Remembering Richard Crandall (1947–2012)

Richard Crandall liked to call himself a “computationalist”. For though he was trained in physics (and served for many years as a physics professor at Reed College), computation was at the center of his life. He used it in physics, in engineering, in mathematics, in biology… and in technology. He was a pioneer in experimental mathematics, and was associated for many years with Apple and with Steve Jobs, and was proud of having invented “at least 5 algorithms used in the iPhone”. He was also an extremely early adopter of Mathematica, and a well-known figure in the Mathematica community. And when he died just before Christmas at the age of 64 he was hard at work on his latest, rather different, project: an “intellectual biography” of Steve Jobs that I had suggested he call “Scientist to Mr. Jobs”.

I first met Richard Crandall in 1987, when I was developing Mathematica, and he was Chief Scientist at Steve Jobs’s company NeXT. Richard had pioneered using Pascal on Macintoshes to teach scientific computing. But as soon as he saw Mathematica, he immediately adopted it, and for a quarter of a century used it to produce a wonderful range of discoveries and inventions.

He also contributed greatly to Mathematica and its usage. Indeed, even before Mathematica 1.0 in 1988, he insisted on visiting our company to contribute his expertise in numerical evaluation of special functions (his favorites were polylogarithms and zeta-like functions). And then, after the NeXT computer was released, he wrote what may have been the first-ever Mathematica-based app: a “supercalculator” named Gourmet that he said “eats other calculators for breakfast”. A couple of years later he wrote a book entitled Mathematica for the Sciences, that pioneered the use of Mathematica programs as a form of exposition.

Over the years, I interacted with Richard about a great many things. Usually it would start with a “call me” message. And I would get on the phone, never knowing what to expect. And Richard would be talking about his latest result in number theory. Or the latest Apple GPU. Or his models of flu epidemiology. Or the importance of running Mathematica on iOS. Or a new way to multiply very long integers. Or his latest achievements in image processing. Or a way to reconstruct fractal brain geometries.

This essay is also in Idea Makers: Personal Perspectives on the Lives & Ideas of Some Notable People »

Richard made contributions—from highly theoretical to highly practical—to a wide range of fields. He was always a little too original to be in the mainstream, with the result that there are few fields where he is widely known. In recent years, however, he was beginning to be recognized for his pioneering work in experimental mathematics, particularly as applied to primes and functions related to them. But he always knew that his work with the greatest immediate significance for the world at large was what he did for Apple behind closed doors.

Richard was born in Ann Arbor, Michigan, in 1947. His father was an actuary who became a sought-after expert witness on complex corporate insurance-fraud cases, and who, Richard told me, taught him “an absolute lack of fear of large numbers”. Richard grew up in Los Angeles, studying first at Caltech (where he encountered Richard Feynman), then at Reed College in Oregon. From there he went to MIT, where he studied the mathematical physics of high-energy particle scattering (Regge theory), and got his PhD in 1973. On the side he became an electronics entrepreneur, working particularly on security systems, and inventing (and patenting) a new type of operational amplifier and a new form of alarm system. After his PhD these efforts led him to New York City, where he designed a computerized fire safety and energy control system used in skyscrapers. As a hobby he worked on quantum physics and number theory—and after moving back to Oregon to work for an electronics company there, he was hired in 1978 at Reed College as a physics professor.

Steve Jobs had ended his short stay at Reed some years earlier, but through his effort to get Reed computerized, Richard got connected to him, and began a relationship that would last the rest of Steve’s life. I don’t know even a fraction of what Richard worked on for NeXT and Apple. For a while he was Apple’s Chief Cryptographer—notably inventing a fast form of elliptic curve encryption. And later on, he was also involved in compression, image processing, touch detection, and many other things.

Through most of this, Richard continued as a practicing physics professor. Early on, he won awards for creating minimal physics experiments (“measure the speed of light on a tabletop with $10 of equipment”). By the mid-1980s, he began to concentrate on using computers for teaching—and increasingly for research. One particular direction that Richard had pursued for many years was to use computers to study properties of numbers, and for example search for primes of particular types. And particularly once he had Mathematica, he got involved in more and more sophisticated number theoretical mathematics, particularly around primes, among other things co-authoring the (Mathematica-assisted) definitive textbook Prime Numbers: A Computational Perspective.

He invented faster methods for doing arithmetic with very long integers, that were instrumental, for example, in early crowdsourced prime discoveries, and that are in fact used today in modified form in Mathematica. And by doing experimental mathematics with Mathematica he discovered a wonderful collection of zeta-function-related results and identities worthy of Ramanujan. He was particularly proud of his algorithms for the fast evaluation of various zeta-like functions (notably polylogarithms and Madelung sums), and indeed earlier this year he sent me the culmination of his 20 years of work on the subject, in the form of a paper dedicated to Jerry Keiper, the founder of the numerics group at Wolfram Research, who died in an accident in 1995, but with whom Richard had worked at length.

Richard was always keen on presentation, albeit in his own somewhat unique way. Through his “industrial algorithm” company Perfectly Scientific, he published a poster of the digits of every new Mersenne prime that was discovered. The price of the poster increased with the number of digits, and for convenience his company also sold a watchmaker’s loupe to allow people to read the digits on the posters.

Richard always had a certain charming personal ponderousness to him, his conversation peppered with phrases like “let me commend to your attention”. And indeed as I write this, I find a classic example of over-the-top Richardness in the opening to his Mathematica for the Sciences: “It has been said that the evolution of humankind took a substantial, discontinuous swerve about the time when our forepaws left the ground. Once in the air, our hands were free for ‘other things’. Toolmaking. …”, and eventually, as he explains after his “admittedly conjectural rambling”, computers and Mathematica

Richard regularly visited Steve Jobs and his family, with his last visit being just a few days before Steve died. He was always deeply impressed by Steve, and frustrated that he felt people didn’t understand the strength of Steve’s intellect. He was disappointed by Walter Isaacson’s highly successful biography of Steve, and had embarked on writing his own “intellectual biography” of Steve. He had years of interesting personal anecdotes about Steve and his interactions with him, but he was adamant that his book should tell “the real story”, about ideas and technology, and should at all costs avoid what he at least considered “gossip”. At first, he was going to try to take himself completely out of the story, but I think I successfully convinced him that with his unique role as “scientist to Steve Jobs”, he had no choice but to be in the story, and indeed to tell his own story along the way.

Richard was in many ways a rather solitary individual. But he always liked talking about his now-15-year-old daughter, whom he would invariably refer to rather formally as “Ellen Crandall”. He had theories about many things, including child rearing, and considered one of his signature quotes to be “the most efficient way to raise an atheist kid is to have a priest for a father”. And indeed as part of the last exchange I had with him just a few weeks before he died, he marveled that his daughter from a “pure blank, white start” … “has suddenly taken up filling giant white poster boards with minutely detailed drawing”.

While his overall health was not perfect, Richard was in many ways still in the prime of his life. He had ambitious plans for the future, in mathematics, in science and in technology, not to mention in writing his biography of Steve Jobs. But a few weeks ago, he suddenly fell ill, and within ten days he died. A life cut off far too soon. But a unique life in which much was invented that would likely never have existed otherwise.

I shall miss Richard’s flow of wonderfully eccentric ideas, as well as the mysterious “call me” messages, and of the late the practically monthly encouragement speech about the importance of having Mathematica on the iPhone. (I’m so sorry, Richard, that we didn’t get it done in time.)

Richard was always imagining what might be possible, then in his unique way doggedly trying to build towards it. Around the world at any time of day or night millions of people are using their iPhones. And unknown to them, somewhere inside, algorithms are running that one can imagine represent a little piece of the soul of that interesting and creative human being named Richard Crandall, now cast in the form of code.

Stephen Wolfram (2012), "Remembering Richard Crandall (1947–2012)," Stephen Wolfram Writings.
Stephen Wolfram (2012), "Remembering Richard Crandall (1947–2012)," Stephen Wolfram Writings.
Wolfram, Stephen. "Remembering Richard Crandall (1947–2012)." Stephen Wolfram Writings. December 30, 2012.
Wolfram, S. (2012, December 30). Remembering Richard Crandall (1947–2012). Stephen Wolfram Writings.

Posted in: Historical Perspectives, Mathematics


  1. From an email of “Craig A. Mattocks”

    “Richard Crandall and Jason Klivington, in the Advanced Computation
    Group at Apple Computer, have written “wicked fast” vectorized
    algorithms for the G4 which allow you to do radix math (arbitrary
    base; 128 bits is a good choice for the quadword Velocity Engine
    architecture), so you can rapidly calculate to whatever (bizarre)
    precision you wish.

    See their articles:

    “Vector implementation of multiprecision arithmetic” and
    “Supercomputer-style FFT library for Apple G4”

    on the AltiVec web site at:

  2. Thanks for this interesting obituary on Richard.

  3. How very sad that he died at the young age of 64. A real idea man. Thank you for a great article, Dr. Wolfram.

  4. A touching piece Stephen

  5. Steve:
    I appreciate your posting this about Richard. Although I never met him personally, I own two of his books and e-mailed him over the Scitech list several times. I normally do not contribute to blogs but here I am making an exception as I thought you might be interested in my connection to Richard because it involves Mathematica also. In June Cambridge Press will bring out the book I wrote with Brian Koberlein entitled “Astrophysics Through Computation With Mathematica Support”. Brian wrote the text based on my Mathematica notebooks. In the section on crystallization of white dwarfs, we quote Richard’s brilliant work on Madelung constant computations. HIs algorithms are implemented in Mathematica 8 and 9 and will appear online for undergraduate students and their instructors to use world-wide. Who knows someday these will reach a future Richard Crandall and continue his work ?
    So are you going to finish Richard’s book on Steve Jobs ?
    -Dave Meisel

  6. A very nice obituary for Richard Crandall. Richard’s capability to gain a deeper quantitative understanding of the world we are a small part of led to a life which was driven by passionate curiosity.

    I have one of his prime number posters right here at the wall of my work space. If people ask me what this even grey color is all about I hand them out the watchmaker’s loupe so they can get glimpses of the huge prime number the poster represents. What a nice way to get at the essence of it!

    Long live the strive to grow humanistic wisdom.


  7. It would be wonderful if enough of Richard’s story about Steve Jobs exists to be published. It sounds like it could shed light on the especially important NeXT phase — something that is inadequately treated in other biographies, Isaacson’s in particular. For instance, why was Objective-C chosen?

  8. Thank you, Stephen, for this very thoughtful and humane portrait of Richard Crandall.

  9. What a wonderful remembrance of Richard — thanks Stephen. I worked with Richard a bit in the last 10 years on vector processing, and he was a brilliant, fun person to interact with. He often called me out of the blue, at work or home, and we had great conversations that I remembered for months afterwards. I will really miss Richard.

  10. I met Richard at a number of Mathematica conferences. He was an originalist and will be sorely missed.

  11. Thank you for this piece on Richard. I was lucky enough to get to know him when I was part of an algorithm development team that did work with Perfectly Scientific over several years time. He was one of the brightest people one could ever hope to meet. For him, numbers and algorithms were a playground, a fertile area from which to unearth amazing synchronicities and invention. You give a good picture of his communication style: relaxed and totally at ease as he set you up for his next stunning revelation. I found him to be totally approachable and if you got him on the right topic you were treated to a deep dive down the rabbit hole of computation! Many of us in the realm of math and computer science hope that our work will move the state of the art forward and in doing so enable others to do the same. Crandall is one of those people who has contributed to so many areas of computation (believe me, through many more avenues than Apple) that many of us will be standing on his shoulders as we reach for that next innovation.

  12. Unlike those of you who knew Richard as a fully-developed person/mathematician, I was lucky enough to have been his 5th grade teacher. Richard was a total joy and we had many “secret” jokes about which we loved to giggle. He had a big head and arms and legs like sticks. Did I ever have to scramble to keep him busy. Old radios/parts and Algebra kept him busy for a few days.

    His father and mother were equally brilliant: He, the youngest Actuary in the world; She, an Opera Mezzo of great talent. She would come to the classroom to sing for us…every now and again.

    I am delighted to be able to share just a bit about 10-year-old Richard Crandall. No, we never called him “Dick”.

    Joanna E Spaulding, PhD

  13. Thanks for this brilliant eulogy of Richard Crandall, who I was advised by at Reed College and later went on to publish a book under his publishing company Perfectly Scientific, Inc. I spent many hours learning electrical engineering from Richard in random places around Portland and his home, as Reed has no engineering program. We’d often take this limo/truck because he had hired the driver full time; one time he ran into me downtown and gave me a ride home. Now my Masters advisor at Stanford, Julius Smith, has even more stories to share about him–my favorite is that one day, when Julius was struggling with a problem, Richard came in and said, “Well, maybe you woke up today in an alternate universe in which that is the right solution.” From his inappropriate jokes about lesbians to his penchant for grading papers at the bar to his confusion about why anyone would want to pause working for a vacation, he is sorely missed.