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Wilder's eclectic and humanist perspective on mathematics appears to have had little influence on subsequent mathematical research. It has, however, had some influence on the teaching of mathematics and on the history and philosophy of mathematics. In particular, Wilder can be seen as a precursor to
308:"The major difference between mathematics and the other sciences, natural and social, is that whereas the latter are directly restricted in their purview by environmental phenomena of a physical or social nature, mathematics is subject only indirectly to such limitations. ...
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for teaching mathematical proof. Moore was initially unimpressed by the young actuary, but Wilder went on to solve a difficult open problem that Moore had posed to his class. Moore suggested Wilder write up the solution for his Ph.D. thesis, which he did in 1923, titling it
304:(1969) proposed that "we study mathematics as a human artifact, as a natural phenomenon subject to empirical observation and scientific analysis, and, in particular, as a cultural phenomenon understandable in anthropological terms." In this book, Wilder wrote:
116:, where he supervised 26 Ph.Ds and became a research professor in 1947. During the 1930s, he helped settle European refugee mathematicians in the United States. Mathematicians who rubbed shoulders with Wilder at Michigan and who later proved prominent included
166:" was a devoted student of southwestern Native American culture. One day he told me that after retiring he would like to be a bartender in a rural area of Arizona or New Mexico, because he found the stories of the folk he met in bars there so fascinating."
77:, he served in the U.S. Navy as an ensign. Brown awarded him his first degree in 1920, and a master's degree in actuarial mathematics in 1921. That year, he married Una Maude Greene; they had four children, thanks to whom they have ample descent.
282:. This change was foreshadowed by his 1944 article "The nature of mathematical proof," and heralded by his address to the 1950 International Congress of Mathematicians, titled "The cultural basis of mathematics," which posed the questions:
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in 1924. That university required that its academic employees sign a loyalty oath, which Wilder was very reluctant to sign because doing so was inconsistent with his lifelong progressive political and moral views.
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The historical, philosophical, and anthropological writings of Wilder's later years suggest a warm, colorful personality. Raymond (2003) attests to this having been the case. For instance:
278:, whose professional curiosity included mathematics as a human activity (White 1947). This encounter proved fateful, and Wilder's research interests underwent a major change, towards the
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Wilder's father was a printer. Raymond was musically inclined. He played cornet in the family orchestra, which performed at dances and fairs, and accompanied silent films on the piano.
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In his "A converse of the Jordan-Brouwer separation theorem in three dimensions" (1930), Wilder showed that a subset of
Euclidean 3-space whose complementary domains satisfied certain
159:(1980) awarded him honorary doctorates. The mathematics department at the University of California annually bestows one or more graduating seniors with an award in Wilder's name.
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conceived of an ideal universe in which resided perfect models ... the only reality mathematical concepts have is as cultural elements or artifacts."
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to the Jordan curve theorem, proved by Schönflies, states that a subset of the 2-sphere is a simple closed curve if it:
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programme, which aimed to study positional invariants of sets in the plane or 2-sphere. A positional invariant of a set
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346:. For an introduction to the limited anthropological research on mathematics, see the last chapter of Hersh (1997).
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289:"How does culture influence the successive stages of the discovery of a mathematical structure?"
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101:. Wilder thus became the first of Moore's many doctoral students at the University of Texas.
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After a year as an instructor at Texas, Wilder was appointed assistant professor at the
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320:(1981), contained yet more thinking in this anthropological and evolutionary vein.
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Members of the United States
National Academy of Sciences
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Evolution of mathematical concepts. An elementary study
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Evolution of mathematical concepts. An elementary study
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Biographical
Memoirs National Academy of Sciences 82
139:, 1950–1951, president 1955–1956, and the Society's
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268:During the 1940s, Wilder met and befriended the
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528:Introduction to the foundations of mathematics
399:Raymond, F., 2003, " Raymond Louis Wilder" in
367:Introduction to the foundations of mathematics
295:Introduction to the foundations of mathematics
175:Wilder's thesis set out a new approach to the
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248:, e.g., his "Generalized closed manifolds in
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143:Lecturer in 1969. He was president of the
112:In 1926, Wilder joined the faculty of the
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225:Is accessible from each of these domains.
222:Is the boundary of each of these domains;
130:University of California at Santa Barbara
88:, thanks to the remarkable influence of
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211:and is the boundary of each of them. A
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1296:20th-century American mathematicians
1266:University of Texas at Austin alumni
470:MAA presidents: Raymond Louis Wilder
80:Wilder chose to do his Ph.D. at the
145:Mathematical Association of America
114:University of Michigan at Ann Arbor
407:Related work cited in this entry:
207:in the 2-sphere has precisely two
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1306:Mathematicians from Massachusetts
1301:People from Palmer, Massachusetts
135:Wilder was vice president of the
381:Mathematics as a cultural system
318:Mathematics as a cultural system
69:in 1914, intending to become an
547:10.1090/s0002-9904-1953-09770-1
507:10.1090/s0002-9904-1950-09349-5
236:Around 1930, Wilder moved from
1276:University of Michigan faculty
219:Has two complementary domains;
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1271:Ohio State University faculty
610:American Mathematical Society
137:American Mathematical Society
82:University of Texas at Austin
23:Raymond Louis Wilder, c. 1955
432:What Is Mathematics, Really?
335:Where Mathematics Comes From
187:is a property shared by all
149:National Academy of Sciences
99:Concerning Continuous Curves
1281:United States Navy officers
574:at the University of Texas.
421:The Mathematical Experience
233:conditions was a 2-sphere.
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863:Theophil Henry Hildebrandt
568:The source for this entry.
444:14: 289–303. Reprinted in
280:foundations of mathematics
36:Santa Barbara, California
1291:Scientists from Michigan
1261:Brown University alumni
1085:Cathleen Synge Morawetz
657:Robert Simpson Woodward
625:John Howard Van Amringe
46:and gradually acquired
740:Leonard Eugene Dickson
270:University of Michigan
258:topological invariants
238:set-theoretic topology
183:with respect to a set
157:University of Michigan
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16:American mathematician
962:Charles B. Morrey Jr.
954:Abraham Adrian Albert
906:Gordon Thomas Whyburn
799:Earle Raymond Hedrick
783:George David Birkhoff
724:Edward Burr Van Vleck
566:Raymond Louis Wilder.
534:Bull. Amer. Math. Soc
494:Bull. Amer. Math. Soc
488:Topology of manifolds
442:Philosophy of Science
360:Topology of Manifolds
254:Topology of Manifolds
209:complementary domains
124:, and the topologist
106:Ohio State University
42:, who specialized in
32:Palmer, Massachusetts
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1231:American topologists
914:Raymond Louis Wilder
732:Ernest William Brown
500:(1, Part 1): 75–77.
316:Wilder's last book,
201:Jordan curve theorem
141:Josiah Willard Gibbs
30:(3 November 1896 in
28:Raymond Louis Wilder
807:Luther P. Eisenhart
716:Henry Burchard Fine
692:William Fogg Osgood
641:George William Hill
452:. Springer: 304–19.
434:Oxford Univ. Press.
205:simple closed curve
120:, the cofounder of
815:Arthur Byron Coble
756:Gilbert Ames Bliss
608:Presidents of the
530:, by R. L. Wilder"
490:, by R. L. Wilder"
242:algebraic topology
38:) was an American
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1029:Andrew M. Gleason
986:Saunders Mac Lane
930:Edward J. McShane
855:Marshall H. Stone
839:Griffith C. Evans
823:Solomon Lefschetz
700:Henry Seely White
482:Eilenberg, Samuel
354:Books by Wilder:
330:Evert Willem Beth
34:– 7 July 1982 in
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1136:James Arthur
1093:Arthur Jaffe
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684:Thomas Fiske
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416:Reuben Hersh
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350:Bibliography
344:Rafael Nunez
333:
324:the work of
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276:Leslie White
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94:Moore method
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1241:1982 deaths
1236:1896 births
1210:(2023–2024)
1202:(2021–2022)
1194:(2019–2020)
1192:Jill Pipher
1186:(2017–2018)
1178:(2015–2016)
1170:(2013–2014)
1168:David Vogan
1162:(2011–2012)
1154:(2009–2010)
1146:(2007–2008)
1144:James Glimm
1138:(2005–2006)
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1103:(1999–2000)
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1005:Lipman Bers
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956:(1965–1966)
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873:(1947–1948)
871:Einar Hille
865:(1945–1946)
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686:(1903–1904)
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676:E. H. Moore
659:(1899–1900)
651:(1897–1898)
643:(1895–1896)
635:(1891–1894)
627:(1888–1890)
326:Howard Eves
75:World War I
65:He entered
54:interests.
1225:Categories
1120:Hyman Bass
1013:R. H. Bing
457:References
191:images of
177:Schönflies
1208:Bryna Kra
1184:Ken Ribet
1112:2001–2024
1021:Peter Lax
997:1975–2000
890:1951–1974
775:1925–1950
668:1901–1924
617:1888–1900
526:"Review:
486:"Review:
403:: 336–51.
300:Wilder's
246:manifolds
151:in 1963.
73:. During
524:(1953).
484:(1950).
430:, 1997.
418:, 1981.
231:homology
213:converse
86:topology
44:topology
71:actuary
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379:1981.
372:1969.
358:1949.
338:, by
310:Plato
414:and
385:ISBN
342:and
203:: A
58:Life
50:and
542:doi
502:doi
383:. (
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328:,
297:.
260:.
132:.
601:e
594:t
587:v
550:.
544::
510:.
504::
424:.
391:)
376:.
369:.
362:.
250:n
197:B
193:A
185:B
181:A
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