Harry Vandiver developed an antagonism to public education and left school at an early age to work for his father's firm.
In 1904 he collaborated with Birkhoff on a paper on the prime factors of an - bn. Birkhoff persuaded him to accept a post at Cornell University in 1919. He worked during the summer with Dickson at Chicago on the History of the Theory of Numbers. In 1924 he moved to the University of Texas.
Vandiver was awarded the Cole Prize by the American Mathematical Society in 1931 for his papers on Fermat's last theorem published in the Transactions of the American Mathematical Society and in the Annals of Mathematics during the preceding five years. In particular special mention was made of the paper entitled On Fermat's last theorem published in the Transactions of the American Mathematical Society in 1929.
In 1952 Vandiver used a computer to study Fermat's Last Theorem and was able to prove it for all primes less than 2000. It is this work on Fermat's Last Theorem for which he is best known.
Vandiver never owned a house and lived with his wife in the Alamo Hotel where he had a large collection of classical recordings.