"The question whether mathematics is discovered or created divides the mathematical community into two camps... Deep in my mind, I am fully convinced that, based on some very elementary and not yet understood endowment of our brain, the fantastic mathematical universe is human-made. This can't be proved mathematically. The best one can hope for are compelling arguments and strong empirical evidence. This is what Klaus Truemper's book The Construction of Mathematics: The Human Mind's Greatest Achievement delivers. It sheds surprising and fascinating new light on the issue. Powerful arguments are provided by using the method of language games invented by the philosopher Ludwig Wittgenstein. Employing results of modern brain science about human cognition, the book also explains how it is possible that eminent mathematicians and scientists arrive at diametrically opposed answers for the creation vs. discovery question."
--Martin Grötschel, mathematician and President, Berlin-Brandenburg Academy of Sciences and Humanities, Germany
"Klaus Truemper has made an original and daring attack on the foundations of mathematics. Readers will enjoy his forthright and unswerving analysis. His ideas should become recognized and influential."
--Reuben Hersh, mathematician and award-winning author of a number of books on the nature, practice, and social impact of mathematics
"This wonderful book addresses the oldest and thorniest question in the philosophy of mathematics: Is mathematics discovery or invention? The key contribution of this book is to use Ludwig Wittgenstein's technique of language games to shed light on this deep philosophical question. Overall this is the most insightful and compelling contribution to the debate that I have read and I am inclined to agree with the conclusions. But the book is much more than an important contribution to a fundamental debate. It is beautifully and lucidly written and, in contrast to most texts on philosophical matters, is enjoyable and easy to read... I cannot recommend it too highly."
--Geoffrey Whittle, mathematician, Victoria University of Wellington, New Zealand
"Klaus Truemper's The Construction of Mathematics: The Human Mind's Greatest Achievement is a unique blend of history and penetrating philosophical analysis. After taking the reader on a dizzying journey through the history of mathematics and computation, Truemper arrives at his central question: Is mathematics discovered or invented? Relying on a range of philosophical approaches and some brilliant argumentation, he arrives at what seems like the only possible answer. Mathematics, he shows, is not "out there," waiting to be discovered; it is, rather, the highest creation of the human mind. Truemper's book is not only insightful and original but also fast-paced and gripping. Whether you are a mathematician, historian, philosopher, or layman, you will find it thought-provoking as well as highly enjoyable."
--Amir Alexander, historian of science and award-winning author of books on the interconnection of mathematics and its social, cultural, and political settings