He became known for his approach of using the methods of
mathematical logic to attack problems in
analysis and
abstract algebra. He "introduced many of the fundamental notions of
model theory". Using these methods, he found a way of using
formal logic to show that there are self-consistent nonstandard models of the
real number system that include infinite and infinitesimal numbers. Others, such as
Wilhelmus Luxemburg, showed that the same results could be achieved using
ultrafilters, which made Robinson's work more accessible to mathematicians who lacked training in formal logic. Robinson's book
Non-standard Analysis was published in 1966. Robinson was strongly interested in the history and philosophy of mathematics, and often remarked that he wanted to get inside the head of
Leibniz, the first mathematician to attempt to articulate clearly the concept of
infinitesimal numbers. While at UCLA his colleagues remember him as working hard to accommodate
PhD students of all levels of ability by finding them projects of the appropriate difficulty. He was courted by
Yale, and after some initial reluctance, he moved there in 1967. In the Spring of 1973 he was a member of the
Institute for Advanced Study. He died of
pancreatic cancer in 1974. ==Publications==