John Wrench

John William Wrench, Jr. (October 13, 1911 – February 27, 2009) was an American mathematician who worked primarily in numerical analysis. He was a pioneer in using computers for mathematical calculations, and is noted for work done with Daniel Shanks to calculate the mathematical constant pi to 100,000 decimal places.

John Wrench
Born(1911-10-13)October 13, 1911
DiedFebruary 27, 2009(2009-02-27) (aged 97)
Alma materUniversity at Buffalo
Yale University
Known forComputing π
Scientific career
InstitutionsDavid Taylor Model Basin

Life and educationEdit

Wrench was born on October 13, 1911, in Westfield, New York, and grew up in Hamburg, New York. He received a BA summa cum laude in mathematics in 1933 and an MA in mathematics in 1935, both from the University at Buffalo. He received his PhD in mathematics in 1938 from Yale University.[1] His thesis was titled The derivation of arctangent relations.[2]

Wrench died on February 27, 2009 of pneumonia in Frederick, Maryland.[3]


Wrench started his career teaching at George Washington University, but switched to doing research for the United States Navy during World War II. His specialty for the Navy was developing high-speed computational methods, and he was a pioneer in using computers for mathematical calculations. He worked on projects involving underwater sound waves, underwater explosions, structural design, hydrodynamics, aerodynamics, and data analysis. He became deputy head of the Applied Mathematics Laboratory at the Navy's David Taylor Model Basin in 1953, and retired in 1974 as the head of the laboratory. He also had academic appointments at Yale University, Wesleyan University, University of Maryland, College Park, and American University.[3]

Wrench had a particular interest in computing the decimal digits of π, and performed some lengthy calculations even before the availability of computers.[3] During the period 1945–1956 Wrench and Levi B. Smith used a desk calculator to produce more and more digits of π, ending with 1160 places.[4] In 1961 Wrench and Daniel Shanks used an IBM 7090 computer to calculate π to 100,000 digits.[5] Harry Polachek had a printout of the 100,000 digits specially bound, inscribed in gold letters, and donated to the Smithsonian Institution.[6]

Wrench also calculated a number of other mathematical constants to high precision, for example the Euler–Mascheroni constant γ to 328 decimal places[7] and Khinchin's constant to 65 places.[8]

He was at one time the editor of the Journal of Mathematics of Computation. Wrench was a member of the National Academy of Sciences and the National Research Council. He published more than 150 scientific papers.


  1. ^ "Obituary: Dr. John Wrench Jr". Frederick News-Post. Frederick, Maryland. March 20, 2009. Archived from the original on 24 March 2009. Retrieved 21 April 2009.
  2. ^ "Notes" (PDF). Bulletin of the American Mathematical Society. Providence, RI: American Mathematical Society. 45 (5): 349–354. May 1939. doi:10.1090/S0002-9904-1939-06990-5. ISSN 0273-0979. Retrieved 2009-04-19.
  3. ^ a b c Schudel, Matt (March 25, 2009). "Mathematician Had a Taste for Pi". Washington Post. p. B05. Archived from the original on 31 March 2009. Retrieved 31 March 2009.
  4. ^ Wrench, Jr., John W. (December 1960). "The evolution of extended decimal approximations to π". The Mathematics Teacher. 53: 644–650.
  5. ^ Shanks, Daniel; John W. Wrench Jr (1962). "Calculation of π to 100,000 Decimals". Mathematics of Computation. American Mathematical Society. 16 (77): 76–99. doi:10.2307/2003813. ISSN 0025-5718. JSTOR 2003813.
  6. ^ Polachek, Harry (1996). James Tomayko (ed.). "Anecdotes: Computers vs. the Human Race". IEEE Annals of the History of Computing. Institute of Electrical and Electronic Engineers. 18 (4): 60. doi:10.1109/mahc.1996.539917. ISSN 1058-6180. Retrieved 2020-07-23. In order to assure the preservation of this document, I arranged for two clear copies of the output to be printed and specially bound (inscribed in gold letters)—one of which I donated to the Smithsonian Institution in Washington, D.C.; the other I kept. The transfer to the Smithsonian took place at a small ceremony, attended by about 25 invited guests.
  7. ^ Wrench, Jr., J. W. (1952). "A new calculation of Euler's constant". Mathematical Tables and Other Aids to Computation. 6: 255.
  8. ^ Shanks, Daniel; J. W. Wrench Jr (April 1959). "Khintchine's Constant". American Mathematical Monthly. Mathematical Association of America. 66 (5): 276–279. doi:10.2307/2309633. JSTOR 2309633.

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