How Elephant Teeth Taught Scientists Extinction Exists

In 1796, Georges Cuvier convinced his fellow researchers that some bones belonged to a species that no longer roamed the Earth.

At the end of the 18th century, Georges Cuvier was thinking quite seriously about elephant teeth. He was working in Paris, in the National Museum of Natural History, where he had unusual access to bones collected from faraway, exotic places—Asia, Africa, Russia, America.
Plenty of people had seen African elephants, which look like this...
…and Asian elephants, which look like this…
…and concluded that they were more similar than different. But Cuvier looked more closely, and he saw that they were two different species. As Elizabeth Kolbert writes in the New Yorker:

'It is clear that the elephant from Ceylon differs more from that of Africa than the horse from the ass or the goat from the sheep,' he declared. Among the animals’ many distinguishing characteristics were their teeth. The elephant from Ceylon had molars with wavy ridges on the surface, 'like festooned ribbons,' while the elephant from the Cape of Good Hope had teeth with ridges arranged in the shape of diamonds.

One reason that Cuvier was so interested in elephants's teeth was that European explorers had turned up similar, but distinct teeth in the swamps of what would become Kentucky and in Siberia. Cuvier looked closely at the jaw of the Siberian "elephant" and found that its teeth were, like the teeth of the Asian and African elephants, different from the other species's. They belonged, Cuvier eventually concluded, to a distinct type of elephant—a giant one, whose kind no longer existed on the planet. A mammoth.
Before Cuvier made this case, a few other scientists had toyed with the idea that there were animals that had once lived on Earth but were now gone. Cuvier, though, became the foremost advocate for the idea of extinction. His contention, controversial at the time, that in the past the planet had played host to a different cast of creatures, upended the idea that God had created a bunch of animals, plopped them down on Earth, and there they'd lived forever after.
By 1812, Cuvier had identified 49 extinct animals. This is no small feat. It's actually quite hard, Ruth Graham reported recently in the Boston Globe, to pin down how many species have gone extinct:

About 1.5 million plant and animal species have been named, but estimates of how many actually exist vary from 2 million to 100 million. Those numbers change every year: New species are discovered, and others wink out of existence, often without us ever knowing they were there at all. So when scientists talk about thousands of species going extinct in a year, they aren’t counting disappearances: They’re making extrapolations based on estimates of habitat loss, and of how many species currently exist, and how many have existed in history.

Since 1600, according to Graham, there have been 800 documented extinctions. And we have even witnessed some of those extinctions in real time: the dodo and the passenger pigeon, for example.