Answer
No, John Horton Conway did not win the Fields Medal, despite his groundbreaking contributions to mathematics. The Fields Medal is awarded every four years to mathematicians under the age of 40 for their outstanding achievements in the field. While Conway received numerous accolades, including the Pólya Prize, the Berwick Prize, and the Nemmers Prize, the Fields Medal eluded him, likely due to the committee's emphasis on groundbreaking theorems and publications.