Totaro participated in the Study of Mathematically Precocious Youth while in grade school and enrolled at Princeton University in 1980 at the age of thirteen, becoming the youngest freshman in its history.

[4] Totaro's work is influenced by the Hodge conjecture, and is based on the connections and application of topology to algebraic geometry.

[5] In 2000, he was elected Lowndean Professor of Astronomy and Geometry at the University of Cambridge.

In the same year, he was awarded the Whitehead Prize by the London Mathematical Society.

[5] He was included in the 2019 class of fellows of the American Mathematical Society "for contributions to algebraic geometry, Lie theory and cohomology and their connections and for service to the profession".