The Art of the Infinite: The Pleasures of Mathematics

The Art of the Infinite The Pleasures of Mathematics Robert Kaplan s The Nothing That Is A Natural History of Zero was an international best seller translated into eight languages The Times called it elegant discursive and littered with quotes and al

  • Title: The Art of the Infinite: The Pleasures of Mathematics
  • Author: Robert M.Kaplan Ellen Kaplan
  • ISBN: 9780195176063
  • Page: 233
  • Format: Paperback
  • Robert Kaplan s The Nothing That Is A Natural History of Zero was an international best seller, translated into eight languages The Times called it elegant, discursive, and littered with quotes and allusions from Aquinas via Gershwin to Woolf and The Philadelphia Inquirer praised it as absolutely scintillating In this delightful new book, Robert Kaplan, writing togeRobert Kaplan s The Nothing That Is A Natural History of Zero was an international best seller, translated into eight languages The Times called it elegant, discursive, and littered with quotes and allusions from Aquinas via Gershwin to Woolf and The Philadelphia Inquirer praised it as absolutely scintillating In this delightful new book, Robert Kaplan, writing together with his wife Ellen Kaplan, once again takes us on a witty, literate, and accessible tour of the world of mathematics Where The Nothing That Is looked at math through the lens of zero, The Art of the Infinite takes infinity, in its countless guises, as a touchstone for understanding mathematical thinking Tracing a path from Pythagoras, whose great Theorem led inexorably to a discovery that his followers tried in vain to keep secret the existence of irrational numbers through Descartes and Leibniz to the brilliant, haunted Georg Cantor, who proved that infinity can come in different sizes, the Kaplans show how the attempt to grasp the ungraspable embodies the essence of mathematics The Kaplans guide us through the Republic of Numbers, where we meet both its upstanding citizens and shadowy dwellers and we travel across the plane of geometry into the unlikely realm where parallel lines meet Along the way, deft character studies of great mathematicians and equally colorful lesser ones illustrate the opposed yet intertwined modes of mathematical thinking the intutionist notion that we discover mathematical truth as it exists, and the formalist belief that math is true because we invent consistent rules for it Less than All, wrote William Blake, cannot satisfy Man The Art of the Infinite shows us some of the ways that Man has grappled with All, and reveals mathematics as one of the most exhilarating expressions of the human imagination.

    One thought on “The Art of the Infinite: The Pleasures of Mathematics”

    1. Wow - I loved this book. It really opened my mind around how numbers are represented and constructed.This is one of the best books I have read that explores the foundations of numbers in a very understandable format. The approach/development of math knowledge in the book was entertaining, with a mix of history and inspiring proofs and examples. I wished I read this book when I was in high school. Topics I really appreciated include the explanation of number fields. In particular, I really enjoye [...]

    2. Well, simply put, this is NOT a book about mathematics. Sure, it has numbers and math as its subject matter, but what authors really wanted you to get out of this book is how wonderfully elitist their English language skills are. Combined with a narrator choice straight out of Downton Abbey (the upstairs kind, of course), this book is impossible to either read or listen to. Even as someone who has a degree in math and loves science, I could not hold on to this book. Long-winded Shakespearian tir [...]

    3. Somewhere between Flatland: A Romance of Many Dimensions and Cosmos, Art of the Infinite is a popularization of mathematics by way of extensive metaphor and cultured references to literature and philosophy. I thought this was just a bit cheesy at first, but after a few times around, I got why they were doing this. The chief metaphor is spatial: math is an exploration into these unimaginably vast vistas in which humans are comfortable with a negligible patch and can imagine only a fraction. The K [...]

    4. Though I was only able to follow about two thirds of the math in The Art of the Infinite, it was extremely informative. I found most interesting the principles of shifting from perspective to perspective, using techniques and processes of one branch of mathematics to interpret techniques and processes of another, the use of mathematical substitutions from seemingly unrelated contexts to sidestep mathematical deadends and the varying styles of thought used to approach math. I especially enjoyed t [...]

    5. Husband and wife team Robert Kaplan and Ellen Kaplan have written a rich exploration of several aspects of the expansive field of mathematics. Through the book they cover the foundations of number and arithmetic, the rigors of mathematical proof, the nature of mathematical insight, the primes, infinite sequences, Euclidean geometry, building algebra from geometry, complex numbers, projective geometry (this was completely new for me), and finish with the nature of different infinities and the lif [...]

    6. Prose so purple I claim it was abused. This book needed an editor to cut out the blathering that the authors thought clever. The references to Rimbaud and Proust, to cite just a couple, were completely unnecessary and distracting.I read the first 3 chapters and then skipped to the last, the chapter on Georg Cantor and aleph-null, aleph-one, and transfinite numbers. (Fun fact: Cantor was a conspiracy theorist!)I was excited when I read this in the introduction:"Many small things estrange math fro [...]

    7. Un excelente libro que une las “dos culturas”: exactas y humanidades. No es un libro de divulgación típico, por eso resalta. Los autores además de esposos son matemáticos, políglotas y como si no fuera suficiente ella historiadora y bióloga. ¿Qué puede salir de esa colaboración? Pues oro puro.Entre pantallazos que muestran cómo funcionan las matemáticas, cómo se adentran en conceptos tan desentrañables como el infinito hay constantes referencias a la poesía y a la historia. Es [...]

    8. Mathematics is something that I find interesting, but definitely wish I knew more about. So, I went to my local library looking for a good book on math to give me an introduction to the subject. When I found this book, I thought I'd found what I was looking for. Boy, was I wrong.The book is written in this weird, florid prose, and just the way it was written made it impossible to read. I tried really hard, but I couldn't get past the first few pages. Finally, I took it back to the library and lo [...]

    9. Man, I used to consider myself decently intelligent when it came to math, but I'm telling you, some of these mathy books I've read this year and last year are making me feel REALLY stupid. I understood about 1/2 of this book, and really *got* it; the other 1/2 went over my head. :( (But I'm consoling myself by saying that the fact that I'm still willing to read them means that I really am still a math geek.) However, the writing is good, the diagrams are good, and I think the authors did a good [...]

    10. Although some of the math stuff was over my head (or patience level), I felt like I understood a remarkable amount of what the authors had to say about the history and nature of infinity. This book blew my mind in several places and gives a nice and readable history of the people and ideas involved in studying the nature of the infinite, which is what you might expect from a guy who wrote a very readable book about the history and nature of zero.

    11. Enjoyable book with a good mix of math concepts and math history. For example, is was very interesting to follow the path over hundreds of years of discoveries that are covered in one semester of abstract algebra. I also enjoyed the creative and philosophical language the authors used to explore the topics with different perspectives.

    12. Not as overwhelming as Journey through Genius, but this book is full of little gems of mathematics. Nearly all the "classic" proofs make an appearance. The prose is flowery and full of allusions, which I like, but it could make some sections (already challenging due to the math in them) less accessible.

    13. Mathematics is such a beautiful art that is often not appreciated as it should. I never liked how it was taught in schools, but his book reveals the artistry of the world's mathematical geniuses and with child-like wonder, I devour their formulae as if deprived of much-needed nutrition. It does get heavy-going at some points but it is okay to skip these if a general idea is what you are after.

    14. The narrative got a bit flowery and hard to follow at times, and the mathematics likewise (toward the end): I'm not sure I particularly enjoyed the chapter on Projective Geometry, and the infinites material was probably more than I was ready for. Still, I learned a few things, and am probably a better person for having gone through this book.

    15. Although the grandiose language in this book is a bit much at times, this is a really great book to appreciate the beauty of mathematics. The author does a great job of making the math accessible without dumbing it down.

    16. Radiant, luminous, poetic, lovely book, written like an adventurous novel, taking the reader through the broad vistas and hidden valleys of mathematics, lifting ancient stones of thought, revealing the natural beauties and deep humanity of numbers.

    17. Well, this is one of my math nerd books, so I obviously enjoy it. It explains a lot of history of Mathematics and gives some alternative ways of looking at proofs. The Calculus portion helped me a lot through my hellish nightmare!

    18. The book is a bit technical and the language used by authors make it even more difficult to understand. I enjoyed only the last chapter (set theory by Cantor and infinities involved). Overall an avoidable book.

    19. a nicely written reminder of what I once learnt at university. adds a lot of history and human endeavour to the theorems which was interesting.

    20. Informative book. When I saw the words "please" and "mathemetics" in the same sentence, I had a feeling I had found my book.

    21. Have always been interested in prime number after I read an article about them in 1958. This book has interest items about prime numbers in i

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