After completing his education Karplus worked at the Institute for Advanced Study in Princeton, where he became interested in the developing, but yet untested, theory of quantum electrodynamics (QED).
The magnetic moment of the electron had been determined very precisely by means of a variety of experiments, but the best theoretical calculations of this quantity, based on quantum mechanics, were seriously at variance with the experimental results.
This was an extremely difficult calculation, requiring more than a year of intense effort from both men; the agreement between their result and the experimental measurements was the first, dramatic confirmation of QED.
When the oldest child, Beverly, was 8, Karplus accepted her invitation to present a science lesson on electricity to her third-grade class, using the Wimshurst machine he had inherited from his grandfather.
Characteristically, Karplus also immediately began generating his own questions about children's thinking, collecting evidence, and developing his own interpretations and explanations of what he observed.
Under the direction of Karplus and Herbert D. Thier, SCIS became a comprehensive, fully tested, hands-on, laboratory-based program in both physical and biological science for grades K-6.
Karplus, however, extended Piaget's methodology to older groups and found that many of these individuals had important gaps in their ability to use abstract reasoning in solving scientific, logical, and mathematical problems.
Karplus further explored and documented the details of college students’ and adults’ thinking as they confronted the issues involved in this critical intellectual transition, finding that many of the issues and problems that he, Piaget, and others had discovered as critical for younger students were still relevant for older individuals, particularly when they were attempting to solve a problem in a discipline that was new to them.
In June 1982 while jogging at Green Lake in Seattle, Washington, Karplus suffered a severe cardiac arrest that ended his academic career.