"Math Whizzes at Conference Prove Just How Exciting The Tate Conjecture Can Be"

August 17, 2007

"One is tempted to feel sorry for mathematicians," columnist Lee Gomes of the Wall Street Journal wrote on August 1.

"In contrast to, say, physicists," Gomes opined, "mathematicians don't have their own Nobel Prize; they rarely get hired by hedge funds; they don't have grand toys like particle accelerators to play with; and their work is usually so recondite that not even their families understand it."

"But save your pity, as this crowd has a blast doing what it does," he noted. "How else can you explain 30 or so renowned mathematicians spending all of last week sitting happily in barely comfortable chairs inside a joyless conference room working 9-to-5 on a dense math problem, without stopping so much as to check their BlackBerrys?"

The location for this mathematical get-together was Palo Alto, at a workshop sponsored by the American Institute of Mathematics. The topic was the Tate conjecture, which was first put forward in the 1960s by mathematician John Tate. Tate, now 82 years old, was in attendance. The Tate conjecture is closely connected with the Hodge conjecture, which is one of seven Millennium Prize Problems. The Clay Mathematics Institute has offered $1 million for the solution to each of these problems.

One explanation of the Tate conjecture, Gomes wrote, is "to say that mathematicians often find it useful to study the solution to a complicated equation by transforming it into a shape. The Tate conjecture provides guidance on how closely that shape corresponds to the numbers in the original solution."

Over the five days of the conference, which ran from July 23-27, 2007, these mathematicians did what people do at many workshops: They listened to presentations, broke up into small groups, gossiped over drinks before dinner, took a group picture, and celebrated with a banquet at a Chinese restaurant.

In the end, the Tate conjecture remained unsolved, but there was progress reported. V. Kumar Murty, of the University of Toronto, said that, as a result of the AIM sessions, he has a new line of attack, based on ideas about Abelian varieties over finite fields, originally formulated by J.S. Milne. Milne himself was also in attendance.

Source: Wall Street Journal, August 1, 2007.