David Anthony Klarner (October 10, 1940 – March 20, 1999) was an American mathematician, author, and educator. He is known for his work in combinatorial enumeration, polyominoes,^[3] and box-packing.^[4][5][6]

Klarner was a friend and correspondent of mathematics popularizer Martin Gardner and frequently made contributions to Gardner's Mathematical Games column in Scientific American.^[7] He edited a book honoring Gardner on the occasion of his 65th birthday.^[8][9] Gardner in turn dedicated his twelfth collection of mathematical games columns to Klarner.^[10]

Beginning in 1969 Klarner made significant contributions to the theory of combinatorial enumeration, especially focusing on polyominoes^[11] and box-packing.^[12][5] Working with Ronald L. Rivest he found upper bounds on the number of n-ominoes.^[4] Klarner's Theorem is the statement that an m by n rectangle can be packed with 1-by-x rectangles if and only if x divides one of m and n.^[1][13]

He has also published important results in group theory^[14] and number theory, in particular working on the Collatz conjecture (sometimes called the 3x + 1 problem).^[15] The Klarner-Rado Sequence is named after Klarner and Richard Rado.^[2]

Klarner was born in Fort Bragg, California, and spent his childhood in Napa, California.^[7] He married Kara Lynn Klarner in 1961. Their son Carl Eoin Klarner was born on April 21, 1969.^[16]

Klarner did his undergraduate work at Humboldt State University (1960–63), got his Ph.D. at the University of Alberta (1963–66), and did post-doctoral work at McMaster University in Hamilton, Ontario (1966–68). He also did post-doctoral work at Eindhoven University of Technology in the Netherlands (1968-1970), at the University of Reading in England working with Richard Rado (1970–71),^[17] and at Stanford University (1971–73). He served as an assistant professor at Binghamton University (1973–79) and was a visiting professor at Humboldt State University in California (1979–80). He returned to Eindhoven as a professor (1980–81), and to Binghamton (1981–82). From 1982 to 1996 he was a professor of computer science at the University of Nebraska, at Lincoln, with a one-year break at Eindhoven in academic year 1991–92. He retired to Eureka, California in 1997 and died there in 1999.^[7]

He was a frequent contributor to recreational mathematics and worked with many key mathematics popularizers including Ronald L. Rivest, John H. Conway, Richard K. Guy, Donald Coxeter, Ronald Graham, and Donald Knuth.^{[18][8][19][11]}

Klarner was a member of the Association for Computing Machinery, the American Mathematical Society, the Mathematical Association of America, and the Fibonacci Association.^[7] He was awarded a National Science Foundation Fellowship Award in mathematics in 1963.^[20] In 1986 Klarner received a University of Nebraska-Lincoln Distinguished Teaching Award in Computer Science.^[21]

The David A. Klarner Fellowship for Computer Science was set up after Klarner's death by Spyros Magliveras a fellow professor in Computer Science at UNL.^[22]

• Asymptotically Optimal Box Packing Theorems: Klarner systems by Michael Reid, Department of Mathematics, University of Central Florida, June, 2008
• A Lifetime of Puzzles edited by Erik D. Demaine, Martin L. Demaine, Tom Rodgers; pp. 221–225: Satterfield's Tomb, a puzzle by David A. Klarner and Wade Satterfield; ISBN 1568812450