Hilbert summary

Formative Years

In Hilbert by Constance Reid, we delve into the life of David Hilbert, a German mathematician who was born in 1862. The book begins by exploring Hilbert's childhood, his early education, and his fascination with mathematics. It describes how he excelled in his studies, showing remarkable talent in geometry, algebra, and number theory, and how he eventually pursued a career in mathematics against his father's wishes.

As Hilbert progresses through his studies, we witness his growing interest in the foundations of mathematics, particularly the study of geometry. His doctoral thesis, which he completed at the age of 23, was a groundbreaking work in the field. This early success laid the foundation for his future contributions to the mathematical world.

Academic Career and Contributions

Throughout Hilbert, we see Hilbert's academic career flourish. He becomes a professor at the University of Königsberg, where he significantly influences the next generation of mathematicians. His famous lecture series on mathematical problems, delivered in 1900, sets the agenda for mathematical research in the 20th century. In these lectures, Hilbert presents 23 unsolved mathematical problems, which become known as 'Hilbert's Problems' and have a profound impact on the development of modern mathematics.

Reid also highlights Hilbert's work in developing the theory of integral equations, his contributions to mathematical physics, and his pioneering efforts in the field of mathematical logic. Hilbert's influence extends to other areas of mathematics as well, including his work on algebraic number theory and his fundamental contributions to the theory of invariants.

Personal Life and Professional Recognition

While Hilbert focuses primarily on his professional achievements, we also gain insights into his personal life. Hilbert marries Käthe Jerosch, and they have a son and a daughter. His family life is marked by tragedy when his son, Franz, dies in World War I. Despite this personal loss, Hilbert continues his work and is eventually recognized as one of the leading mathematicians of his time.

In 1930, Hilbert delivers a famous address in Paris, where he famously states, 'We must know, we will know.' This declaration encapsulates his unyielding belief in the power of human intellect to solve the most challenging problems, a belief that continues to inspire mathematicians to this day.

Later Years and Legacy

The latter part of Hilbert covers Hilbert's later years, marked by the rise of the Nazi regime in Germany. Despite the increasing persecution of Jews, Hilbert remains in Germany, refusing to leave, as he believes in the power of reason and the universality of mathematics. However, the anti-Semitic policies of the Nazis impact his professional life, and he is eventually forced to retire.

Hilbert passes away in 1943, leaving behind a legacy that continues to influence mathematics. His work has had a profound impact on various branches of the discipline, and his name remains associated with numerous mathematical concepts, theorems, and problems. In Hilbert, Constance Reid provides a comprehensive and insightful account of this extraordinary mathematician's life and his enduring contributions to the field.