If mathematical brilliance generated electricity, there'd be enough wattage at this restaurant table – a stone's throw from the American Institute of Math – for a good 20 million homes. The conversation flows from food to hobbies to, well, zeta functions. But as dinner winds down, George Csordas, a distinguished-looking functions theorist from the University of Hawaii, confesses that he never balances his checkbook. "I hate doing the math," he says with a broad smile.

Victor Vinnikov from Israel's Ben Gurion University jumps in. "It's restaurant checks for me," he says. "I can calculate the 15 percent tip, but adding it back in – forget it."

These two are part of a group of 28 mathematicians who recently assembled to ponder some of the hardest math problems since Archimedes – part of a week-long workshop at the institute.

Now, before you flip away to read about something simpler – like, say, the Middle East – let me state up front just how much math you'll need to understand for this article: zero.

Let me also state the most important number for this group of mathematicians: zero.

Finally, let me offer a definition of math from David Farmer, director of programming at the institute: Math is about making connections, especially where they aren't obvious.

In other words, it's a dating service for numeric ideas. These 28 experts play Cupid.

To do its work, the institute chooses some of the brightest mathematicians from disparate specialties and provides a focused but informal schedule packed with good food and libations, along with lots of small workspaces where no one is ever far from a whiteboard. Week-long workshops focus on problems from braid groups to keeping graduate students devoted to math.

The institute's executive director, Brian Conrey, jokes that the definition of an extroverted mathematician is one who looks at the other person's shoes in a conversation. But this is decidedly not the case with the 21 men and seven women who make up this week's group. Despite spending considerable mental time in places that would take half a book to explain, they laugh, chat, banter, and presumably mow their lawns much like everyone else, with nary a pocket protector in sight.

This particular group is puzzling a number of problems this week, the most famous of which is the Riemann Hypothesis. It was posited in 1859 by Bernhard Riemann, a German mathematician who was smart in the same way that Einstein was something of an idea man. Proving the hypothesis has become the math equivalent of hunting down the FBI's most wanted.

The good news is that the hypothesis involves an equation that can be written in the space of a postage stamp. The bad news is that it can take lifetimes to understand.

So let's say this: It involves a seemingly harmless set of numbers called prime – numbers divisible only by themselves and by 1. Where they occurred was unpredictable, until Riemann came up with his equation. Mathematicians believe that zeros will be the key to proving the equation, which is why they are so ardently pursuing the great goose eggs. Explaining it further would require that half a book. But here's something easy to grasp – whoever proves the hypothesis first will get a million-dollar reward.

Who says there's no real-world benefit to pure math?

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