Maxime Bôcher (August 28, 1867 – September 12, 1918) was an American mathematician who published about 100 papers on differential equations, series, and algebra.

Bôcher received an excellent education from his parents and from a number of public and private schools in Massachusetts.

At Harvard, he studied a wide range of topics, including mathematics, Latin, chemistry, philosophy, zoology, geography, geology, meteorology, Roman art, and music.

Bôcher was awarded many prestigious prizes, which allowed him to travel to Europe to do research.

The University of Göttingen was then the leading mathematics university, and he attended there lectures by Felix Klein, Arthur Moritz Schoenflies, Hermann Schwarz, Issai Schur and Woldemar Voigt.

He was awarded a doctorate in 1891 for his dissertation Über die Reihenentwicklungen der Potentialtheorie (German for "On the Development of the Potential Function into Series"); he was encouraged to study this topic by Klein.

Bôcher's equation is a second-order ordinary differential equation of the form: The Bôcher Memorial Prize is awarded by the American Mathematical Society every five years for notable research in analysis that has appeared in a recognized North American journal.

Winners have included James W. Alexander II (1928), Eric Temple Bell (1924), George D. Birkhoff (1923), Paul J. Cohen (1964), Solomon Lefschetz (1924), Marston Morse and Norbert Wiener (1933), and John von Neumann (1938).