Obituary: Professor Stephen Kleene

Stephen Cole Kleene, mathematician: born Hartford, Connecticut 5 January 1909; Research Assistant in Mathematics, Princeton University 1930-35; Instructor, University of Wisconsin 1935- 37, Assistant Professor 1937-41; Associate Professor, Amherst College 1941-42; Associate Professor, University of Wisconsin 1946-48, Professor 1948-64, Cyrus C. McDuffee Professor of Mathematics 1964-74, Dean, College of Letters and Science 1969-74, Professor of Mathematics and Computer Science 1974-79, Emeritus Dean and Emeritus Professor of Mathematics and Computer Science 1979-94; Member, National Academy of Science 1969-94; National Medal of Science 1990; married 1942 Nancy Elliot (died 1970; three sons, one daughter), 1978 Jeanne Steinmetz; died Madison, Wisconsin 25 January 1994.

STEPHEN KLEENE was one of that small group of brilliant researchers, including Alan Turing in Britain, who tried to remake mathematics in the 20th century, by intellectually mapping out the computable world and its boundaries. The physical development of the computer inevitably flowed from the theoretical framework which they provided.

Kleene was the first explorer of the mysterious world of the uncomputable. His extraordinary body of work has become basic to much of theoretical computer science, in which real-world considerations of computational power are incorporated. However, the question first raised by the early pioneers from the 1930s, that of the exact relationship between the solvable and unsolvable problems, has still to be fully answered. The answer promises to have significance far beyond the esoteric confines of contemporary mathematics.

Kleene's early research at Princeton between 1930 and 1935 took place in a period of great excitement following the discoveries of Kurt Godel. Godel's Incompleteness Theorem said that the comprehensiveness of any theory is limited in a very basic way. This had brought into question the earlier 'onward and upward' view of mathematics even more dramatically than Bertrand Russell's paradox in set theory had done 25 years earlier.

Stephen Kleene's father, Gustav Kleene, was a professor of economics, his mother, Alice, a published poet. He grew up in Hartford, Connecticut, spending his summers on a family farm in Maine. He took his doctorate under the eminent mathematician Alonzo Church in 1934, at the height of the Depression. He spent most of his distinguished career as a professor of mathematics at the University of Wisconsin at Madison, where he went in 1935. As many other aspiring logicians will have done, I read with excitement the ideas put forward in his famous book Introduction to Metamathematics, published in 1952, and still in print. He won the National Medal of Science in 1990, having been elected to the US National Academy of Sciences in 1969, a rare honour for a mathematician.

It is hard to give an adequate account of Kleene's work to the non- specialist, highly technical as much of it is. The subject of recursion theory which he founded (along with his New York co-worker Emily Post) is notorious for its ever-increasing complexity, and current workers in the field are often admired for their heroism of intellectual endeavour, but little understood even by their fellow mathematicians. But his interests in the foundations of computability were broad, and after his war service in the US Navy he applied his ideas within intuitionism, a radical and peculiarly European reconstruction of mathematics along constructivist lines. He produced a significant breakthrough in the theory of finite automata while working for the RAND Corporation in the summer of 1951.

Kleene will probably be best remembered for his work in classifying the world of the uncomputable. This involved two different approaches: first, the more traditional hierarchical framework, in which layers of ever less computable objects are built up according to the logical complexity of their descriptions, a process which was ingeniously iterated into the transfinite and extended to very general classes of objects; secondly, the 'degree theoretic' approach, in which the relative solvability (of essentially unsolvable problems) is assessed and given an algebraic structure, using the notion of an 'oracle' (a hypothetical provider of real- world inaccessible data). These two approaches were related in a beautiful and comprehensive fashion, enabling well-known unsolvable problems to be given a precise context relative to each other.

My vividest memory of Stephen Kleene is of a tall, still vigorous 70- year-old climbing the steep hillside at Delphi accompanied by his second wife Jeanne. All that week he had attended every talk at the 1980 Patras conference of the Association of Symbolic Logic, listening attentively to every one. Many youthful contributors will remember their first conference appearance with special pride because of his presence.

(Photograph omitted)

Start your day with The Independent, sign up for daily news emails
  • Get to the point
Latest stories from i100
Have you tried new the Independent Digital Edition apps?
Independent Dating
and  

By clicking 'Search' you
are agreeing to our
Terms of Use.

iJobs Job Widget
iJobs People

Recruitment Genius: HR and Payroll Manager

£35000 - £38000 per annum: Recruitment Genius: This dynamic outsourced contact...

Recruitment Genius: Production & Quality Control Assistant

£19000 - £21000 per annum: Recruitment Genius: An excellent opportunity for a ...

Ashdown Group: Group HR Advisor - Kettering - £32,000

£28000 - £32000 per annum: Ashdown Group: Group HR Advisor with an established...

Guru Careers: HR Manager / HR Generalist

£40 - 50k (DOE) + Bonus: Guru Careers: We are seeking a HR Manager / HR Genera...

Day In a Page

General Election 2015: The masterminds behind the scenes

The masterminds behind the election

How do you get your party leader to embrace a message and then stick to it? By employing these people
Machine Gun America: The amusement park where teenagers go to shoot a huge range of automatic weapons

Machine Gun America

The amusement park where teenagers go to shoot a huge range of automatic weapons
The ethics of pet food: Why are we are so selective in how we show animals our love?

The ethics of pet food

Why are we are so selective in how we show animals our love?
How Tansy Davies turned 9/11 into her opera 'Between Worlds'

How a composer turned 9/11 into her opera 'Between Worlds'

Tansy Davies makes her operatic debut with a work about the attack on the Twin Towers. Despite the topic, she says it is a life-affirming piece
11 best bedside tables

11 best bedside tables

It could be the first thing you see in the morning, so make it work for you. We find night stands, tables and cabinets to wake up to
Italy vs England player ratings: Did Andros Townsend's goal see him beat Harry Kane and Wayne Rooney to top marks?

Italy vs England player ratings

Did Townsend's goal see him beat Kane and Rooney to top marks?
Danny Higginbotham: An underdog's tale of making the most of it

An underdog's tale of making the most of it

Danny Higginbotham on being let go by Manchester United, annoying Gordon Strachan, utilising his talents to the full at Stoke and plunging into the world of analysis
Audley Harrison's abusers forget the debt he's due, but Errol Christie will always remember what he owes the police

Steve Bunce: Inside Boxing

Audley Harrison's abusers forget the debt he's due, but Errol Christie will always remember what he owes the police
No postcode? No vote

Floating voters

How living on a houseboat meant I didn't officially 'exist'
Louis Theroux's affable Englishman routine begins to wear thin

By Reason of Insanity

Louis Theroux's affable Englishman routine begins to wear thin
Power dressing is back – but no shoulderpads!

Power dressing is back

But banish all thoughts of Eighties shoulderpads
Spanish stone-age cave paintings 'under threat' after being re-opened to the public

Spanish stone-age cave paintings in Altamira 'under threat'

Caves were re-opened to the public
'I was the bookies’ favourite to be first to leave the Cabinet'

Vince Cable interview

'I was the bookies’ favourite to be first to leave the Cabinet'
Election 2015: How many of the Government's coalition agreement promises have been kept?

Promises, promises

But how many coalition agreement pledges have been kept?
The Gaza fisherman who built his own reef - and was shot dead there by an Israeli gunboat

The death of a Gaza fisherman

He built his own reef, and was fatally shot there by an Israeli gunboat