How Mathematicians Think
eBook - ePub

How Mathematicians Think

Using Ambiguity, Contradiction, and Paradox to Create Mathematics

William Byers

  1. 424 pages
  2. English
  3. ePUB (mobile friendly)
  4. Available on iOS & Android
eBook - ePub

How Mathematicians Think

Using Ambiguity, Contradiction, and Paradox to Create Mathematics

William Byers

Book details
Table of contents
Citations

About This Book

To many outsiders, mathematicians appear to think like computers, grimly grinding away with a strict formal logic and moving methodically--even algorithmically--from one black-and-white deduction to another. Yet mathematicians often describe their most important breakthroughs as creative, intuitive responses to ambiguity, contradiction, and paradox. A unique examination of this less-familiar aspect of mathematics, How Mathematicians Think reveals that mathematics is a profoundly creative activity and not just a body of formalized rules and results.
Nonlogical qualities, William Byers shows, play an essential role in mathematics. Ambiguities, contradictions, and paradoxes can arise when ideas developed in different contexts come into contact. Uncertainties and conflicts do not impede but rather spur the development of mathematics. Creativity often means bringing apparently incompatible perspectives together as complementary aspects of a new, more subtle theory. The secret of mathematics is not to be found only in its logical structure.
The creative dimensions of mathematical work have great implications for our notions of mathematical and scientific truth, and How Mathematicians Think provides a novel approach to many fundamental questions. Is mathematics objectively true? Is it discovered or invented? And is there such a thing as a "final" scientific theory?
Ultimately, How Mathematicians Think shows that the nature of mathematical thinking can teach us a great deal about the human condition itself.

Frequently asked questions

How do I cancel my subscription?
Simply head over to the account section in settings and click on “Cancel Subscription” - it’s as simple as that. After you cancel, your membership will stay active for the remainder of the time you’ve paid for. Learn more here.
Can/how do I download books?
At the moment all of our mobile-responsive ePub books are available to download via the app. Most of our PDFs are also available to download and we're working on making the final remaining ones downloadable now. Learn more here.
What is the difference between the pricing plans?
Both plans give you full access to the library and all of Perlego’s features. The only differences are the price and subscription period: With the annual plan you’ll save around 30% compared to 12 months on the monthly plan.
What is Perlego?
We are an online textbook subscription service, where you can get access to an entire online library for less than the price of a single book per month. With over 1 million books across 1000+ topics, we’ve got you covered! Learn more here.
Do you support text-to-speech?
Look out for the read-aloud symbol on your next book to see if you can listen to it. The read-aloud tool reads text aloud for you, highlighting the text as it is being read. You can pause it, speed it up and slow it down. Learn more here.
Is How Mathematicians Think an online PDF/ePUB?
Yes, you can access How Mathematicians Think by William Byers in PDF and/or ePUB format, as well as other popular books in Mathématiques & Histoire et philosophie des mathématiques. We have over one million books available in our catalogue for you to explore.

Information

Publisher
Princeton University Press
Year
2010
ISBN
9781400833955
Topic
Mathématiques
Subtopic
Histoire et philosophie des mathématiques

Table of contents

  1. Cover
  2. Half title
  3. Title
  4. Copyright
  5. Contents
  6. Acknowledgments
  7. Introduction Turning on the Light
  8. Section I The Light of Ambiguity
  9. Section II The Light as Idea
  10. Section III The Light and the Eye of the Beholder
  11. Notes
  12. Bibliography
  13. Index
Citation styles for How Mathematicians Think

APA 6 Citation

Byers, W. (2010). How Mathematicians Think ([edition unavailable]). Princeton University Press. Retrieved from https://www.perlego.com/book/734464/how-mathematicians-think-using-ambiguity-contradiction-and-paradox-to-create-mathematics-pdf (Original work published 2010)

Chicago Citation

Byers, William. (2010) 2010. How Mathematicians Think. [Edition unavailable]. Princeton University Press. https://www.perlego.com/book/734464/how-mathematicians-think-using-ambiguity-contradiction-and-paradox-to-create-mathematics-pdf.

Harvard Citation

Byers, W. (2010) How Mathematicians Think. [edition unavailable]. Princeton University Press. Available at: https://www.perlego.com/book/734464/how-mathematicians-think-using-ambiguity-contradiction-and-paradox-to-create-mathematics-pdf (Accessed: 14 October 2022).

MLA 7 Citation

Byers, William. How Mathematicians Think. [edition unavailable]. Princeton University Press, 2010. Web. 14 Oct. 2022.