The Laureates

Copyright © Klaus Tschira Stiftung / Peter Badge

William Morton Kahan

Born 5 June 1933, Toronto, Ontario, Canada

ACM A.M. Turing Award (1989) “for his fundamental contributions to numerical analysis. One of the foremost experts on floating-point computations, Kahan has dedicated himself to ‘making the world safe for numerical computations’.”

William Kahan was born in Canada to Jewish immigrants from Eastern Europe. In Toronto they owned a factory that produced fashionable dresses his mother designed. They sacrificed some comforts to provide their sons with the best available educations. William and his brother Fred (an accomplished biochemist) acknowledge that they aren’t self-made men, but the products of a superior educational system plus affectionate and supportive spouses. William earned BA (1954) and PhD (1958) degrees in Mathematics at the University of Toronto. A two-year Post-Doc at Cambridge, England, was followed in 1960 by a resumption of teaching duties, now as an Assistant Professor of Mathematics and Computer Science, that he began in 1954 as a graduate student. He had been programming computers since 1953, and in the 1960s contributed to SHARE, the users-group for IBM mainframes. In particular, he earned some notoriety by participating in a SHARE committee that in 1967 induced IBM to retrofit, at some considerable expense, necessary emendations to its System /360’s floating-point arithmetic.

Prof. Kahan has honorary doctorates from the University of Waterloo in Canada, and the Chalmers University of Technology in Gothenburg, Sweden. He is a member of the U.S. National Academies of Arts and Science, and of Engineering. Besides the ACM Turing Award he has a S.I.A.M. von Neumann Lecture and an IEEE Emanuel A. Piore Award. What did he do to get them?

Prof. Kahan analyzes errors in approximate computations most of his time. Computers have neither space nor time for infinite strings of digits like 1.41421356…, the square root of 2. Digits beyond some preassigned position must be rounded away. This and other intentional errors seem ignorable when committed but can get amplified during some computations to obscure desired results, sometimes (rarely) completely. Numbers wrong but not obviously wrong can sometimes mislead engineers, scientists, economists, financiers… badly. Catastrophes are rare — we cannot know how rare — but very costly when they occur. The error-analyst’s task is first to predict whether obscuration can ever get too bad and, if so, to dispel it without prolonging computation too much.

In the 1970s “Truth in Lending” laws used to require that interest rates be stated accurately taking all fees and “points” into account. When computerized, rules of thumb published in handbooks were less accurate, in many circumstances, than required by law. Kahan devised better mathematical methods to compute interest rates, among other things, impeccably accurately and fast for HP financial shirt-pocket calculators like the hp-12C. Issued in 1981, it became a standard in the financial world and is still on sale after over thirty years. What other electronic device enjoys such longevity?

In 1978, Kahan persuaded Intel to give away most of the mathematics he had put into the design of floating-point for their 8086/87 microprocessors. He had shown how floating-point’s approximation could be kept mathematically tractable without sacrificing much speed. He and Prof. H. Stone and J. Coonen, a graduate student at Berkeley, wrote it up in a way that ultimately gained the votes of the engineers on Stewart’s committee. “Their altruism was remarkable”, says Kahan. “They placed the ease of programmers ahead of the challenges to electronic engineers implementing the proposed standard.” It was a de facto standard by 1985 when it became official.

Kahan is either frugal or fond of old things. “I repair my old household appliances and plumbing; I work with several computers, some over two decades old; I keep two thirty-year old Peugeot 505 cars running in daily service; and I have still the same old wife after almost sixty years”, he confesses.