David P. Robbins

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David P. Robbins (born August 12, 1942 in Brooklyn , † September 4, 2003 in Princeton , New Jersey ) was an American mathematician .

Robbins studied at Harvard University (with Andrew Gleason ) and received his PhD from the Massachusetts Institute of Technology in 1970. He then taught at the Fieldston School in Manhattan (which he had also attended as a student), the Philips Exeter Academy (where he wrote a math textbook with his colleague Richard G. Brown ), Hamilton College in Clinton and Washington and Lee University in Virginia. From 1980 he was a research mathematician at the Institute for Defense Analyzes Center for Communications Research (IDA-CCR) in Princeton. Most of the work done there is secret. At Princeton, he was Chairman of the Princeton School Board . He died of pancreatic cancer. When he received the final diagnosis, he began to work on solving a problem that had preoccupied him for school days, a generalization of Heron's formula ( devised by Heron for triangles) to polygons.

In 1982 he introduced Alternating Sign Matrices (ASM) with William H. Mills and Howard Rumsey Jr. and proved the MacDonalds Conjecture. Robbins also published an article on this in the Mathematical Intelligencer . A conjecture made by Robbins and colleagues about the number of nxn ASMs for each n was proven in 1992 by Doron Zeilberger . In its own attempt to prove the conjecture came Robbins and colleagues on the relationship between ASM Descending dimensional partitions (Descending Plane Partitions, DPP) and were a presumption of Ian MacDonald (1979) about the number of cyclic symmetric two-dimensional partitions (Cyclically Symmetric Plane Partitions, CSPP) prove.

In 2008, Buchholz and MacDougall named Robbins Pentagons after him (cyclic pentagons with rational side lengths and areas). Robbins had given an area formula for cyclic pentagons in the manner of Heron's theorem for triangles.

The Robbins constant is named after him.

The David P. Robbins Prize of the AMS and the David P. Robbins Prize of the MAA were donated in his honor.

Fonts

  • with Richard Brown: Advanced Mathematics, an introductory course. Houghton Mifflin, 1975

Web links

Individual evidence

  1. ↑ Father of Dan Brown
  2. ^ Dying mathematician spends last days on area of ​​polygon , Wall Street Journal July 29, 2003
  3. ↑ Quadratic matrices with values ​​(0, 1, −1), so that the sum over every column and row is 1 and the values ​​(1, −1) alternate in every column and row
  4. ^ Mills, Robbins, Rumsey Proof of the Macdonald conjecture , Inventiones Mathematicae, Volume 66, 1982, pp. 73-87
  5. ↑ Mills, Robbins, Rumsey Alternating sign matrices and descending plane partitions , Journal of Combinatorial Theory, Series A, Volume 34, 1983, pp. 340-359
  6. ↑ Robbins The story of 1, 2, 7, 42, 429, 7436 ... , Mathematical Intelligencer, Volume 13, 1991, pp. 12-19. The series of numbers indicates the number of ASMs for each n.
  7. ↑ See also David Bressoud, James Propp, How the alternating sign matrix conjecture was solved , Notices AMS, 1999, No. 6, pdf
  8. ↑ That means the corners lie on a circle
  9. ↑ Ralph H. Buchholz, James A. MacDougall Cyclic polygons with rational sides and area , Journal of Number Theory, Volume 128, 2008, pp. 17-48
  10. ↑ Robbins Areas of polygons inscribed in a circle , The American Mathematical Monthly, Volume 102, 1995, pp. 523-530
personal data
SURNAME Robbins, David P.
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH August 12, 1942
PLACE OF BIRTH Brooklyn , New York
DATE OF DEATH September 4, 2003
Place of death Princeton , New Jersey