Richard stanley biography

Quick Info

Born
23 June 1944
Manhattan, New York City, New York, USA
Summary
Richard P Stanley's contributions to combinatorics have revolutionised the subject. His books have made combinatorics an organised topic. He has won several major prizes including the Leroy P Steele Prize for Lifetime Achievement.

Biography

Richard P Stanley was the son of Alan Emmet Stanley (1921-2003) and Shirley Silver (1922-2001). Alan Stanley, born 17 May 1921 in Manhattan, New York, was the son of Bernard Isaacson and Carrie Oestriecher. He appears in the 1940 census as Alan Isaacson but must have changed his name shortly after this, graduating from Virginia Polytechnic Institute, Blacksburg, in the class of 1942 as a metallurgist. He worked with the United Aircraft Corporation and became engaged to Shirley Silver in July 1942(see [48]). On 21 August 1942 he enlisted at Fort Jay Governors Island, New York and became an Aviation Cadet. Later that year he married Shirley in Baltimore, Maryland, on 24 December 1942. Shirley, the daughter of Frederick and Anna Silver of 48 Ellsworth Road, Larchmont, New York [50]:-
... graduated from Mamaroneck High School and from Allegheny College Meadville Pennsylvania. She was elected to Phi Beta Kappa Delta Sigma Rho and Alpha Xi Delta.
Alan and Shirley Stanley had three children, Richard Stanley born 23 June 1944, the subject of this biography being the first. When Richard was born, his father was serving overseas and his mother was living with her parents in Larchmont, New York. Richard had two younger siblings, Juliet Susan Stanley (born 9 July 1946, died 13 August 1973) and Lawrence A Stanley (born 1 December 1947).

Richard explained that when World War II ended and Alan Stanley was demobbed [47]:-
... we moved to New York City, where my father worked for my mother's father trying to set up a wire business. Around a year later my father got a job with National Lead Company in Tahawus.
At Tahawus the National Lead Company was mining titanium dioxide and Alan Stanley began working there in 1946. Tahawus is in Newcomb, Essex County, New York and in 1950, when Richard Stanley was five years old, the family were living at 9 Stanford Drive, Newcomb, Essex, New York. In 1953 the Stanley family left Tahawus when Richard's father was transferred to a plant in Arlington, Massachusetts but were only about a year there before moving to Lynchburg, Virginia. Richard wrote [47]:-
I became interested in astronomy and for several years wanted to be an astronomer. From the ages of nine to thirteen I lived in Lynchburg, Virginia. One of my friends knew a woman named Mrs Cochran (whom I thought of as an elderly person). Mrs Cochran saw that I liked mathematics (though at that time I had no special interest in the subject), so she taught me the standard synthetic algorithm for finding the square root of a positive real number. This rule seemed like complete magic to me. I understood why the analogous synthetic algorithm for division ("long division") worked, but I had not the slightest understanding of the square root algorithm. ... I asked Mrs Cochran about this, but she only replied that I would understand it when I was older. ... I did spend lots of time computing square roots and trying to impress my parents that I could determine whether a positive integer was a perfect square.
In 1958 the family moved again when Richard's father was transferred to a plant in Savannah, Georgia. Richard attended Wilder Junior High School where he sat next to Irvin Asher in the mathematics classes. (Asher later went on to obtain a B.S. and Ph.D. in physics from M.I.T., moved to Israel, and died in 2010.) Asher told Richard Stanley that the complicated calculation which he was doing was working out how to calculate nth roots of a number and he'd already worked it out for n=4,5,6,7,8. Stanley, who had always been the best student in his mathematics class, suddenly thought he had met a mathematical genius in Asher. He wrote [47]:-
I became determined to learn as much mathematics as I possibly could. It was on this fateful day that I was bitten by the mathematical bug and became incurably infected.
Stanley purchased G E Moore's Outline of College Algebra in the Barnes and Noble College Outline Series which he read carefully. He then began to study all the mathematics texts he could find in the Savannah Public Library and the Savannah High School library. In particular he found Martin Gardner's articles in Scientific American and was enthralled by hexaflexagons, Möbius strips and the mathematical problems he posed. Also at this time he joined the Mathematical Association of America and began reading the American Mathematical Monthly but found almost all the articles incomprehensible.

Savannah High School announced its honours role for the 1961-62 session (see [43]). The Twelfth Grade Honor Role listed 19 students including Richard Stanley and, of course, his classmate Irvin Asher whom we mentioned above. Both also appeared on the list of Twelfth Grade Six-week Honor Students. We note that Richard's sister Juliet Stanley is on the list of Tenth Grade Six-week Honor Students for the 1961-62 session. In fact session 1961-62 marks Stanley's first attempts at research when he produced results connected to linear recurrences with constant coefficients. Richard Stanley graduated from Savannah High School at a ceremony in the Grayson Stadium on 4 June 1962.

It was at the California Institute of Technology (Caltech) that Stanley began his university studies in 1962. Although by this time he was fairly certain that he wanted to major in mathematics, he kept his options open for possibly majoring in physics. He found the first two of the trimesters hard since they involved a lot of analysis. The final trimester, however, contained more algebra and Stanley found the linear algebra and matrix theory much more to his liking. His thoughts that he was more cut out to be an algebraist rather than an analyst were confirmed by receiving an A+ in the examinations on the algebraic approach. Stanley took a course on analytic number theory given by Tom Apostol which he found fascinating. He took a year long course on quantum mechanics in his third year.

Michael Aschbacher was a fellow student, entering Caltech in the same year as Stanley, and took a similar route moving from physics to algebra. Interest in algebra made Stanley turn to Marshall Hall. Hall was a leading expert on group theory and also had a strong influence in combinatorics. It is interesting that, influenced by Marshall Hall, Aschbacher became interested in combinatorics but later changed to become a world leader in group theory while Stanley, also influenced by Marshall Hall, became interested in group theory but later became a leading expert in combinatorics. Stanley was so sure at this stage that combinatorics was not for him that he did not even take Marshall Hall's combinatorics course at Caltech.

Indirectly Marshall Hall did influence Stanley towards combinatorics since he suggested that he apply for a summer job as a Research Scientist at the at the Jet Propulsion Laboratory at Pasadena. He was interviewed by Edward Posner (1933-1993), head of the coding theory group, who had a Ph.D. in ring theory with Irving Kaplansky as his advisor. Stanley expected the interview to be difficult but after Posner's first question, "What are the Sylow theorems?," everything went well. He worked for five summers, 1965-1969, in the coding theory group which was designing the error correcting codes that the Mariner and Voyager spacecrafts were using. The work was highly mathematical and a problem he worked on led to him reading the paper On the foundations of combinatorial theory I. Theory of Möbius functions(1964) by Gian-Carlo Rota. In fact Rota eventually became Stanley's Ph.D. thesis advisor but, at this time, Stanley never thought of combinatorics as a research topic.

At Caltech Stanley also took a course by Donald Knuth who encouraged him to take an interest in computer science problems. At this stage in his career, however, Stanley was certain that algebra was the topic for him. Caltech had established the Eric Temple Bell Undergraduate Mathematics Research Prize in 1963 and Stanley decided to submit a research paper to compete for the prize. He wrote his paper Zero Square Rings under the guidance of Richard A Dean, one of his professors. Richard Albert Dean (1924-2022) had been awarded a B.S. from Caltech in 1945 and a PhD from Ohio State University in 1953. He had been appointed to Caltech in 1954 and, at the time he was advising Stanley, was completing writing his book Elements of Abstract Algebra(1966). Aschbacher also submitted an outstanding research paper for the Eric Temple Bell Prize and both were awarded the 1965 Prize. You can read details of the Eric Temple Bell Prize and of Stanley's winning paper at THIS LINK.

Stanley graduated from Caltech with a B.S. in 1966 as one of the three best students of his year. The other two were Michael Aschbacher and Vern Sheridan Poythress who went to Harvard and, with Garrett Birkhoff as his advisor, was awarded a Ph.D. for his thesis Partial Algebras. He then went on to have a career as a leading philosopher, theologian and New Testament scholar. Stanley also went to Harvard University to undertake graduate studies. When he entered Harvard he hoped to be able to undertake research in group theory advised by Richard Brauer. Once at Harvard he began to understand how the project to classify finite simple groups was taking shape. It was clear that very many cases would have to be studied and already several hundreds of pages had been published. This caused group theory to lose its appeal for Stanley. He then decided to switch to number theory and changed advisors from Brauer to John Tate. He began learning algebraic number theory but his summer job at the Jet Propulsion Laboratory suddenly played a part in his career.

Although he never thought of the combinatorics problems he had studied at the Jet Propulsion Laboratory as potential research problems, he found them interesting and asked mathematicians at Harvard about them. He was told that these were the type of problems that interested Gian-Carlo Rota who was at the Massachusetts Institute of Technology (M.I.T.). He said in the interview [6]:-
Rota was very enthusiastic, suggesting all kinds of combinatorics that I should learn and convinced me that I should work with him in combinatorics. But I actually ended up doing most of the work on my own, just talking to him about other topics, not directly related to my research.
At Harvard, Stanley had taken a first level graduate complex variable course taught by David Mumford. He also took a course on algebraic topology taught by Albrecht Dold (1928-2011), who was visiting from Heidelberg University for the academic year. By the time he took this course he had become interested in combinatorics, so as the algebraic topology course was examined by a paper of his choice, he wrote on the homology of finite topological spaces. He attended Oscar Zariski's course on algebraic curves which proved a lucky choice [58]:-
When a graduate student felt ready to write a Minor Thesis, he or she was given a topic based on the courses taken so far. The topic was supposed to be unrelated to the courses, so the student had to learn something entirely new. The Minor Thesis had to be handed in three weeks after it was assigned. Since I had only audited Zariski's course (rather than taking it for credit), it did not appear on my record. Therefore I was given the topic "the Riemann-Roch theorem for curves." This turned out to be a central result in Zariski's course, so I didn't have to do much more than transcribe my notes.
Stanley was appointed as a Teaching Assistant at Harvard University during 1968-1970, and then as C L E Moore Instructor of Mathematics at M.I.T. He began publishing papers, the first being Zero Square Rings, the paper he had submitted for the Eric Temple Bell Prize at Caltech. The next was Structure of incidence algebras and their automorphism groups which research announcement submitted to the Bulletin of the American Mathematical Society. It was communicated by Gian-Carlo Rota on 9 June 1970 and gave Stanley's address as the Massachusetts Institute of Technology.

Stanley attended the Second Chapel Hill Conference on Combinatorial Mathematics and its Applications was held at the University of North Carolina, Chapel Hill on 8-13 May 1970 and presented the paper A chromatic-like polynomial for ordered sets which was published in the conference proceedings. Bill Tutte wrote in a review:-
The chromatic polynomial of a graph G can be interpreted as the number of (appropriately defined) mappings of G into a complete n-graph. This paper discusses analogous polynomials concerned with mappings of a partially ordered set P into a totally ordered set of n elements.
In fact Stanley had published nine papers before submitting his Ph.D. thesis Ordered structures and partitions to Harvard University in 1971. His official Harvard University advisor had remained John Tate(who remained his advisor on condition he did not have to read Stanley's thesis) but his actual advisor had been Gian-Carlo Rota. The thesis was published as a book in 1972 and you can read more about it at THIS LINK.

Stanley spoke about his activities at Harvard other than mathematics in the interview [58]:-
I spent a lot of time in the Common Room involved in such activities as blitz chess, bridge, table shuffleboard, and foosball. My time at Harvard took place during the Vietnam War. Many of the graduate students in the Mathematics Department were extremely politically active. I got converted from a conservative into a liberal who opposed the war. I was involved in some political activity such as the famous march on Washington in November, 1969, and on another occasion I spent a couple of hours in jail (with a lot of other people) for disturbing a public assembly, before bail was raised. Eventually I was fined $10.
In fact Stanley completed all the requirements for the degree of Ph.D. in 1970 but chose not to apply for graduation until 1971, thinking that it would stop him being drafted because of the Vietnam War. In fact deferment of the draft for more than four years was usually not allowed and indeed his request for an extension was turned down. He became eligible for the draft, was called for a medical which he passed, but was not drafted.

In 1971 Stanley married Doris Sandra Skulsky (born 1945) in Queens, New York City. Doris had attended George W Wingate High School in Brooklyn, New York. She then studied at Barnard College in Manhattan, New York and, after majoring in French with German as a minor, she graduated with a B.A. in 1966. She then studied for a Master of Arts in Teaching at Yale University and was awarded the degree in 1967. Richard and Doris Stanley have two children who both went on to obtain doctorates, Kenneth Owen Stanley (born in Boston on 16 May 1975), who became a computer scientist, and Sharon Adele Stanley (born 11 September 1977), who became a professor of Political Science.

In 1971, Stanley was appointed as Miller Research Fellow, University of California, Berkeley holding that position until 1973. While a Miller Research Fellow, he had the paper Supersolvable lattices published in Algebra Universalis. The paper had been communicated to the journal by Robert Palmer Dilworth, an expert on lattice theory who was a professor at Caltech. In 1973 Stanley was appointed as an Assistant Professor of Mathematics at the Massachusetts Institute of Technology where he worked until he retired in 2018. At M.I.T., he was promoted to Associate Professor of Mathematics in 1975, then to Professor of Applied Mathematics in 1979. He was named Norman Levinson Professor of Applied Mathematics at M.I.T. in 2000, holding this position until 2010.

In addition to his first book, which was essentially his Ph.D. thesis, Stanley has written several other important books: Combinatorics and commutative algebra(1983); Enumerative combinatorics. Vol. I (1986); Enumerative combinatorics. Vol. 2(1999); A combinatorial miscellany(2010); Algebraic combinatorics: Walks, trees, tableaux, and more(2013); Catalan numbers(2015); and Conversational problem solving(2020). Let us give an indication of the exceptional quality of these books by quoting from Darren Glass's review of the Second Edition of Enumerative combinatorics. Vol. I [16]:-
Some books seem like they shouldn't need reviews: The Bible, Moby Dick, Great Expectations, Euclid's Elements. Their names are so ingrained in our minds as the pinnacle of what a great book should be that it almost doesn't occur to us that a review is a good idea. Who is going to decide whether to read Shakespeare based on what folks on Amazon think of it? Now, Richard Stanley's Enumerative Combinatorics, Volume I is probably not quite at the level of the above-named classics, but it is about as close as a graduate-level text in mathematics can be. Don't believe me? Look at what others said about the first edition:

In a little over 300 pages of careful exposition, the author has packed a tremendous amount of information into this book." - MathSciNet

"This is a masterful work of scholarship which is, at the same time, eminently readable and teachable. It will be the standard work in the field for years to come." - Citation for 2001 Leroy Steele Prize For Mathematical Exposition, which Stanley won for the two volumes of his book.

"Historically then this is a book of major importance. It provides a widely accessible introduction to many topics in combinatorics ... Furthermore, it is sure to become a standard as an introductory graduate text in combinatorics." - George Andrews, writing in the Bulletin of the American Mathematical Society.

"Best of all, Stanley has succeeded in dramatising the subject, in a book that will engage from start to finish the attention of any mathematician who will open it at page one." - Gian-Carlo Rota, in the preface to the first edition.
For more information about all these books, see THIS LINK.

In addition to the Eric Temple Bell Undergraduate Prize mentioned above, Stanley has won four major awards: the SIAM George Pólya Prize in Applied Combinatorics (1975); the Leroy P Steele Prize for Mathematical Exposition (2001); the Rolf Schock Prize in Mathematics (2003); and the Leroy P Steele Prize for Lifetime Achievement (2022). The Leroy P Steele Prize for Mathematical Exposition was awarded for the two volumes of the book Enumerative combinatorics.
For more information about all these awards, see THIS LINK.

Stanley has received a number of honours in addition to these prizes. For example he was awarded a Guggenheim Fellowship (1983-84), elected a fellow of the American Academy of Arts and Sciences(1988), elected a member of the National Academy of Sciences(1995), made an Honorary Doctor of Mathematics by the University of Waterloo (2007), made an Honorary Professor of Nankai University (2007), and elected a fellow of the American Mathematical Society(2013).

He has been an invited speaker at many conferences; let us just mention two. He was an invited speaker in the Algebra Section of the International Congress of Mathematicians, Warsaw, 1983, and gave the talk Combinatorial applications of the hard Lefschetz theorem. He was a plenary speaker at the International Congress of Mathematicians in Madrid, 2006, giving the talk Increasing and decreasing subsequences and their variants. He gave the following Abstract:-
We survey the theory of increasing and decreasing subsequences of permutations. Enumeration problems in this area are closely related to the RSK algorithm. The asymptotic behaviour of the expected value of the length is(w) of the longest increasing subsequence of a permutation w of 1, 2, ... , n was obtained by Vershik-Kerov and (almost) by Logan-Shepp. The entire limiting distribution of is(w) was then determined by Baik, Deift, and Johansson. These techniques can be applied to other classes of permutations, such as involutions, and are related to the distribution of eigenvalues of elements of the classical groups. A number of generalisations and variations of increasing/decreasing subsequences are discussed, including the theory of pattern avoidance, unimodal and alternating subsequences, and crossings and nestings of matchings and set partitions.
Asked in the interview [58] which of his results he considered most influential, he replied:-
My most influential results are all influential for basically the same reasons: the concepts and techniques turn out to be useful in other contexts, and they suggest extensions and generalisations for which much further progress can be made. These results are: (1) the theory of P-partitions, (2) combinatorial reciprocity, (3) applications of commutative algebra (especially face rings) and algebraic geometry (mainly, the hard Lefschetz theorem) to combinatorics, (4) stable Schubert polynomials (also called "Stanley symmetric functions") and their connection with reduced decompositions of permutations, and (5) chromatic symmetric functions. There is some other work that has had some influence, such as supersolvable lattices, order and chain polytopes, D-finite power series, a combinatorial interpretation of Schubert polynomials (with Sara Billey and William Jockusch), and a conjectured formula (proved by Valentin Feray) for the normalized character values of the symmetric group.
In 2014 Stanley was appointed Arts and Sciences Distinguished Scholar at the University of Miami. He retired from M.I.T. in 2018 and was appointed Emeritus Professor of Applied Mathematics.

Asked about is hobbies in the interview [23] by Hyun Soo Kim, he replied:-
I like juggling, although I'm not very active now. Bridge is something I enjoy. I like chess problems. I don't really like chess, but I like chess problems. It's a serious area that is very small and extremely well‐developed into an art form.

  1. 2001 Steele Prizes, Notices of the American Mathematical Society48(4)(2001), 404-407.
  2. A Combinatorics Conference in Honor of Richard Stanley, National Science Foundation(2004).
    https://www.nsf.gov/awardsearch/showAward?AWD_ID=0401211&HistoricalAwards=false
  3. An Erdös anecdote, University of California San Diego.
    https://mathweb.ucsd.edu/~fan/ep/stanley.pdf
  4. E J Barbeau, Review: Conversational problem solving, by Richard P Stanley, Mathematical Reviews MR4249565.
  5. D Callan, Review: Catalan numbers, by Richard P Stanley, Mathematical Reviews MR3467982.
  6. S Chen, Interview with Richard P Stanley, Notices of the American Mathematical Society69(7)(2022), 1231-1235.
    http://people.reed.edu/~davidp/372/resources/stanley.pdf
  7. L K Durst, Review: Ordered structures and partitions, by Richard P Stanley, Mathematical Reviews MR0332509(48 #10836).
  8. W M Dymacek, Review: Enumerative Combinatorics Vol I, Mathematical Reviews MR1442260(98a:05001).
  9. D Eisenbud and J Weyman, Remembering Davis Buchsbaum, Notices of the American Mathematical Society 69(1)(2022), 76-87.
    https://www.ams.org/journals/notices/202201/202201FullIssue.pdf?cat=fullissue&trk=fullissue202201
  10. Erdös Lectures: Richard Stanley, Einstein Institute of Mathematics, Hebrew University of Jerusalem(1999).
    https://mathematics.huji.ac.il/node/54300
  11. D V Feldman, Review: Algebraic combinatorics: Walks, trees, tableaux, and more, by Richard P Stanley, Choice: Current Reviews for Academic Libraries51(8)(2014), 1442.
  12. D V Feldman, Review: Conversational problem solving, by Richard P Stanley, Choice: Current Reviews for Academic Libraries58(12)(2021), 1206.
  13. P Hersh, T Lam, P Pylyavskyy and I Reiner (eds.), Selected Works of Richard P Stanley (American Mathematical Society, 2017).
  14. I M Gessel, Review: Enumerative combinatorics. Vol. 2, by Richard P Stanley, Mathematical Reviews MR1676282(2000k:05026).
  15. I M Gessel, Review: Enumerative combinatorics. Vol. 2, by Richard P Stanley, Bulletin of the American Mathematical Society39(1)(2002), 129-135.
  16. D Glass, Review: Enumerative Combinatorics Vol I (2nd edition), by Richard P Stanley, Mathematical Association of America(25 February 2012).
    https://maa.org/press/maa-reviews/enumerative-combinatorics-vol-i
  17. Information on 'Enumerative Combinatorics', Massachusetts Institute of Technology.
    https://math.mit.edu/~rstan/ec/
  18. Information on 'Catalan Numbers', Massachusetts Institute of Technology.
    https://math.mit.edu/~rstan/catalan/
  19. Information on 'Algebraic Combinatorics: Walks, Trees, Tableaux, and More', Massachusetts Institute of Technology.
    https://math.mit.edu/~rstan/algcomb/index.html
  20. D Jackson, Review: Enumerative Combinatorics Vol I (2nd edition), by Richard P Stanley, SIAM Review55(1)(2013), 193-194.
  21. G Kalai, Cheerful news in difficult times: Richard Stanley wins the Steele Prize for lifetime achievement!, Combinatorics and more, Gil Kalai's blog(21 December 2021).
    https://gilkalai.wordpress.com/2021/12/21/cheerful-news-in-difficult-times-richard-stanley-wins-the-steele-prize-for-lifetime-achievement/
  22. G Kalai, Happy Birthday Richard Stanley! Seven Early Papers by Richard Stanley That You Must Read, Gil Kalai's blog(27 June 2017).
    https://gilkalai.wordpress.com/2014/06/27/happy-birthday-richard-stanley/
  23. H S Kim, Interview with Professor Stanley, Math Majors Magazine1(1)(December 2008), 28-33.
    https://www.math.ucla.edu/~pak/lectures/Cat/Stanley-interview.pdf
  24. Leroy P Steele Prize for Lifetime Achievement, Notices of the American Mathematical Society69(4), 666-667.
  25. G Leversha, Review: Catalan numbers, by Richard P Stanley, Mathematical Gazette 101(551)(2017), 377-378.
  26. P McMullen, Review: Combinatorics and commutative algebra, by Richard P Stanley, Mathematical Reviews MR0725505(85b:05002).
  27. H Powers, MIT Professor to Deliver Kliakhandler Lectures, Mathematical Sciences Blog, Michigan Tech (21 September 2016).
    https://blogs.mtu.edu/math/2016/09/mit-professor-to-deliver-kliakhandler-lectures/
  28. Prof Richard Stanley Gave a Talk at AMSS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences(2014).
    http://english.amss.cas.cn/ns/es/201410/t20141022_129791.html
  29. J Propp, Lessons I learned from Richard Stanley, in V Reiner, P Hersh, P Pylyavskyy and T Lam (eds.), Mathematical Legacy of Richard P Stanley(American Mathematical Society, 2016), 279-286.
  30. Richard P Stanley, Massachusetts Institute of Technology.
    https://math.mit.edu/~rstan/
  31. Richard P Stanley: Curriculum Vitae (2021), Massachusetts Institute of Technology(2021).
    https://math.mit.edu/~rstan/minicv/index.html
  32. Richard P Stanley: Photos, Massachusetts Institute of Technology.
    https://math.mit.edu/~rstan/photos/index.html
  33. Richard P Stanley: Miscellaneous, Massachusetts Institute of Technology.
    https://math.mit.edu/~rstan/misc.html
  34. Richard P Stanley wins AMS Steele Prize, combinatorics.net (11 January 2001).
    http://www.combinatorics.net/Words/Stanley/stanley-Steel.htm
  35. Richard P Stanley receives 2022 Steele Prize for Lifetime Achievement, American Mathematical Society News(16 December 2021).
    http://www.ams.org/news?news_id=6892
  36. Richard P Stanley, National Academy of Sciences.
    https://www.nasonline.org/member-directory/members/67742.html
  37. Richard Stanley Receives the Schock Prize, combinatorics.net(2003).
    http://www.combinatorics.net/Words/Stanley/stanley-Schock.html
  38. Richard Stanley, Clay Mathematics Institute.
    https://www.claymath.org/people/richard-stanley/
  39. Richard Stanley awarded an honorary DMath Degree, University of Waterloo(15 June 2007).
    https://uwaterloo.ca/combinatorics-and-optimization/news/richard-stanley-awarded-honorary-dmath-degree
  40. Richard Stanley's Short Curriculum Vitae, in P Hersh, T Lam, P Pylyavskyy and I Reiner (eds.), Selected Works of Richard P Stanley (American Mathematical Society, 2017), xiii-xvi.
  41. V Reiner, P Hersh, P Pylyavskyy and T Lam (eds.), Mathematical Legacy of Richard P Stanley(American Mathematical Society, 2016).
  42. J Roberts, Review: Enumerative combinatorics. Vol. I, by Richard P Stanley, Mathematical Reviews MR0847717(87j:05003).
  43. Savannah High Announces 64 on Yearly Honor Role, Savannah High School Class of 1962, Savannah High School.
    http://shs62.com/gallery_photo.php?photoid=2101&pageid=1
  44. R P Stanley, Publications, with commentary by the author, in V Reiner, P Hersh, P Pylyavskyy and T Lam (eds.), Mathematical Legacy of Richard P Stanley(American Mathematical Society, 2016), 1-38.
  45. R P Stanley, Letter to the Editor, Notices of the American Mathematical Society69(1)(2022), 5.
    https://www.ams.org/journals/notices/202201/202201FullIssue.pdf?cat=fullissue&trk=fullissue202201
  46. R P Stanley, Letter to the Editor, Notices of the American Mathematical Society69(1)(2022), 5.
    https://www.ams.org/journals/notices/202201/202201FullIssue.pdf?cat=fullissue&trk=fullissue202201
  47. R P Stanley, The Early Years, in P Hersh, T Lam, P Pylyavskyy and I Reiner (eds.), Selected Works of Richard P Stanley (American Mathematical Society, 2017), 1-2.
  48. Stanley family, ancestry.com.
  49. Stanley-Silver engagement, Hartford Courant, Hartford, Connecticut (Tuesday 28 July 1942).
  50. Stanley-Silver marriage, The Standard-Star, New Rochelle, New York (4 January 1943).
  51. The power of negative thinking: Combinatorial and geometric inequalities, Igor Pak's blog(14 Septembr 2023).
    https://igorpak.wordpress.com/tag/richard-stanley/
  52. The Rolf Schock Prizes 2003: Press Release, The Royal Swedish Academy of Sciences(14 May 2003).
    https://www.kva.se/en/news/rolf-schockprisen-2003-fran-matematikens-filosofi-till-musikaliskt-artisteri-2/
  53. Vladimir Arnold and Richard Stanley, Università degli studi di Roma "Tor Vergata".
    https://www.mat.uniroma2.it/~brenti/Arnold_Stanley.htm
  54. M Weiss, Review: A combinatorial miscellany, by Anders Björner and Richard P Stanley, Mathematical Reviews MR2768279(2012e:05002).
  55. V Welker, Review: Combinatorics and commutative algebra (Second edition), by Richard P Stanley, Mathematical Reviews MR1453579(98h:05001).
  56. E G Whitehead, Jr, Review: Enumerative combinatorics. Vol. I, by Richard P Stanley, SIAM Review30(1)(1988), 170-171.
  57. F Zaldivar, Review: Algebraic combinatorics: Walks, trees, tableaux, and more, by Richard P Stanley, Mathematical Association of America(14 December 2015).
    https://maa.org/press/maa-reviews/algebraic-combinatorics-walks-trees-tableaux-and-more
  58. T Mansour, Interview with Richard P Stanley, Enumerative Combinatorics and Applications1(2021), 1-8.
    https://math.mit.edu/~rstan/papers/ecainterviewRichard.pdf
  59. R P Stanley, How the Upper Bound Conjecture Was Proved, Annals of Combinatorics 18(2014), 533-539.

Additional Resources (show)

Written by J J O'Connor and E F Robertson
Last Update March 2024