This week’s challenge was suggested by Adam Kucharski, a lecturer in mathematical modeling at the London School of Hygiene & Tropical Medicine, where he studies the dynamics of infectious diseases, particularly emerging infections. Adam is also an award-winning writer, and author of “The Perfect Bet: How Science and Math Are Taking the Luck Out of Gambling,” the story of the mathematicians who make millions by doing the impossible: cracking the code of gambling.
Next week we’ll feature a second puzzle from Adam along with a sampling from “The Perfect Bet” (scheduled to be released on Feb. 23). Until then, let’s try —
The St. Petersburg Lottery
Suppose we play the following game. I toss a coin repeatedly until it comes up heads. If heads appears on the first throw, I pay you $2. If it appears on the second throw, I give you $4; if on the third, I pay $8 and so on, doubling each time.
How much would you be willing to pay me to play this game?
And as a bonus item: Do you value correctness or creativity? In any field there are two personalities that make the discipline go round: One striving for the right answer, even if it’s boring or predictable. The other wanting to innovate or provoke, even if the result is a bit wacky. We see this in our Numberplay conversations each week — a productive clash.
The Stanford band is a good example of pure provocation. This collection of eccentrics is perhaps unique in football halftime entertainment for its ability to insult the opposition. Perhaps best in small doses.
The best creative work builds on a base of competence, generating meaningful controversy instead of mere annoyance. An inspiring example is the recent hip-hop-infused gymnastics routine by Sophina DeJesus, a U.C.L.A. gymnast who broke the floor exercise paradigm. (In case you missed it: “U.C.L.A. Gymnast Slips In Hip-Hop Moves, and the Online Crowd Goes Wild.”) The YouTube video has since been viewed over ten million times.
O.K. But could something like this ever happen in, say, mathematics, a discipline that seems — from a distance, at least — to be as dry as dust? Keith Devlin, a mathematician at Stanford who’s made a career of expressing the beauty of math to millions, recently told me about the following example: a Ph.D. dissertation by Piper Heron, who just completed her studies at Princeton. Piper introduces the dissertation, “The Equidistribution of Lattice Shapes of Rings of Integers of Cubic, Quartic, and Quintic Number Fields: an Artist’s Rendering,” with the following:
A fascinating tale of mayhem, mystery and mathematics. Attached to each degree nnumber field is a rank n−1 lattice called its shape. This thesis shows that the shapes of Sn-number fields (of degree n = 3, 4, or 5) become equidistributed as the absolute discriminant of the number field goes to infinity. The result for n = 3 is due to David Terr. Here, we provide a unified proof for n = 3, 4, and 5 based on the parametrizations of low rank rings due to Bhargava and Delone–Faddeev. We do not assume any of those words make any kind of sense, though we do make certain assumptions about how much time the reader has on her hands and what kind of sense of humor she has.
Mr. Devlin calls this amazing piece of work “the math Ph.D. dissertation to end all such.”
Humor plus math, dance plus gymnastics. Ordinary ingredients combined to create something extraordinary. I’m just as moved by the courage and authenticity as I am by the creative works themselves.
Let’s close with the latest from the inventive, athletic alt-pop band OK Go, a favorite of Adam Kucharski. Hop aboard and prepare to be upended.
With that we wrap up the week. As always, once you’re able to read comments for this post, use Gary Hewitt’s to correctly view formulas and graphics. (Click here for an intro.) And send your favorite puzzles to gary.antonick@NYTimes.com.