It is with great sadness that the present bloggers announce the passing of their dear colleague Richard Crandall, who died Thursday December 20, 2012, after a brief bout with acute leukaemia—the week before his 65th birthday on December 29.

Crandall had a long and colorful career. He was a physicist by training, studying with Richard Feynman as an undergrad at the California Institute of Technology, and receiving his Ph.D. in physics at MIT, under the tutelage of Victor Weisskopf, the Austrian-American physicist who discovered what is now known as the Lamb Shift and who was one of the most influential post-war physicists. Richard often commented that he thought digitally in the fashion of an electrical engineer.

Crandall was for many years at Reed College in Portland, Oregon, where he directed the Center for Advanced Computation. At the same time, he also worked for Next Computers (as “Chief Scientist”), and subsequently for Apple Computers (as “Distinguished Scientist”), where he was the head of Apple’s Advanced Computation Group.

Crandall’s research spanned both the theoretical and practical realms: prime numbers, cryptography, data compression, signal processing, fractals, epidemiology, and, of considerable interest to the present authors, experimental mathematics. He held several patents. He produced many algorithms that are incorporated into Apple’s products, including the iPod and the iPhone. The library of fast Fourier transforms that was produced by his Advanced Computation Group at Apple was described by a colleague of ours as “miraculously” fast. He worked on image processing techniques for Pixar for 13 years, the last two to remove artifacts that reportedly could only be seen on Steve Jobs’ personal projector or to meet Jobs’ exacting personal requirements that raindrops should look like they did on celluloid (Richard’s tool was too natural for modern film goers).

Indeed, Crandall was a close colleague of Steve Jobs for many years. Crandall was preparing to write a biography of Jobs, which biography sadly will now not be written. Here is a photo with Crandall (on the left) and Jobs (on the right) at the Reed College Commencement in 1991, when Jobs received the Vollum Award (courtesy Reed College website):

The present authors have written numerous papers co-authored with Crandall. We have found him to be unusually bright, and his background in computational physics often brought novel insights into our work. Here are the papers that one or both of us have written with him, listed in approximate chronological order, with links to online copies where available:

- David H. Bailey, Jonathan M. Borwein and Richard E. Crandall, “On the Khintchine constant,”
*Mathematics of Computation*, vol. 66 (1997), pg. 417-431. PDF - Jonathan M. Borwein, David M. Bradley and Richard E. Crandall, “Computational strategies for the Riemann zeta function,”
*Journal of Computational and Applied Mathematics*, vol. 121 (2000), pg. 247-296. PDF - David H. Bailey and Richard E. Crandall, “On the random character of fundamental constant expansions,”
*Experimental Mathematics*, vol. 10, no. 2 (Jun 2001), pg. 175-190. PDF - David H. Bailey and Richard E. Crandall, “Random generators and normal numbers,”
*Experimental Mathematics*, vol. 11, no. 4 (2002), pg. 527-546. PDF - David H. Bailey, Jonathan M. Borwein, Richard E. Crandall and Carl Pomerance, “On the binary expansions of algebraic numbers,”
*Journal of Number Theory Bordeaux*, vol. 16 (2004), pg. 487-518. PDF - Jonathan M. Borwein and Richard E. Crandall, “On the Ramanujan AGM fraction, I: The real-parameter case,”
*Experimental Mathematics*, vol. 13 (2004), pg. 275-285. PDF - Jonathan M. Borwein and Richard E. Crandall, “On the Ramanujan AGM Fraction, II: The complex-parameter case,”
*Experimental Mathematics*, vol. 13 (2004), pg. 287-295. PDF - David H. Bailey, Jonathan M. Borwein and Richard E. Crandall, “Integrals of the Ising class,”
*Journal of Physics A: Mathematical and General*, vol. 39 (2006), pg. 12271-12302. PDF - David H. Bailey, Jonathan M. Borwein and Richard E. Crandall, “Box integrals,”
*Journal of Computational and Applied Mathematics*, vol. 206 (2007), pg. 196-208. PDF - David Borwein, Jonathan M. Borwein, Richard E. Crandall and R. Mayer, “On the dynamics of certain recurrence relations,”
*Ramanujan Journal*(Special issue for Richard Askey’s 70th birthday), vol. 13 (2007), pg. 63-101. PDF - David H. Bailey, David Borwein, Jonathan M. Borwein and Richard Crandall, “Hypergeometric forms for Ising-class integrals,”
*Experimental Mathematics*, vol. 16 (2007), no. 3, pg. 257-276. PDF - David Borwein, Jonathan M. Borwein and Richard E. Crandall, “Effective Laguerre Asymptotics,”
*SIAM Journal on Numerical Analysis*, vol. 6 (2008), pg. 3285-3312. PDF - David H. Bailey, Richard E. Crandall and Jonathan M. Borwein, “Resolution of the Quinn-Rand-Strogatz constant of nonlinear physics,”
*Experimental Mathematics*, vol. 18 (2009), pg. 107-116. PDF - Jonathan M. Borwein, O-Yeat Chan and Richard Crandall, “Higher-dimensional box integrals,”
*Experimental Mathematics*, vol. 19 (2010), pg. 431-446. PDF - David H. Bailey, Jonathan M. Borwein and Richard E. Crandall, “Advances in the theory of box integrals,”
*Mathematics of Computation*, vol. 79, no. 271 (Jul 2010), pg. 1839-1866. PDF - David H. Bailey, Jonathan M. Borwein and Richard E. Crandall, “Computation and theory of extended Mordell-Tornheim-Witten sums,”
*Mathematics of Computation*, 2012, to appear. PDF - David H. Bailey, Jonathan M. Borwein, Richard E. Crandall and Michael G. Rose, “Expectations on fractal sets,”
*Applied Mathematics and Computation*. Accepted November 2012. PDF - David H. Bailey, Jonathan M. Borwein, Richard E. Crandall and John Zucker, “Lattice sums arising from the Poisson equation,”
*Journal of Physics A: Mathematical and Theoretical*, to appear, 5 Feb 2012. PDF. - Jonathan M. Borwein and Richard E. Crandall, “Closed forms: What they are and why we care,”
*Notices of the American Mathematical Society*, vol. 60, no. 1 (Jan 2013), pg. 50-65. PDF

As the reader can easily see, our collaboration has continued literally up to the present day, with the manuscript on lattice sums being completed and submitted just one month ago, and the article on closed forms appearing on the *Notices of the AMS* website just a few days ago.

Had Richard been willing to fly, many more people would know of one of the most remarkable scientists of our age. Richard will be sorely missed!

**Postcripts ** Since we posted this obituary comments have poured in.

1. Andrew Mattingly from IBM Australia, who only recently had started to communicate with Richard, recalled his “searing intelligence”. John Zucker commented:

Richard and I were in constant e-mail communication over the past 25 years on topics of mutual interest. Richard was ever courteous in receiving answers to his queries, or in reverse when answering questions and providing solutions to problems posed to him. Our mutual respect never wavered, and only recently our interests combined with others to produce work of some regard. Along with many others I have lost a valued colleague, and though we never met a good friend as well. (John Zucker, see also John’s note on Richard and Madelung’s constant)

2. We also highly recommend Steve Wolfram’s personal memories of Richard, now available at: S. Wolfram, “Remembering Richard Crandall (1947-2012) “, ACM Communications in Computer Algebra **47**(1) March 2013, http://www.sigsam.org/cca/

3. Nelson Beebe (March 20) wrote that he had just compiled a comprehensive bibliography of Richard’s scientific work.

I’ve just installed in the BibNet Project archive the first edition of a bibliography of Richard Crandall’s publications, based on data collected from existing local archives, and numerous online sources. See http://www.math.utah.edu/pub/bibnet and http://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.html

4. It seems appropriate to celebrate Richard’s most famous book *Prime Numbers* (2001). Jeremy Teitelbaum’s review ends

But most importantly, Prime numbers, like Knuth’s work, teaches the unity of mathematics, and the inherently mathematical nature of efficient computation, by freely drawing on a wide range of mathematical techniques to illustrate computational problems from many points of view and by emphasizing the mathematical ideas which make eefficient computation possible. It’s rare to say this of a math book, but open Prime numbers to a random page and it’s hard to put down. Crandall and Pomerance have written a terric book

5. Richard played a significant role in the development of *Ma*thematica.

*This is also described in his “official” and beautiful obituary at Reed College (Jan 14, 2013), and as evidenced by Steve Wolfram’s article. This obituary was written in conjunction with a January 26 Memorial at Reed College (at which a larger version of this fine picture is lodged). Nicholas Wheeler, reflecting on this memorial, lamented: **Sorry you could not be present at the memorial. Odd feeling to sit in a room (the chapel inwhich Richard and Tess were married) with 150+ people who knew nearly that many different Richards. His mother was present, and so was Job’s widow and a son.*

6. Colleagues of Richard Crandall have set up an email for communicating stories, memories, anecdotes, photos and other material on Richard’s life: rememberingrichard@apple.com.

7. Shortly before his death, Richard and Michael Berry participated in a Riemann Zeta Function Workshop on November 2 at the IRMACS centre in Vancouver. Here are two pictures of Richard who, while clearly not well, gave a marvellous lecture—as he always did.