He studied at University College, Hull obtaining a BSc (external degree of the University of London) in 1954.He obtained his PhD in Zoology at the same institution, (by then Hull University) in 1957. He went to the University of Birmingham for post-doctoral work, and was appointed Lecturer in the Department of Zoology and Comparative Physiology in 1959. He worked for a year at Harvard Medical School then returned to Birmingham as a Senior Lecturer in 1968, a position he held until 1987. His former students include Sir Paul Nurse winner of the 2001 Nobel Prize for Medicine, and Dr Arthur Jones, a proponent of intelligent design. In 1974 the University of Birmingham awarded him a DSc for his work.
During 1987 to 1989 he was Senior Embryological Advisor and Manager of Laboratories at the IVF/Infertility Clinic of a London private hospital. During 1995 to 1996 he was Visiting Professor at the Weizmann Institute, Israel. From 1996 to 2000 he was a consultant at the University of Warwick jointly to the Ecosystems Unit of the Biology Dept and the Mathematics Institute. He is currently an Honorary Professor at the Mathematics Institute of the University of Warwick and a Visiting Professor at Durham Business School.
He has published in prestigious journals such as Nature and written textbooks such as Living Embryos - an Introduction to the Study of Animal Development (1967) and Reproduction (1977). His theory of sperm redundancy has been important in studies of fertility and treatment of infertility. He is a Fellow of the Institute of Biology.
Cohen has worked as a consultant for both science fiction television shows and science fiction novelists on how to construct plausible alien. His collaborators and associated works include Anne McCaffrey for the Dragonriders of Pern; the Legacy of Heorot collaboration of Larry Niven, Jerry Pournelle and Steven Barnes; several works by Terry Pratchett; James White of Sector General fame; and David Gerrold, whom he helped to design the Chtorr ecology.
He has also collaborated with fellow University of Warwick researcher Ian Stewart to write deep books on epistemology, and the science of the Discworld.
Jack Cohen is a member of the high IQ society Mensa. He was one of the small group of British Mensans who persuaded science fiction author Isaac Asimov to visit the United Kingdom in June 1974.
In 1999 Terry Pratchett made both Jack and Professor Ian Stewart "Honorary Wizards of the Unseen University" at the same ceremony at which the University of Warwick gave Terry Pratchett an honorary degree.
He has a long standing interest in the design and natural balance of (particularly manmade)lake ecosystems, having designed new filtration systems but also led in reinstating Victorian designed systems at various locations around the UK.
In 2009, he became a patron of the anti-circumcision charity NORM-UK.
His hobbies, according to the author profiles in his books, include boomerang-throwing and keeping strange animals.