In his professional work, Rivet is known for his theory that South America was originally populated in part by migrants who sailed there from Australia and Melanesia.

Trained as a physician, in 1901 he took part in the Second French Geodesic Mission for survey measurements of the length of a meridian arc to Ecuador.

He remained for five years in South America, where he was mentored by Federico González Suárez, an Ecuadorian bishop, historian and archaeologist.

[1] Returning to France, Rivet went to work with the Muséum national d'histoire naturelle, directed by René Verneau.

In 1926, Rivet participated in founding the Institut d'ethnologie in Paris, together with Marcel Mauss and Lucien Lévy-Bruhl.

On knowing that the Germans were failing to scientifically prove racial difference and superiority, Boas said, "We should never stop repeating the idea that racism is a monstrous error and an imprudent lie."

This exchange took place at a luncheon organised by Boas at the Columbia Faculty Club in honour of Rivet.