Mathematics has turned into an unusually lucrative profession for Maxim Kontsevich. First, Dr. Kontsevich, 49, who works at the Institute of Advanced Scientific Studies outside Paris, won the 2012 Shaw Prize in Mathematical Sciences, an honor accompanied by a $1 million award. Then a couple of months later, he was among nine people who received a new physics prize — and $3 million each — from Yuri Milner, a Russian who dropped out of graduate studies in physics and became a successful investor in Internet companies like Facebook.

A few weeks ago, Dr. Kontsevich heard from Mr. Milner again. Mr. Milner told him he was one of five inaugural winners of the Breakthrough Prize in Mathematics, financed by Mr. Milner and Mark Zuckerberg, the founder of Facebook; that prize also comes with $3 million. Mr. Milner officially announced the winners on Monday.

“I was a bit embarrassed, I have to say,” Dr. Kontsevich said of his good fortune.

Mr. Milner recalled: “I think he was laughing. He’s a well-deserving individual. He really sits in the middle between physics and mathematics. And what he’s rewarded for now is pure mathematics as opposed to physics. His work here is really very different from what he got his other prize for.”

Image Terence Tao Credit... Breakthrough Prize in Mathematics

The citation notes a wide swath of mathematical fields where Dr. Kontsevich repeatedly bumped into unexpected connections. For example, about 15 years ago, he collaborated on what looks like a simple procedure called interval exchange transformations, which is essentially like taking a piece of rope, cutting it into pieces and shuffling them together in a different order. The mathematics of cutting and reshuffling turns out to be complex, and recently reappeared in a new area of abstract algebra used in some theoretical physics models — “which was a really great surprise,” Dr. Kontsevich said.