This book is devoted to the history of Hilbert's problems and their solutions. The collection of 23 mathematical problems presented by David Hilbert at the ICM in Paris in 1900 became soon a guiding inspiration for mathematicians in the 20th century. The book under review starts with a description of Hilbert's biography and the background of his work and his problems. Then the author describes the achievements and success of people who devoted their lives to solve Hilbert's problem. The first part is about problems 1, 2 and 10 (set theory and real numbers), the second part explains problems 3, 4, 5 and 6 (geometry, specific areas), the third part describes problems 7, 8, 9, 11 and 12 (number theory), the fourth part is devoted to problems 14, 15, 16, 17 and 18 (modern algebra, geometry and graph theory) and the last part discusses problems 13, 19, 20, 21, 22 and 23 (analysis). In all cases, the mathematical substance of these problems, their solutions or the attempts to solve them, short biographical information on mathematicians involved and interesting historical aspects are described. This part of the book can also be appreciated by readers who are not mathematicians. An appendix contains Hilbert's lecture delivered at the Second International Congress of Mathematicians in 1900 (in English) and reprinted from the Bulletin of the American Mathematical Society 8(1902). Ample notes, an extensive selected bibliography and an alphabetical index are included. The book can be recommended to everybody who wants to know more about the birth of modern mathematics in the first half of the 20th century.

Reviewer:

mnem