july/august 2010

After breakfast one morning in August, the mathematician Terence Tao opened an email from three physicists he didn’t know. The trio explained that they’d stumbled across a simple formula that, if true, established an unexpected relationship between some of the most basic and important objects in linear algebra.

The formula “looked too good to be true,” says Tao, who is a professor at UCLA, a Fields medalist, and one of the world’s leading mathematicians. “Something this short and simple—it should have been in textbooks already,” he said. “So my first thought was, no, this can’t be true.”

Then he thought about it some more.

The physicists—Stephen Parke of Fermi National Accelerator Laboratory, Xining Zhang of the University of Chicago, and Peter Denton of Brookhaven National Laboratory—had arrived at the mathematical identity about two months earlier while grappling with the strange behavior of particles called neutrinos.

Democracy depends on the consent of the losers. For most of the 20th century, parties and candidates in the United States have competed in elections with the understanding that electoral defeats are neither permanent nor intolerable. The losers could accept the result, adjust their ideas and coalitions, and move on to fight in the next election. Ideas and policies would be contested, sometimes viciously, but however heated the rhetoric got, defeat was not generally equated with political annihilation. The stakes could feel high, but rarely existential. In recent years, however, beginning before the election of Donald Trump and accelerating since, that has changed.

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Is a color-blind political system possible under our Constitution? If it is, the Supreme Court’s evisceration of the Voting Rights Act in 2013 did little to help matters. While black people in America today are not experiencing 1950s levels of voter suppression, efforts to keep them and other citizens from participating in elections began within 24 hours of the Shelby County v. Holder ruling and have only increased since then.

In Shelby County’s oral argument, Justice Antonin Scalia cautioned, “Whenever a society adopts racial entitlements, it is very difficult to get them out through the normal political processes.” Ironically enough, there is some truth to an otherwise frighteningly numb claim. American elections have an acute history of racial entitlements—only they don’t privilege black Americans.

Yesterday, strong winds and rainstorms pushed water levels in Venice, Italy, to the second-highest levels ever recorded. The high-water mark hit 74 inches (187 centimeters), just short of the record set in 1966. This exceptional acqua alta has flooded businesses and historic structures, sank boats, and been blamed for one death so far.

Remember these numbers. You’ll be asked about them at the end of the test: 70, 73, 76, and 78.

These are the ages of the leading candidates in the 2020 presidential election: Elizabeth Warren, Donald Trump, Joe Biden, and Bernie Sanders, respectively. In most any other line of work, people in their eighth decade are usually retired. For most of human history—and still in most of the world today—people of this age were usually dead.

Last month, Jimmy Carter, the 95-year-old former U.S. president, said that the office requires a person “to be very flexible with [one’s] mind,” and that by age 80 he wouldn’t have felt able to do the job. He joined the growing ranks of those suggesting they would support an upper age limit for the office, either for purposes of breaking up the gerontocracy or to ensure a person has the physical and cognitive capacity. “You have to be able to go from one subject to another and concentrate on each one adequately and then put them together in a comprehensive way,” Carter said.