Customer Reviews

Hilbert

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"Hilbert" is justly famous as one of the best mathematical biographies around. Constance Reid, who also wrote a biography of Hilbert's student Courant, initially ran into some resistance from Hilbert's associates when she started work on this book. Max Born was not keen on the idea of a woman, who was neither German nor a mathematician, writing a study of Hilbert's life. Born was enthusiastic about the final product, however, and it has become a classic.

Hilbert took over from Poincare the title of the most famous mathematician in the world. His mathematical achievements are numerous and varied; Reid does a good job of providing an overview of the impact Hilbert had on many different fields, and of his style; his strengths and weaknesses. There is a good deal of coverage of the famous twenty-three Hilbert problems, presented to the Second International Congress of Mathematicians in Paris in 1900, including a large section of the talk Hilbert gave.

Reid paints a vivid picture of the mathematical circle at Gottingen, a luminous collection of talents. Minkowski and Hilbert were close friends; Klein was the director of the institute there; Emmy Noether was there; Hurwitz; Zermelo; Landau; the list is long and impressive. It's all the more sad to read about the way the Institute was destroyed by the Nazis in the name of racial purity. Almost without exception the leading mathematicians emigrated, one by one, to America. Hilbert, who had retired in 1930 (retirement at age 68 was mandatory) was forced to watch as the work of decades was dismantled. The last years, of age, fading memory and the privations of war, are mercifully given less than a dozen pages.

Hilbert's life leads from the great days of the mid-nineteenth century to the Nazis and the atomic bomb. Reid has done a wonderful job of capturing the feel of Germany over his long life, and the mathematic impact and importance of his work. A compulsory book for those interested in modern mathematical history.

"Hilbert" tells, in a direct and pleasant way, about both the history and mathematics of this great German mathematician. I recommend it to whoever is interested in learning about the social, scientific and political contexts of mathematics in Germany at the beginning of our century. It's an important source of information for those interested in history of mathematics. Important references are also made regarding the developments of physics in Germany prior to the 2nd World War. The book is a source of information on the roots of some developments of science which are, nowadays, fundamental to courses in areas of mathematics, physics and engineering (such as calculus of variations, integral equations, foundations of mathematics and mathematical physics). As informative and well written as "Courant", by the same author.

Very well written. Gives a great feel for who Hilbert was as a person. It also does a good job of placing his achievments amoung the other mathematians of his time. I have attempted reading a few biography's of other mathematicians that focus on the math and not the person. They are almost unreadable. This book does not make this mistake. I have just bought "Foundations of Geometry" because of this book. I highly recommend it. PS - 4 stars is as high a rating as I give. I like having room to move for the truely fantastic.

David Hilbert was arguably one of the greatest mathematicians
ever!. He contributed to several branches of mathematics,
including functional analysis, mathematical physics,
calculus of variations, and algebraic number theory.
(Everyone knows what a Hilbert space is right!)

At the turn of the 20th century, Hilbert enumerated
23 unsolved problems of mathematics that he considered worthy
of further investigation. To this day, very few of these, including
the 10th problem, on the finite solvability of Diophantine
equations, have been resolved! (thanks to
Yuri Matiyasevich, Martin Davis and Julia Robinson!).
Besides, Hilbert was also a character (read the section
when Norbert Weiner of cybernetics fame, came to give
a talk at Gottingen, and .... :-)).

Incidentally the author Constance Reid is the sister of
Julia Robinson (of Hilbert's 10th problem fame!),
hence there can no one better to write about
Hilbert!. Besides Constance Reid is a well known chronicler
of mathematicians lives (this one is a tour de force and
her best!).

No one can can call himself/herself a mathematician without
having Reid's book on his/her bookshelf. Strongly
recommended!

i almost cried when i got up to the death of minkowski, hilbert's closest friend and a great mathematician in his own right. such is the completely engaging power of constance reid's biography of hilbert. reid did an amazing job integrating the details of professor hilbert's life with the german zeitgeist, all the while providing some exposition of the mathematics for a general audience.

as a student and teacher of mathematics, i went into this book expecting to learn more about one of my heroes, the legendary david hilbert, perhaps best known to most for the famous twenty-three hilbert problems. hilbert did research in an impressive number of areas within mathematics, as well as branched out to physics and the philosophy of mathematics. hilbert's breadth and depth is what gave him the right to influence the course of twentieth century mathematics through the hilbert problems. suffice it to say, hilbert is very important in the mathematical community and i was more than a bit wide-eyed even before reading page one of reid's biography. after turning the last page, i feel like i understand more of the man actually standing on the well-deserved pedestal. my respect for hilbert has only grown knowing of his human flaws and what he has accomplished in spite of them.

it should be made explicit that this book is not just for math nerds. any intelligent reader with any interest in mathematics should be able to enjoy and benefit from reading reid's biography. perhaps you've heard of hilbert or the hilbert problems from some newspaper article somewhere and you wondered how mathematicians really lived. if so, that one spark of interest will be rewarded by reid's thorough biography.

of particular interest to me was the other side of the professorial life: teaching. research is the most important part of a mathematician's life, but i'm glad that reid even goes into details on hilbert's teaching style. apparently, hilbert didn't sufficiently prepare for lectures and would often get confused while teaching, needing the help of his assistants to get out of trouble. these mishaps were because of hilbert's strong desire to offer the students the most important points of the lessons, and the details would sometimes suffer because of this emphasis. hilbert would also repeat things as much as five times on purpose in order to get students to remember because he didn't have confidence in their abilities. half of his lecture time would also be spent reviewing the material from the previous lecture, again in order to really ingrain the material in the students' minds. i found these pedagogical details quite fascinating.

outside of hilbert's life, reid does a fantastic job transporting the reader to germany. the germans have a rich history and complex culture, but many folks can only think of the "n" word when it comes to germany. it's a pet peeve of mine that a large number of people cannot distinguish between "nazi" and "german." at göttingen university, mathematicians of all backgrounds, and even from different countries, were able to come together and work on mathematics under the leadership of david hilbert. göttingen was the epicenter of mathematical thought and it was gutted and spiritually destroyed by the nazis in their misguided quest for racial purity. hilbert himself was anti-nazi and it must've torn his heart apart watching the math department suffer such a great downfall because of nazi policies. this human story of political madness turning its sword on the purist of realms should hopefully dispel some negative german stereotypes. it is hoped that the reader will appreciate the tragedy of german identity a little more afterward.

those looking for a similar style of biography meshed with some explanations of higher mathematics for a non-specialized audience should also check out benjamin yandell's "the honors class: hilbert's problems and their solvers." yandell covers the hilbert problems in more depth than they are in reid's book. finally, reid also wrote "courant," a biography of one of hilbert's students. "courant" is regarded as the sequel to "hilbert" and should be read to complete the story. all three of these books are excellent and will immeasurably enrich the curious reader.

A excellent biography of the German mathematician David Hilbert. Particularly poignant is the loss of Minknowski and the decline of mathematics at Gottingen following the Nazi prosecutions.

Constance Reid is a non-mathematician author, so she is the best person who can explain the 'abstract' modern math to the curious non-mathematicians. By following the book on the Greatest mathematician in 20th AD, the readers can understand the major development of Modern Math evolved around Hilbert and all the world's top mathematicians gathered in Gottingen before WWII.
Most of us learn abstract math without knowing the background from which these abstract concepts were derived. In this book (chapter VI: Changes) I learn from Reid the simple yet revealing explanation of 'Ideals' being born out of conflict of 'Algebraic Number Field' with the 'Fundamental Law of Arithmetics', and Kummer's Ideal Number, Kronecker and Dedekind's complicated 'Ideal Primes', and finaly David Hilbert's great contribution in the 'Ideal Primes' theory.

David Hilbert was arguably one of the greatest mathematicians
ever!. He contributed to several branches of mathematics,
including functional analysis, mathematical physics,
calculus of variations, and algebraic number theory.
(Everyone knows what a Hilbert space is right!)

At the turn of the 20th century, Hilbert enumerated
23 unsolved problems of mathematics that he considered worthy
of further investigation. To this day, very few of these, including
the 10th problem, on the finite solvability of Diophantine
equations, have been resolved! (thanks to
Yuri Matiyasevich, Martin Davis and Julia Robinson!).
Besides, Hilbert was also a character (read the section
when Norbert Weiner of cybernetics fame, came to give
a talk at Gottingen, and .... :-)).

Incidentally the author Constance Reid is the sister of
Julia Robinson (of Hilbert's 10th problem fame!),
hence there can no one better to write about
Hilbert!. Besides Constance Reid is a well known chronicler
of mathematicians lives (this one is a tour de force and
her best!).

No one can can call himself/herself a mathematician without
having Reid's book on his/her bookshelf. Strongly
recommended!