April 30, 2006

The Joy of Numbers

This blog post was started on reading the books, Imagining Numbers by Barry Mazur and The Joy of Pi by David Blatner. I hope to add to it by including books, interesting snippets, and sometimes my own comments as I read and research the joy of numbers and mathematics in this thread.


Etymology of Algebra: Via Italian, Spanish or mediaeval Latin, from Arabic 'al-jabr' or the ‘reunion, resetting of broken parts’, used in the title of al-Khwarizmi’s influential work, ‘ilm al-jabr wa’l-muqābala, or 'the science of restoration and equating like with like’.

Pre-Modern Algebra (pdf)

Bertrand Russell's Definition of a Number


Some books shortlisted to read
Number by Tobias Dantzig
The Constants of Nature : From Alpha to Omega--the Numbers That Encode the Deepest Secrets of the Universe by John Barrow

A related book is Just Six Numbers: The Deep Forces That Shape the Universe by Martin J. Rees, which discusses the recurring six numbers that come up in explaining the universe around us – which are:

  • nu (a ratio of the strength of electrical forces that hold atoms together compared to the force of gravity which is 10 to the 37th power)
  • epsilon (how firmly the atomic nuclei bind together which is 0.004)
  • omega (amount of material in the universe)
  • lambda (force of cosmic "antigravity" discovered in 1998, which is a very small number)
  • Q (ratio of two fundamental energies, which is 1/100,000)
  • delta (number of spatial dimensions in our universe)

Other related books of interest on numbers:

1. A History of Pi by Petr Beckmann

2. Pi: A Biography of the World's Most Mysterious Number by Alfred Posamentier & Ingmar Lehmann

3. Squaring the Circle by Tom Stoppard

4. The Golden Ratio : The Story of PHI, the World's Most Astonishing Number by Mario Livio

5. Zero: The Biography of a Dangerous Idea by Charles Seife

6. To Infinity and Beyond by Eli Maor

7. The Infinite Book by John D. Barrow

8. An Imaginary Tale Hardcover by Paul J. Nahin

9. Fortune's Formula by William Poundstone

10. e by Eli Maor

11. The Heart of Mathematics : An invitation to effective thinking by Edward Burger

12. Coincidences, Chaos, and All That Math Jazz by Edward B. Burger & Michael Starbird

13. Beyond Coincidence : Amazing Stories of Coincidence and the Mystery and Mathematics Behind Them by Martin Plimmer

14. Trigonometric Delights by Eli Maor

15. Gamma : Exploring Euler's Constant by Julian Havil

16. Prime Obsession : Berhhard Riemann and the Greatest Unsolved Problem in Mathematics by John Derbyshire

17. The Riemann Hypothesis: The Greatest Unsolved Problem in Mathematics by Karl Sabbagh (On the subject, for a mathematical treatise, read: Riemann's Zeta Function by Harold M. Edwards)

18. The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry by Mario Livio

19. Fermat's Enigma : The Epic Quest to Solve the World's Greatest Mathematical Problem by Simon Singh

20. The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles of Our Time by Keith J. Devlin

21. The Equation That Couldn't Be Solved by Mario Livio

22. The Mathematical Universe : An Alphabetical Journey Through the Great Proofs, Problems, and Personalities by William Dunham

23. God Created the Integers: The Mathematical Breakthroughs That Changed History by Stephen W. Hawking

24. The Triumph of Numbers: How Counting Shaped Modern Life by I. B. Cohen

25. Wonders of Numbers: Adventures in Math, Mind, and Meaning by Clifford A. Pickover

26. Meta Math! : The Quest for Omega by Gregory Chaitin, renowned for finding another proof of Kurt Godel's incompleteness theorem and another for Alan Turing's "halting problem" in computation and discoverer of the Omega number, which is an exquisitely complex representation of unknowability in mathematics.

Also see my compilation of links on Mathematics.

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