Seidenberg was born on June 2, 1916, to Harry and Fannie Seidenberg in Washington D.C. He graduated with a B.A. from the University of Maryland in 1937. He completed his Ph.D. in mathematics from Johns Hopkins University in 1943. His Ph.D. thesis, written under the direction of Oscar Zariski, was on Valuation Ideals in Rings of Polynomials in Two Variables.
Seidenberg became an instructor in mathematics at the University of California, Berkeley in 1945. He reached the rank of full professor in 1958. He retired from Berkeley in 1987.
Seidenberg was known for his research in commutative algebra, algebraic geometry, differential algebra, and the history of mathematics. He published Prime ideals and integral dependence written jointly with Irvin Cohen, which greatly simplified the existing proofs of the going-up and going-down theorems of ideal theory. He also made important contributions to algebraic geometry. In 1950, he published a paper called The hyperplane sections of normal varieties, which has proved fundamental in later advances. In 1968, he wrote Elements of the theory of algebraic curves, a book on algebraic geometry. He published several other important papers.
Seidenberg married Ebe Cagli. She was a writer, and the sister of Yole Cagli, Zariski's wife. Ebe and her family immigrated to the United States from Italy. The couple frequently visited Italy and Seidenberg held a visiting professorship at the University of Milan.
