“Five … four … three … two … one …” went the official countdown one year ago today in the spacious mathematics common room at Princeton University. Everyone screamed, “Happy Pi Day!” and the party got under way.

Each year in March, the third month, on this 14th day, at precisely 1:59:26 p.m., number nerds gather around the world in celebration of the beloved mathematical constant π: 3.1415926 …

This most-celebrated ratio — that of a circle’s circumference to its diameter — figures into countless scientific formulae in engineering, architecture, statistics and astronomy. In physics, it pops up in the cosmological constant, in Heisenberg’s uncertainty principle and in Albert Einstein’s field equation of general relativity (by the way, Pi Day was Einstein’s birthday in 1879).

Pie is not allowed,” says Conway. “I suspect it would be the cause of my death.

The π-eyed proclaim it the single most important number in the history of human development, though putting one’s finger on precisely why is about as elusive as the transcendental entity itself.

Still, were mathematicians ever to find a pattern among the ancient number’s infinite decimals, they believe humanity would be much the wiser.

And so its calendrical cognate is cause for widespread celebration. Club Infinity at York University honours the date with an annual party at which no mention of mathematics is allowed; last year, the department of mathematics at the University of Alberta held a pie-baking contest; MIT dished out pizza pie (and it usually mails out acceptance letters on this date); and at Berkeley a man was spotted with the Greek symbol shaved into his beard.

At Princeton, there was a contest to see who could recite the most digits for π, with its irrationally never-ending and never-repeating decimals. The first contestant managed no greater than 20 digits by memory. The second contestant blanked after 91, the last few numerical groupings issued with increasing uncertainty: “482534 … 2117? … 0679821?”

Then came Adam Hesterberg, 18, who fired off the mathematical equivalent of The Flight of the Bumble Bee — a staccato, allegro recitation of pi to 140 decimal places that had spectators finger-snapping and foot-tapping to his tempo — until, in a moment of distraction, he paused.

“He’s calculating!” hollered a heckler.

Mr. Hesterberg gave a shrug and gave up. “I’ve lost my place.” This was a disappointment — his personal best was 243 decimal places.

Venerable mathematician John Horton Conway played adjudicator, augmenting the speed-reading skills of student judges who followed along with multi-page π printouts. Prof. Conway invented the Game of Life, another notorious mathematical time-waster, and discovered “surreal” numbers. In his prime, he could recite π to 1,111 digits, often taking Sunday walks rattling it off, relay-style, 100 numbers at a time, with his second wife.

The history of this mnemonic tradition is uncertain. Would Isaac Newton have joined any π-reciting antics while a student at Cambridge circa the 1660s? “He was definitely that kind of guy,” said James Gleick, author of a notable Newton biography. “Newton was obsessed with the pure computation of numbers.”

But he couldn’t have recited pi to hundreds of decimal place – as Mr. Gleick pointed out, “Where would he have found it?” In 2002, a computer calculated π to 1.24 trillion decimal places. But in the 1660s, “if you were Isaac Newton and wanted to know π, you had to work it out yourself. So he did — to about 15 places. Which was a lot — way more than anyone needed.”

Mr. Hesterberg, who will compete in the contest at Princeton again today, hasn’t been practising lately, reducing his limit to about 100. “Of course,” he says in an e-mail, “100 digits is still about 90 more than any engineer would ever need, and about 98 more than I need. … Memorizing π was an amusing distraction — bedtime reading, actually — but not otherwise useful to me.”

The current unofficial record is held by a Japanese mental-health counsellor, Akira Haraguchi, who recited 100,000 decimals in 2006.

As the Princeton contestants took their tries, Prof. Conway’s lips followed along in silent nostalgia. Occasionally, he barked disqualifications: “Ahh! You missed one!” With the five competitors done, Yang Mou, president of the math club, wheedled the professor to participate, having heard rumours of his prowess.

“No, no, I’m sorry. I haven’t been practising. I always mean to, but I forget,” said Prof. Conway, chary of any estimates of his current capabilities (later in the hallway, he easily climbed to 100 decimal places, only once gasping for breath).

After Mr. Hesterberg received his prize — a binary clock — next came the pie-eating contest. “I haven’t recovered from last year — that was an awful spectacle,” said Prof. Simon Kochen, known for his expertise in the foundations of quantum mechanics and number theory, and most recently co-author with Prof. Conway of the Free Will Theorem (which, using geometry, physics and philosophy, claims to prove the existence of free will).

Contestants were apportioned three minutes and 14 seconds to devour as much of a pie as possible, utensils optional. The diminutive departmental chair, Andrew Wiles, famous for solving Fermat’s Last Theorem, retreated to his office before pie started to fly.

“I’m strongly tempted to take part in this,” Prof. Conway said. “But I suspect it would be the cause of my death.” He had survived a triple bypass and more recently a stroke. There was a lot of oatmeal and dry toast in his diet. “Pie is not allowed.”

The contestants took their seats, took their marks and dug in. Then, with no more than one minute on the stopwatch, Prof. Conway, 71 but a self-admitted eternal child, lost his self-control.

After surveying the selection of apple, pecan, blueberry, peach, cherry and even a very bouffant lemon meringue, he chose pumpkin, angled his scraggily bearded mouth for the best approach, and took a monster bite. Then another, and another and another, chomping his way around the pie’s circumference.

His colleagues and students laughed and cheered, ushering the professor to victory. He caught his breath, rubbed his sated stomach and accepted his binary clock.

“I already have one of these,” he said.