Ulam was born in Lemberg, Poland, Austrian Empire (now L'viv, Ukraine). His master in mathematics was Stefan Banach a great Polish mathematician, one of the moving spirits of the Lvov school of mathematics.
Ulam came to the US in 1938 as a Harvard Junior Fellow. When his fellowship was not renewed, he served on the faculty at the University of Wisconsin, and supported his brother, Adam, who had fled from Poland on the eve of World War. While there, in the midst of World War II, his friend John von Neumann invited him to a secret project in New Mexico. To research the invitation, Ulam checked out a book on New Mexico from the University Library, and found, listed on the library check-out card, those who had successively disappeared from the campus at the UW. Ulam then joined the Manhattan Project.
Ulam then went on to devise a better method himself. He was the first one to realize that you could place all the of H-bomb's components inside one casing, put a fission bomb at one end and thermonuclear material at the other, and use shock waves from the fisson bomb to compress and detonate a fusion fuel.
Teller resisted this idea at first, then saw its merit, and suggested the use of radiation rather than shock waves. "Radiation implosion," as the method came to be called, has been the standard method of creating H-bombs ever since.
Ulam also invented nuclear pulse propulsion, and at the end of his life, declared it the invention of which he was most proud.
His autobiography was published in 1983: Ulam, S.M., Adventures of a mathematician, Charles Scribner's sons, New York (1983)