The following excerpt from Jeremy Bernstein's 1964 book on the early history of computers, The Analytical Engine, describes the invention of the first working, all-purpose digital computer by the physicist, Howard Aiken.

In 1937, Howard Aiken ... began work at Harvard on his Ph.D. thesis in physics. The theoretical aspects of the thesis involved the solution of so-called nonlinear ordinary differential equations, which could be done only by means of numerical approximation, and the computations needed to reach these approximate solutions proved to be extremely long. Aiken began considering possible methods of doing the computations on machines, and he soon invented a machine that would evaluate simple polynomials. After a year or two, during which he invented variations on this machine that would solve more complex kinds of problems, it occurred to him that all these machines were, in their logical organization, essentially identical, and he started thinking about the construction of a single general-purpose machine, capable of dealing with any of the problems. He was able to get support for his project from the International Business Machines Corporation, and in 1939 work on the machine -- the Automatic Sequence Controlled Calculator, Mark I, as it became known--was begun at I.B.M. in a collaboration between Aiken and four I.B.M. engineers.... The Mark I was completed in 1944, and was put into operation at Harvard.

(Because the Aiken Mark I used relays for bits, some people give to ENIAC the title of "first all-electronic digital computer." Charles Babbage's design of a century earlier, which required more money and more precise machining than were available to him, might have worked had it been built [a model has just recently been executed]. Aiken became aware of Babbage's work after the Mark I was completed. One of the two principal investigators on ENIAC was also a physicist, so physicists were involved in whichever machine one counts as "first.")