The 20th Century has rightfully been called the American Century. After World War II, there was no question to our position as a superpower in the world, and beyond military power, Americans had great influence in industry, the arts and sciences and education as well.
In the 19th Century, not so much. We were a long way away from Europe and Europe was the happening place. Even in the English speaking world, the United Kingdom was the pre-eminent power and we were still a struggling former colony.
In American history classes, we give a special place to the American inventors like Eli Whitney, Robert Fulton, Thomas Edison and Samuel Morse. There were also important inventors in Europe from the same era, but they were not just tinkerers but theorists. For example, it's only Americans that think Samuel Morse invented the telegraph. There was a working telegraphic system at the University of Gottingen in what is now Germany four years before Morse got his telegraph working. The designers were the great mathematician Carl Gauss and his partner Wilhelm Weber. Morse deserves credit for the code named after him, but the mechanical device itself was developed by others, and anyone in the sciences in Europe at the time would have known about it.
The title of first important American theoretical physicist belongs to Josiah Willard Gibbs. He was the first American to get a Ph.D. in engineering, which he was awarded after completing his studies at Yale. Being at the top of his field in a backwater town, he went to Europe to continue his studies, where he worked with the chemist and mathematician Kirchhoff and the physician turned physicist Von Helmholtz. After three years in Europe, he returned to New Haven and took a position at Yale, where he would remain for the rest of his career.
On the theoretical side, Gibbs' best work were papers explaining the effects of thermodynamics in physical chemistry. In math, the Gibbs phenomenon is named after him, which states that a Fourier series approximation of a function will have small errors at the end points. There is also the Gibbs phase rule, a physical state called Gibbs free energy and the Gibbsian example.
His published papers at first garnered only a little attention in Europe, largely because they were published in English. Once translated into German, he began to gain the attention he deserved. His first great supporter in Europe was the Scottish physicist James Clerk Maxwell. When the papers only existed written in English, it may have been Maxwell alone who knew both enough English and enough math to appreciate them. While America was a backwater former colony of England at the time, even being in Britain was a handicap for serious physicists of the day, since most of the important work was being published in German or French.
It is said a prophet is little known in his own land, and that was certainly the case with Gibbs. There was no one in the United States anywhere near his level in theoretical physics at the time. When Maxwell traveled to the Philadelphia to accept membership into the American Philosophical Society in 1875, he was met by the luminaries and august members of the organization and thrown a party befitting a great man crossing the ocean to visit his colonial colleagues. His first question after shaking hands all around was "Where's Gibbs?" The Yanks in Philadelphia had no idea they had someone at the same level as Maxwell living not 200 miles to the north in New Haven.
Gibbs' name has not been forgotten. When the Post Office put together a series of stamps to honor great American scientists in 2005, the four people so honored were John Von Neumann, the only immigrant in the group, Richard Feynman, Barbara McLintock and Josiah Willard Gibbs.