I will outline what we know about this their compatibility, which is one of the most interesting and important problems in theoretical science, as well as explain some outstanding open questions.

Arthur Jaffe, professor at Harvard University, is a member of the American Academy of Arts and Sciences and of the U.S. National Academy of Sciences, as well as an Honorary Member of the Royal Irish Academy. Arthur was the president of the American Mathematical Society. He received the Dannie Heineman Prize for Mathematical Physics from the American Institute of Physics，medal from the Collège de France in 1990, and Physical Science Prize from the New York Academy of Sciences.
He conceived the Clay Mathematics Institute, serving as a Founding Member and Director, as well as its Founding President. In this role he designed and implemented most of their initial programs, including the Millennium Prize Problems in mathematics. Jaffe served for 21 years as Chief Editor of Communications in Mathematical Physics, a leading journal in the field.