[2] In 2012 she won the Henri Poincaré Prize for mathematical physics that she shared with Freeman Dyson, Barry Simon and fellow Frenchwoman Sylvia Serfaty.

[4] Anantharaman was included for her work in "quantum chaos, dynamical systems and Schrödinger equation, including a remarkable advance in the problem of quantum unique ergodicity".

[5] In 2011 she won the Salem Prize which is awarded for work associated with the Fourier Series.

She also took the Grand Prix Jacques Herbrand [fr] from the French Academy of Sciences in 2011.

[8] In 2018, for her work related to “Quantum Chaos”, Anantharaman won the Infosys Prize (in Mathematical Sciences category), one of the highest monetary awards in India that recognize excellence in science and research.