Daniel J. Velleman

Julian H. Gibbs 1946 Professor of Mathematics
Department of Mathematics
Amherst College
Amherst, MA 01002-5000
413-542-2196

Editing

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

Books

• 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 Blackwell Publishers.

Software

• 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, a Macintosh program that simulates a four-dimensional version of Rubik's cube. It will run in OS 9, or in the Classic environment of OS X, but it is not compatible with the "Millions of Colors" monitor setting. To make it work, you will need to use the Monitors Control Panel to switch to "Thousands of Colors". 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.

Selected Papers

• 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.

Unpublished Papers

• The Fundamental Theorem of Algebra: A Visual Approach

My family on the internet

• My wife, Shelley.
• My brother Paul.
• My brother David and his wife, Kitty.
• Lily and Natasha.