Foundations of Mathematics

Mathematical and Formal Logic

What contributions did David Hilbert make to mathematics?

German mathematician David Hilbert (1862–1943) contributed a great deal to mathematical logic, as well as mathematics in general. In 1890 his proof of the theorem of invariants replaced earlier work on the subject and paved the way for modern algebraic geometry; by 1897, his algebraic number theory lead to many developments in that field. His contributions also included discoveries in number theory, mathematical logic, differential equations, multivariable calculus, Euclidean geometry, and even mathematical (theoretical) physics.

Hilbert is most well-known for presenting “Hilbert’s problems,” which originally were a set of 23 unsolved mathematical problems that he hoped would eventually lead to many more disciplines within the field of mathematics. His idea worked: As mathematicians attempted to solve the problems, their efforts led to mathematical discoveries in the 20th century, although a number of the problems have yet to be solved. (For more information about Hilbert, see “History of Mathematics.”)


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