167:, in the north west of England, the son of a local cotton dealer. In his schooling at the Bolton Grammar School, he studied classics, but no mathematics was taught in the school. He was recognised as the best scholar at the school, and the local vicar guaranteed him a scholarship at Cambridge, but his father would not allow him to go. Instead, he left school at age 14 to work in his father's office.
306:. Any six points on a conic may be joined into a hexagon in 60 different ways, forming 60 different Pascal lines. Extending previous work of Steiner, Kirkman showed that these lines intersect in triples to form 60 points (now known as the Kirkman points), so that each line contains three of the points and each point lies on three of the lines. That is, these lines and points form a
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Kirkman married Eliza Wright in 1841; they had seven children. To support them, Kirkman supplemented his income with tutoring, until Eliza inherited enough property to secure their living. The rectorship itself did not demand much from
Kirkman, so from this point forward he had time to devote to
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on sets of up to ten elements. However, as with much of his work on polyhedra, Kirkman's work in this area was weighed down by newly invented terminology and, perhaps because of this, did not significantly influence later researchers.
499:
for his research on pluquaternions and partitions. He was also an honorary member of the
Literary and Philosophical Society of Manchester and the Literary and Philosophical Society of Liverpool, and a foreign member of the
174:, working as a private tutor to support himself during his studies. There, among other subjects, he first began learning mathematics. He earned a B.A. in 1833 and returned to England in 1835.
431:, over a century before the work of Halin on these graphs. He showed that every polyhedron can be generated from a pyramid by face-splitting and vertex-splitting operations, and he studied
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373:> 3. Kirkman's paper was dedicated to confirming Cayley's assertions concerning two equations among triple-products of units as sufficient to determine the system in case
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has handed out an annual
Kirkman medal, named after Kirkman, to recognise outstanding combinatorial research by a mathematician within four years of receiving a doctorate.
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Fifteen young ladies in a school walk out three abreast for seven days in succession: it is required to arrange them daily, so that no two shall walk twice abreast.
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467:, over the poor reception of his works on polyhedra and groups and over issues of priority. Much of his later mathematical work was published (often in
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published an enumeration of the knots with up to ten crossings. He remained active in mathematics even after retirement, until his death in 1895.
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337:, subsequently to become Kirkman's most famous result. He published several additional works on combinatorial design theory in later years.
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In 1850, Kirkman observed that his 1846 solution to
Woolhouse's problem had an additional property, which he set out as a puzzle in
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135:. Despite being primarily a churchman, he maintained an active interest in research-level mathematics, and was listed by
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and concentrating on simple polyhedra (the polyhedra in which each vertex has three incident edges). He also studied
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263:. Despite Kirkman's and Woolhouse's contributions to the problem, Steiner triple systems were named after
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in polyhedra, and provided an example of a polyhedron with no
Hamiltonian cycle, prior to the work of
210:, where he would stay for 52 years until his retirement in 1892. Theologically, Kirkman supported the
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In the early 1860s, Kirkman fell out with the mathematical establishment and in particular with
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131:(31 March 1806 – 3 February 1895) was a British mathematician and ordained minister of the
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as one of ten leading 19th-century
British mathematicians. In the 1840s, he obtained an
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who wrote a later paper in 1853. Kirkman's second research paper, in 1848, concerned
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by a prize offered beginning in 1858 (but in the end never awarded) by the
451:. His contributions in this area include an enumeration of the transitive
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222:. He published many tracts and pamphlets on theology, as well as a book
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On his return to
England, Kirkman was ordained into the ministry of the
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Proceedings of the
Literary and Philosophical Society of Liverpool
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Lectures on Ten
British Mathematicians of the Nineteenth Century
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determined by the intersection points of opposite sides of a
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Arthur Cayley: Mathematician Laureate of the Victorian Era
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Philosophical Transactions of the Royal Society of London
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criticised it as "the most curious crochet I ever saw".
27:
British church minister and mathematician (1806–1895)
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Kirkman's first mathematical publication was in the
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170:Nine years later, defying his father, he went to
495:In 1857, Kirkman was elected as a fellow of the
777:Kirkman, Th. P. (1856), "On the enumeration of
767:, p. 143 on Kirkman's collaboration with Cayley
562:The Bulletin of the London Mathematical Society
509:Institute of Combinatorics and its Applications
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282:for schoolchildren. It was not successful, and
381:= 4. By 1900 these number systems were called
385:, and later treated as part of the theory of
253:that had been published two years earlier in
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479:. However, in 1884 he began serious work on
397:Beginning in 1853, Kirkman began working on
738:London and Edinburgh Philosophical Magazine
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32:For other people named Thomas Kirkman, see
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247:Cambridge and Dublin Mathematical Journal
560:(1981), "T. P. Kirkman, mathematician",
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667:MacTutor History of Mathematics Archive
621:, New York: John Wiley & Sons, Inc.
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781:-edra having triedral summits and an (
875:19th-century English Anglican priests
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840:19th-century English mathematicians
785: − 1)-gonal base",
294:Next, in 1849, Kirkman studied the
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218:, and was also strongly opposed to
198:. In 1839 he was invited to become
721:(2002), "Steiner triple systems",
365:a representative of a system with
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163:Kirkman was born 31 March 1806 in
25:
865:Alumni of Trinity College Dublin
471:) in the problem section of the
443:Kirkman was inspired to work in
323:The Lady's and Gentleman's Diary
256:The Lady's and Gentleman's Diary
249:in 1846, on a problem involving
237:. His wife died ten days later.
233:Kirkman died 4 February 1895 in
34:Thomas Kirkman (disambiguation)
765:Johns Hopkins University Press
724:Encyclopaedia of Design Theory
224:Philosophy Without Assumptions
1:
333:This problem became known as
870:Fellows of the Royal Society
405:, beginning with a proof of
335:Kirkman's schoolgirl problem
290:Kirkman's schoolgirl problem
206:, a newly founded parish in
153:Kirkman's schoolgirl problem
118:Kirkman's schoolgirl problem
349:Squares". Generalizing the
274:In 1848, Kirkman published
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662:"Thomas Penyngton Kirkman"
449:French Academy of Sciences
151:theory, while the related
147:that founded the field of
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399:combinatorial enumeration
278:, a book on mathematical
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672:University of St Andrews
502:Dutch Society of Science
393:Polyhedral combinatorics
308:projective configuration
276:First Mnemonical Lessons
159:Early life and education
126:Thomas Penyngton Kirkman
43:Thomas Penyngton Kirkman
18:Thomas Penyngton Kirkman
690:The Fifteen Schoolgirls
178:Ordination and ministry
796:10.1098/rstl.1856.0018
465:James Joseph Sylvester
415:William Rowan Hamilton
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261:Wesley S. B. Woolhouse
251:Steiner triple systems
172:Trinity College Dublin
145:Steiner triple systems
613:Macfarlane, Alexander
204:Croft with Southworth
74:, Lancashire, England
759:A. J. Crilly (2006)
747:17 June 2014 at the
658:Robertson, Edmund F.
574:10.1112/blms/13.2.97
401:problems concerning
387:associative algebras
383:hypercomplex numbers
216:John William Colenso
155:is named after him.
149:combinatorial design
137:Alexander Macfarlane
855:British topologists
656:O'Connor, John J.;
475:and in the obscure
433:self-dual polyhedra
357:, Kirkman called a
302:inscribed within a
835:People from Bolton
695:Black Apollo Press
491:Awards and honours
485:Peter Guthrie Tait
411:Hamiltonian cycles
284:Augustus De Morgan
860:British geometers
845:Combinatorialists
742:Google books link
719:Cameron, Peter J.
473:Educational Times
369:imaginary units,
184:Church of England
141:existence theorem
133:Church of England
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429:Halin graphs
419:Icosian game
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377:= 3 but not
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296:Pascal lines
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214:position of
194:and then in
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125:
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85:(1895-02-03)
29:
830:1895 deaths
825:1806 births
789:: 399–411,
685:Tahta, Dick
483:, and with
481:knot theory
351:quaternions
241:Mathematics
220:materialism
819:Categories
423:enumerated
310:of type 60
208:Lancashire
95:Manchester
64:1806-03-31
439:Late work
403:polyhedra
355:octonions
280:mnemonics
97:, England
745:Archived
687:(2006),
660:(1996),
615:(1916),
469:doggerel
226:(1876).
108:Minister
582:0608093
417:on the
300:hexagon
805:108592
803:
701:
580:
235:Bowdon
200:rector
188:curate
165:Bolton
91:Bowdon
72:Bolton
801:JSTOR
515:Notes
426:cubic
421:. He
93:near
699:ISBN
463:and
353:and
196:Lymm
192:Bury
143:for
80:Died
58:Born
791:doi
570:doi
259:by
202:of
190:in
129:FRS
821::
799:,
763:,
697:,
693:,
670:,
664:,
628:^
590:^
578:MR
576:,
566:13
564:,
523:^
504:.
435:.
389:.
325::
318:.
314:60
271:.
808:.
793::
783:x
779:x
728:.
708:.
623:.
585:.
572::
379:a
375:a
371:a
367:a
363:a
361:Q
347:n
316:3
312:3
66:)
62:(
36:.
20:)
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