Cohen began his undergraduate studies at the Massachusetts Institute of Technology before transferring to Stanford University, where he received his bachelor's degree in human biology.
He then went to the Rockefeller University, where he trained under Victor Wilson, Donald Pfaff, and Susan Schwartz Giblin, receiving his Ph.D. in 1985 for his work on the pudendal nerve evoked response and its modulation by steroid hormones.
From 1988 to 1990 he directed the applications program at Advanced NMR Systems in Woburn Massachusetts, a small startup dedicated to the creation of a practical echo planar imaging instrument.
He joined the faculty at Harvard Massachusetts General Hospital in 1990, where he directed the "Hyperscan" fast imaging laboratory and was the director of the MRI education program until 1993.
While at Advanced NMR Systems he partnered with Jack Belliveau and others at Harvard University to create the first functional images of the human brain by MRI [1] using the ultra-fast instrument he and his collaborators built.
As a co-inventor of functional MRI, Cohen created an iconic cover for Science magazine that became a canonical standard for presentation of such data, and that has been reproduced widely.
With his original training in neurophysiology, Cohen was interested developing a practical means of recording brain electrical signals EEG simultaneously with fMRI.