAM NEWS, October 2003.

Meteorology isn't rocket science, is it? You bet it is! This article explains how Kalman filters, a "data assimilation" method used to keep rockets on course, can help predict the weather. In 1999, the winter storm Lothar wreaked havoc on the gardens of Versailles and killed more than 100 people in Europe. It caught the British and French weather services totally off guard. But the possibility of such a severe storm could have been anticipated with ensemble Kalman filters.

Tailor-Made Vision Descends to the Eye of the Beholder, Science, 14 March 2003, 1654-5.

Adaptive optics, designed to help telescopes see more sharply through atmospheric distortions, are now being used to correct subtle aberrations in the eye. One application you may have heard of -- or will soon -- is "wavefront LASIK." Adaptive optics can also be used to look into the eye and study eye disease at a cellular level.

The Science of Surprise, Discover, February 2002,  58-63.

Complexity theory enables biologists to model the flocking of birds, companies to control tightly interwoven supply chains, ... and insurers to deal with the ramifications of an unforeseen catastrophe like September 11. This was one of my most difficult articles to write, as the events of September 11 dramatically changed what it was going to be about.

Wavelets: Seeing the Forest -- and the Trees, Beyond Discovery, National Academy of Sciences.

Wavelets are a beautiful example of mathematics with significance far beyond its original context. They are used to process a signal into components that are compact both in time and in frequency. The original applications were in audio, but the really exciting ones are in video, where you can build up an image at different scales of resolution. If you've seen any recent digitally animated movie (e.g., A Bug's Life), you've seen what wavelets can do.

Mathematical Biology

Ramping Up To Multiscale, Biomedical Computation Review, Spring 2006.

Computer scientists and biologists have made huge strides in designing realistic models of the human body, from individual cells to whole organs. The most difficult thing to do, though, is to integrate models that work at different scales. For example, how does the flow of ions through individual cells precipitate an arrhythmia of the whole heart? This article describes some approaches that work.

No Age Limits: Can Mathematical Models of Fish Shed Light on Human Aging? SIAM News, April 2005, 4-6.

The rockfish is an amazing fish: Some species live up to 200 years, but others live for only a dozen years or so. Mathematical models suggest that the variety of life spans evolved because they enabled the species to avoid competing with one another. Not too much here about humans, actually, in spite of the title.

Making Sense of Stents, SIAM News, May 2004, 1-3.

In less than 20 years, stents (which prop open an occluded artery) have gone from an experimental procedure to a routine treatment for cardiovascular disease. But about a quarter of stented arteries eventually clog up again. Mathematicians are developing models that explain why and what we can do about it.

Making Sense of a Heart Gone Wild, Science, 6 February 2004.

You've seen automatic defibrillators in medical dramas on TV. You know that they bring people back to life who would otherwise die in minutes. But did you realize that no one understands why they work? Mathematical models have identified two possible explanations. The models may also help engineers design pain-free implantable defibrillators for people who are susceptible to arrhythmias.


Communication Speed Nears Terminal Velocity, New Scientist, 9 July 2005.

All communications, whether you're downloading files over the Internet or radioing instructions to a satellite, have to obey a fundamental speed limit known as the Shannon limit. Try to go faster and your data will be garbled. Engineers have now developed not one but two codes that allow communication speeds within an eyelash of the Shannon limit.

The Code War, Beyond Discovery, National Academy of Sciences

With the arrival of the Internet and electronic commerce, codes are no longer the exclusive province of spies and generals: They are part of our everyday life. Today's hardest-to-crack codes are based on the mathematics of number theory. Tomorrow's may exploit the quantum structure of the universe.


Graph Theory Uncovers the Roots of Perfection, Science, 5 July 2002, 38.

Some graphs (or networks) are easier to "color" than others. Mathematicians now have a simple test for perfect graphs, a large class of graphs that are optimal for coloring problems. Claude Berge, who originally proposed this test and was one of the big names in graph theory, heard about the proof of his conjecture on his deathbed. (He died just before this article came out.)


Vital Statistics, New Scientist, 26 June 2004, 36-41.

The "hard sciences" of physics and astronomy seem like the last place where you would have to deal with the ambiguities of statistics. But physicists and astronomers are gradually (and sometimes reluctantly) learning from the "soft sciences" how to deal with the ambiguities in their data. Three case studies: the Higgs particle, dark matter, and neutrino oscillations.

Computer Science

What in the Name of Euclid is Going On Here? Science, 4 March 2005, 1402-3.

Computerized proof verifiers have been mostly scorned or ignored by mathematicians, but they are starting to get to the point where they can check the proofs of serious theorems. They may be just in time, because more and more papers in recent years have grown to gargantuan sizes (several hundred pages), making it impossible for anyone to be completely sure they are right.

Games and Recreations

The Cycling Speed Freaks of Battle Mountain, New Scientist, 4 December 2004.

Once a year, the fastest human-powered vehicles in the world come to a flat stretch of highway outside Battle Mountain, Nevada, and their riders strive to become the world's fastest human. Forget Lance Armstrong--these bikes go almost twice as fast as he does.

Non-Trivial Pursuits, SIAM News, December 2004, 1-4.

To be a successful mathematician, do you have to give up all your other interests? Not necessarily! Read about five people people who have balanced math with other hobbies: swing dancing, soaring, photography, musical composition, scrapbooking, and taking care of zoo animals. (This may be the first time you will ever see a mathematician and a giraffe in the same photo.)

The Mathematics of ... Shuffling: The Stanford Flip, Discover, October 2002, 22-23.

Persi Diaconis, a former magician and blackjack card counter, defects to the other side and helps the casinos figure out why their shuffling machines aren't producing random shuffles.

Top Young Problem Solvers Vie for Quiet Glory, Science, 27 July 2001, 596-599.

The International Mathematics Olympiad came to the U.S. in 2001. The Chinese stole the show but the Americans did pretty well, especially Reid Barton, who became the first person to win four gold medals in four years.

Exploring Origami, Exploratorium, Summer 1999, 20-24.

This one is a little bit older than the others, but it's worth checking out because the Exploratorium did such a fantastic job of Web-ifying my article. See Jeremy Shafer fold a paper crane while the paper is on fire! See his "flasher" hat that can instantly expand to two feet wide or collapse so that it can fit into your pocket! Also see a gallery of other fascinating and unusual origami creations, with some helpful explanatory text by yours truly.

Mathematics in Arts and the Media

Beautiful Mind's Math Guru Makes Truth = Beauty, Science, 1 February 2002, 789-791.

A profile of Dave Bayer, who was responsible for making sure the math in the Oscar-winning movie would pass mathematicians' sniff test. The link points to a slightly condensed version of the article that was reprinted, with permission, on the Swarthmore College website. (Bayer and I both studied at Swarthmore and took one class together.)


Boomtown, New Scientist, 26 May 2007, 48-51.

Ever since Frank Lloyd Wright, people have compared cities to living organisms. Turns out they're not like living creatures in one important way: as cities get bigger, their pace of life speeds up. This has troubling implications for sustainable growth, because it seems to imply mathematically that cities must go through boom and bust cycles.

Whose Gift is it Anyway? New Scientist, 24-31 December 2005.

For the holiday issue, I took a look at gift cards, a hugely popular marketing tool in America that was just beginning to establish a foothold in England. The trouble with gift cards is the fine print: cards that expire after a certain time, or that have hidden fees. Some US states have banned these practices, but in the UK it was still very much "Recipient beware."

Soft Cash, New Scientist, 23 July 2005.

Frequent-flier miles. Loyalty cards. Subway cards that can be used to buy coffee, too. Cell phones that can pay for concert tickets. The line between cash and other forms of payment is fast becoming blurred. Some economists have predicted the "death of cash" for years. It probably won't happen, but it does seem that many parallel "currencies" are emerging that will exist alongside the previously monolithic dollar (or pound sterling).

Voting Theory and Practice

Plurality Rules, Swarthmore College Bulletin, September 2004, 17-19.

Learn about instant runoff voting, a way of choosing a winner in multi-candidate elections that gives minority groups a better chance to make their voices heard, according to Swarthmore alumna Cynthia Terrell. Also in the same issue, read my article Voting Power, which explains how to find the "right" number of at-large seats for a city council or any representative body, according to Swarthmore alumnus and mathematician/lawyer Paul Edelman.

Hacking the Ballot Box, Discover, May 2004, 22-23.

When you cast your ballot, will your vote really go to the candidate you intended it to? If you're voting on an electronic voting machine with no paper trail, you're taking your chances.

May the Best Man Lose, Discover, November 2000, 84-91.

My semi-prophetic piece about why the most popular candidate doesn't necessarily win an election. It has nothing to do with hanging chads, but with the vagaries of plurality-based elections. Find out why John McCain might have won in 2000 if we had a different election system!

Making Sense Out of Consensus, SIAM News, October 2000.

Another article about the mathematics of elections. This one focuses especially on the work of Don Saari (University of California, Irvine) and assumes a little bit more mathematical background.

Particle Physics

Free Fall, New Scientist, 10 February 2007.

A team of physicists at Stanford prepares a new experiment to measure the force of gravity on an atomic scale. Think of it as a cross between quantum physics and Galileo's experiment of dropping cannonballs off the Tower of Pisa. The goal: confirm some never-before-tested predictions of Einstein's theory of general relativity, or else discover new physics.

When God Plays Dice, New Scientist, 4 November 2006.

Twistors, a mathematical gadget invented by Roger Penrose in the 1960s, are now dramatically simplifying the computation of processes that go on in particle colliders. Twistor theory, which was the best candidate for a "theory of everything" before physicists dumped it in favor of string theory, may turn out to be the right way to look at spacetime after all.

Super Computer vs. Particle Accelerator: The Great Physics Heavyweights, New Scientist, 13 August 2005.

Once you get past the overblown prize-fight metaphor (sorry, my editors made me do it), this is an article about lattice QCD (quantum chromodynamics), which is a way to make the equations of particle physics work in a universe divided into pixels. This is perfect, of course, for computers. Physicists have now managed to use lattice QCD to predict the results of certain experiments to within 1 or 2 percent, before the experimenters actually announced their results.

Spinning Into Posterity, SIAM News, March 2003.

This year marks the 75th anniversary of one of the most fundamental equations in physics: Dirac's equation for the electron, which explained the phenomenon of electron spin and predicted the existence of antimatter.

Solar System

The Gritty Problem of Moon Dust, New Scientist, 28 May 2005.

When the Apollo astronauts walked on the Moon, they could not have ventured out for a fourth Moon walk because their space suits were so fouled up by Moon dust. If we ever want to go back for longer stays, scientists will have to figure out how to control the stuff.  That means they need some fake Moon dust to experiment with, because there isn't enough real Moon dust to go around. But how do you make fake Moon dust? Easier said than done!

Here Comes the Sun, Discover, May 2004, 62-69.

Our seemingly mild-mannered Sun can kick up a fuss sometimes, as it did last fall when a spectacular solar storm released two of the most powerful X-ray flares on record. The effects on Earth were minor -- this time -- but out in space there was a long roster of damaged or dead satellites. This article, along with Discover's usual gorgeous graphics, explains how solar researchers are working to understand and predict the Sun's behavior.

The Loneliest Lab, New Scientist, 31 January 2004, 32-33.

In January, George W. Bush proposed a multi-year plan to send astronauts to the Moon and Mars. Mars gets most of the publicity, but there is lots of good science that could be done at a Moon base: exploring the South Pole-Aitken basin, looking for ice deposits at the poles, and building a telescope under perpetually dark skies.


Anselm's Question, Swarthmore College Bulletin, June 2003, 16-21.

A profile of Sandra Faber, a multi-talented astronomer who found the first evidence that the universe is not expanding uniformly, and helped identify the largest known structure in the universe, the so-called "Great Attractor."


Journey to the Center of the Earth, SIAM News, December 2007, 1.

A geologist and an applied mathematician collaborate on a new way of creating images of the core-mantle boundary, and find an unexpectedly complex pattern of reflecting layers. They might be signals of a phase transition that was previously only theoretical, and if so they will help to pin down how rapidly heat flows from Earth's core.

What Killed the Dinosaurs? Ask, October 2005.

My first foray into writing for kids, this article describes the widely accepted theory that a meteorite impact caused the catastrophic climate change that killed the dinosaurs. I also mention an alternative theory, that volcanic mega-eruptions did the dirty work of climate change, and the meteorite impact was only the straw that broke the dinosaur's back.

Seismic Shift, Discover, September 2001, 60-67.

Seismologist Terry Wallace was the first person to tell what really happened in the Kursk submarine disaster -- even though he was thousands of miles away.


Ahead of Its Time?, Smithsonian, January 2005, 26-28.

New Philadelphia, a town on the Illinois prairie, prospered from 1836 to about 1870, when the railroad passed it by. Frank McWorter, the first black man ever to found a town legally in America, used the proceeds from land sales to buy his family out of slavery. Archaeologists are now excavating New Philadelphia's remains, and hope to learn how blacks and whites lived together in one of America's most racially mixed pre-Civil War communities.


The Tenure Chase Papers, in Starting Our Careers (Amer. Math. Society, 1999), pp. 79-100. Also available right here!

In an category by itself is my memoir on how I was denied tenure at Kenyon College. It's full of unexpected twists and turns and good lessons for young professors on the tenure track. The website www.phds.org called it "required reading for all academics and would-be academics." I have gotten far more reader feedback from this article than any other article that I have ever written.


The Hook and Ladder Trick, Chess Life, July 2007, pp. 44-45.

A little-known middlegame trap catches amateurs and grandmasters alike. This was one of my earliest and most popular lectures for ChessLecture. The "Hook and Ladder Trick" can go by other names (it's basically a deflection sacrifice), but it's a distinctive enough pattern that I felt it deserved its own name.

Sac Your Queen on Move Six! (A New Anti-Computer Variation), Chess Life, March 2007, pp. 30-33.

I spent two years working out an amazingly early sacrifice of the queen (normally the most valuable piece) in the Sicilian Defense. Eventually I got to the point where I could beat the strongest computer chess program, set to maximum strength, with this variation. And then I got my first chance to play it against a human...