Cohen completed a postdoctoral fellowship in chemistry at Stanford University in 2007. He received a Ph.D. in experimental physics from Stanford in 2006 with W.E. Moerner and a Ph.D in theoretical physics from Cambridge University, where he was a Marshall Scholar, in 2003. He graduated Phi Beta Kappa and summa cum laude from Harvard College with an A.B. in chemistry and physics. He attended Hunter College Elementary School & Hunter College High School, a gifted magnet school in New York City. He is the son of Joel E. Cohen, Abby Rockefeller Mauze Professor of Populations at Rockefeller University in New York.
Cohen's research combines building physical tools to probe biological molecules, using nanofabrication, lasers, microfluidics, electronics and biochemistry to generate data. His current research includes single-molecule spectroscopy of microbial rhodopsins, the motion of bacteria in mucus, and new magneto-optical and chiroptical effects in organic molecules. In 2010 and 2011, Cohen taught Physical Sciences 1, Harvard's introductory course in chemistry and physics, with Hongkun Park.
In fifth grade, Cohen invented an "alarm" clock that woke him by playing a prerecorded message. In high school, Cohen created an eye-tracking apparatus for neuroscience experiments to benefit the disabled, an electrochemical hard disk drive, and a device that applies physics to allow his eye movements to maneuver his computer cursor. He also invented and built a nanoscale patterning technique using an electrochemical scanning tunneling microscope in his bedroom, which led to winning the Westinghouse Science Talent Search. For his dissertation at Stanford, Cohen invented the Anti-Brownian Electrokinetic trap, known as the ABEL trap, a machine capable of trapping and manipulating individual biomolecules in solution. His success in the Westinghouse competition led the then mayor of New York City, Rudy Giuliani, to declare March 12, 1997 "Adam Ezra Cohen Day."
In 2012 Popular Science named Cohen one of the "Brilliant 10: the 10 most promising young scientists working today." In 2010 he won the Presidential Early Career Award for Scientists and Engineers under the Department of Defense. and a NIH Director's New Innovator Award. In 2007, he was named to the MIT Technology Review TR35 as one of the top 35 innovators in the world under the age of 35. In high school, Cohen won the Westinghouse Science Talent Search, now Intel Science Talent Search, for an invention that involved building a scanning tunneling microscope in his bedroom. He was also inducted into the National Gallery for America’s Young Inventors for the same invention.
In 2014, he won the inaugural national Blavatnik National Award for Young Scientists, awarded by the Blavatnik Family Foundation and the New York Academy of Sciences to "celebrate America’s most innovative and promising faculty-rank scientists and engineers.",
Cohen, along with a fellow scientist Benjamin Rapoport, have visited Liberia working on science education. On their first trip in June 2009, the two toured the nation, while in 2010 they conducted an intensive training program at the University of Liberia that combined science basics, classroom teaching, laboratory techniques, and independent research.