Julian H. Gibbs 1946 Professor of Mathematics

Department
of Mathematics

Amherst College

Amherst,
MA 01002-5000

413-542-2196

I was the Editor of the American Mathematical Monthly 2007-2011.

*How To Prove It*, published by Cambridge University Press.*Which Way Did The Bicycle Go?*, coauthored with Stan Wagon and Joe Konhauser, published by the Mathematical Association of America.*Philosophies of Mathematics*, coauthored with Alexander George, published by Wiley-Blackwell.

- Proof Designer, a java applet that writes outlines of proofs in
elementary set theory, under the guidance of the user. It is designed to
help students learn to write proofs. Proof Designer's approach to
proof-writing is similar to the approach used in my book
*How to Prove it*. An old Mac Classic version of Proof Designer is also available. - Tess, an old Macintosh program that simulates a four-dimensional version of Rubik's cube. It will run in OS 9, but not OS X. To download it, you will need software that can decode a BinHexed file, such as StuffIt Expander. You will also need Microsoft Word, or a program that can read Word files, to read the documentation. If you want to download the software and documentation, click here.

- Simplified morasses,
*Journal of Symbolic Logic***49**(1984), pp. 257-271. - ω-Morasses, and a weak form of Martin's axiom provable in ZFC,
*Transactions of the American Mathematical Society***285**(1984), pp. 617-627. - Simplified gap-2 morasses,
*Annals of Pure and Applied Logic***34**(1987), pp. 171-208. - Gap-2 morasses of height ω,
*Journal of Symbolic Logic***52**(1987), pp. 928-938. - Partitioning pairs of countable sets of ordinals,
*Journal of Symbolic Logic***55**(1990), pp. 1019-1021. - Versatile coins (with István Szalkai),
*American Mathematical Monthly***100**(1993), pp. 26-33. - Constructivism liberalized,
*Philosophical Review***102**(1993), pp. 59-84. - Pascal's matrices (with Gregory Call),
*American Mathematical Monthly***100**(1993), pp. 372-376. - Permutations and combination locks (with Gregory Call),
*Mathematics Magazine***68**(1995), pp. 243-253. - Fermat's last theorem and Hilbert's program,
*Mathematical Intelligencer*vol. 19 no. 1 (Winter 1997), pp. 64-67. - Another proof of the fundamental theorem of algebra,
*Mathematics Magazine***70**(1997), pp. 216-217. - Characterizing continuity,
*American Mathematical Monthly***104**(1997), pp. 318-322. - Two conceptions of natural number (with Alexander George), in
*Truth in Mathematics*, Garth Dales and Gianluigi Oliveri (eds.), Oxford University Press, 1998, pp. 311-327. - Probability and quantum mechanics,
*American Journal of Physics***66**(1998), pp. 967-969. - Review of
*The Principles of Mathematics Revisited*, by Jaakko Hintikka,*Mind***108**(1999), pp. 170-179. - Multivariable calculus and the plus topology,
*American Mathematical Monthly***106**(1999), pp. 733-740. - The mean value theorem in second order arithmetic (with Christopher Hardin),
*Journal of Symbolic Logic***66**(2001), pp. 1353-1358. - Simpson symmetrized and surpassed,
*Mathematics Magazine***77**(2004), pp. 31-45. - The generalized Simpson's rule,
*American Mathematical Monthly***112**(2005), pp. 342-350. - Variable declarations in natural deduction,
*Annals of Pure and Applied Logic***144**(2006), pp. 133-146. - If the IRS had discovered the quadratic formula...,
*Math Horizons*, April 2007, p. 21. - The even-odd hat problem,
*Fundamenta Mathematicae***219**(2012), pp. 105-110. - What to expect in a game of memory (with Gregory Warrington),
*American Mathematical Monthly***120**(2013), pp. 787-805. - A drug-induced random walk,
*American Mathematical Monthly***121**(2014), pp. 299-317.