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Enjoy this curated selection of theme-related dances for celebrations and holidays, or find a dance associated with a special calendar day, or EVEN your own birthday!
The Pi Bike is a fully functional bicycle designed by Martijn Koomen and Tadas Maksimovas, handmade from carbon fibre material in the shape of the mathematical symbol, Pi (π).
Aug 17
August Days
Fermat's Bicycle
Other Scottish Country Dances for this Day
Today's Musings, History & Folklore
Fermat scribbled in the margin one day:
“I’ve found the proof—but there’s no room. Okay?”
For centuries mathematicians tried—
Then Wiles proved Fermat hadn’t lied!
The title and alternative title of this dance, "August in Erlangen" pays tribute to French mathematician Pierre de Fermat (1607–1665) and one of the most celebrated problems in the history of mathematics.
Around 1637, Fermat famously wrote in the margin of his copy of an ancient Greek mathematical text that he had discovered a “truly marvelous proof”—but that the margin was too small to contain it. His claim concerned a deceptively simple-looking equation. While a² + b² = c² has plenty of whole-number solutions, Fermat asserted that aⁿ + bⁿ = cⁿ has no positive whole-number solutions when n > 2.
Unfortunately, Fermat never left us his marvelous proof.
For more than 350 years, mathematicians tried to find one. Individual cases were solved, but the general theorem stubbornly resisted every attempt and became one of mathematics’ most famous unsolved problems.
Enter British mathematician Andrew Wiles, who had been fascinated by Fermat’s Last Theorem since childhood. After working on the problem in secrecy for years, Wiles announced a proof in 1993. A flaw was subsequently discovered, but Wiles, working with mathematician Richard Taylor, found a way around it. The corrected proof was completed in 1994 and published in 1995.
And no, it most definitely would not have fitted into Fermat’s margin. 😄
But how did Fermat’s Last Theorem end up in a Scottish country dance devised in Erlangen, Germany—and what do bicycles have to do with it?
That connection comes through the dance’s devisers, mathematicians Alice Silverberg and Karl Rubin, who were working for a term at the University of Erlangen when they devised the dance for the Erlanger SCD group in August 1994. Rubin had an especially direct connection to the story: he was Andrew Wiles’s first PhD student.
The timing could hardly have been better. Wiles had announced his proof the previous year, and in 1994—the very year Silverberg and Rubin devised the dance—the final obstacle to the proof was overcome.
And the bicycles? 🚲
Those come from Erlangen, a famously bicycle-friendly city. The devisers incorporated a bicycle motif into the choreography, with figures suggesting wheels and spokes. So the dance manages to combine a 17th-century mathematical mystery, a 20th-century mathematical triumph, a personal connection to Andrew Wiles—and a little bit of everyday life in Erlangen.
As the original dance notes explain:
“This dance was devised for the Erlanger SCD group by Alice Silverberg and Karl Rubin in August of 1994. They had been working here for a term as mathematicians at the university. Over 350 years ago, Pierre de Fermat (1601-1665) stated a mathematics conjecture, which became known as Fermat’s Last Theorem. Andrew Wiles (whose first PhD student was Karl) announced a proof of the conjecture in June of 1993. The dance was written in honor of Wiles’ announcement of a proof of Fermat’s Last Theorem. The bicycle motif that occurs in the dance (note the wheels and spokes) commemorates the fact that Erlangen is a very bicycle-friendly town.”
As an interesting side note, in 2003 Silverberg and Rubin also introduced the CEILIDH cryptosystem, whimsically named by Silverberg after her cat—giving their mathematical work yet another dancing connection!
So there you have it: Fermat → Wiles → Rubin & Silverberg → Erlangen → bicycles → Scottish country dancing. 🕺 💃 💙 💙 💙 🧮 ✍️ 📜 ➗ ♾️ 🤔 💡 🎓 🏆 💃 🕺 🚲 🇩🇪 🐱
Fermat's Bicycle
August 17th marks the birthday of Pierre de Fermat (17 August 1601 (or 1607) – 12 January 1665), a French lawyer and mathematician who is given credit for early developments that led to infinitesimal calculus.
In particular, he is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines, which is analogous to that of the differential calculus, then unknown, and for his research into number theory. He also made notable contributions to analytic geometry, probability, and optics.
He is best known for his conjecture, usually referred to as "Fermat's Last Theorem," which he famously described in a note (in 1637) at the margin of a copy of Diophantus' Arithmetica. This was first discovered by his son and included the statement that the margin was too small to include the proof.
In number theory, Fermat's Last Theorem states that no three positive integers a, b, and c can satisfy the equation a^n + b^n = c^n for any integer value of n greater than two.
The first successful proof was released in 1994 by British mathematician Andrew Wiles, using techniques unavailable to Fermat, and formally published in 1995, after 358 years of effort by mathematicians. The unsolved problem stimulated the development of algebraic number theory in the 19th century and the proof of the modularity theorem in the 20th century. It is among the most notable theorems in the history of mathematics and prior to its proof it was in the Guinness Book of World Records for "most difficult mathematical problems".
See this video below for a good overview of the history of this theorem.
This dance was devised for the Erlangen (Germany) Scottish Country Dance group in August of 1994 in honor of the announcement by Andrew Wiles, in June of 1993, of a proof of Fermat's Last Theorem.
The bicycle motif that occurs in the dance (via wheels and spokes) commemorates the fact that Erlangen is a very bicycle-friendly town. The dance is known as "Das Fermatische Fahrrad" (Fermat's Bicycle) or "August in Erlangen."
For a video of the dance being performed in Fanwood, New Jersey, 2012, see below.
And for more on Fermat, click the artistic rendering of "Fermat's Last Theorem" by artist John Kuhn. It consists of glass pieces arranged as cubes inside this cube which triggered the Fermat's Last Theorem connection on a revolving mirror base. Photo by Al_HikesAZ.
Click the dance cribs or description below to link to a printable version of the dance!
