The Mathematical Experience: A National Book Award Winner

A very interesting book about the philosophy and psychology of mathematics and mathematicians, it presented the different philosophical views of mathematics, it's pros and cons while remaining fair and unbiased as much as possible. Discussed othe interesting topics related to mathematics as well. Highly recommended for people interested in mathematics.

This is ultimately a book on the philosophy of mathematics. Rather than a tedious and dry slog though, the authors use a very broad array of mathematical vignettes - often only a page or two long - to probe into various aspects of mathematics and the activity of doing mathematics in order to illuminate to the reader the position they ultimately present; namely, that mathematics occupies a third philosophical category alongside those of physical reality and subjective reality. For them, "mathematics is an objective reality that is neither subjective nor physical. It is an ideal (i.e., nonphysical) reality that is objective (external to the consciousness of any one person)." This is explicitly not Platonism ("mathematics is not the study of an ideal, preexisting nontemporal reality"); instead, mathematics is a free creation of the mind, and they consider the meaning of mathematics "is to be found in the shared understanding of human beings, not in an external nonhuman reality", and go on to say "in this respect, mathematics is similar to an ideology, a religion, or an art form". What makes mathematics unique from these other areas is "its science-like quality", whereby the ideal nature of the objects of study in mathematics render its conclusions "compelling" and creating "facts" about this third philosophical category.Wherever one stands on this this particular philosophy, the book can be read on multiple levels without agreeing with the philosophy. The short vignettes can be read as enjoyable interesting mathematical and historical snippets, each independent of the other. It can be read as an exposition of the human activity which comprises mathematical investigations and discoveries (or are they creations?). Finally, it can be read as probes into the philosophy and foundations of mathematics.A fair bit of mathematical knowledge (undergrad/grad-level) and some history of mathematics is recommended, and an understanding of philosophy of mathematics and FOM would be helpful if one wants to get the most out of this book. However, anyone with a motivated interest in mathematics should find this book worthwhile.

I had this book and loaned it and it never came back to me. I missed it so I rebought it.As a mathematician this book always represented the joy of mathematics to me. It has some great stories and really encompasses the mathematical experience.

Los temas son los mismos que se tratan en otros libros. Sin embargo, creo que el enfoque de los autores sí es diferente y permite obtener un nuevo punto de vista de la práctica matemática.

As an aspiring mathematican I found this book both very inspiring and ......... I had, like many mathematicians, a view on mathematics as just a formalist game with symbols and abstract concepts before I read this book. However, the book challenges this view, and portraits Mathematics as a fallible science, in which the mathematician's role is not only the toying with symbols, but also the invention of mathematics. And that's a hard process: guessing, wishful thinking, and so on.After I read this book, I have been trying to be a little more Platonist than I used to.

This book was recommended to me by my boyfriend. I teach high school math, so it seems like an ideal book for me. I haven't had a chance to read it yet, but maybe I can get to it during spring break.

Fine, but I though it was more amuse to read, in other words it is not a book to learn maths, it is just to know different aspects of this matter

This is a book I read through and return to again and again. It is truly illuminating about mathematics and the philosophy of mathematics (at least for this chemist).

If you are the kind of person who enjoys Horizon and other science programs but wishes they were less stripped of technicalities and more in depth: if you are very curious about physics and mathematics, you may find this a very stimulating read. After all you don't need to be a good comedian to enjoy watching comedy, so with little mathematical knowledge you can enjoy this very wide ranging discussion of many exotic fields of maths and gain a sense of the range and significance and methodologies of this field at the outer limits of human abstract thought. This very readable, demanding, though provoking book that can occupy you for weeks and sustain several re-readings.

My grandson opened it, skimmed, and emitted approving noises immediately. That's a compliment!

Fantastic discussion of the real nature of mathematics, it covers a huge amount of territory and contains a lot of musings. The gist of it is that platonism is a mirage, mathematics being the science of all patterns and logic, it is not some abstract nonentity existing in an abstract world or cave (cf. Plato, or Penrose) but merely the distillation of all abstract thought and rules, as observed my mankind. Some very interesting recent mathematics theorems and discoveries make it really different from the usual philosophical approaches to math analysis. A very intelligent and rewarding book, worth reading a few times to grasp all the contents, and quite long (I compare with books today which stop at about 300 pp.) to boot!

Llegó perfecto de Trumpland, todo bien y lo bueno es que no te cobran los impuestos que allá tienen ya que termina aquí el producto. Super buen libro que más que matemáticas te mete en la filosofía e historia de qué son.

super book for general audience.