Thomas Penyngton Kirkman FRS (31 March 1806 – 3 February 1895) was a British mathematician and ordained minister of the Church of England.

Despite being primarily a churchman, he maintained an active interest in research-level mathematics, and was listed by Alexander Macfarlane as one of ten leading 19th-century British mathematicians.

[1][2][3] In the 1840s, he obtained an existence theorem for Steiner triple systems that founded the field of combinatorial design theory, while the related Kirkman's schoolgirl problem is named after him.

[4][5] Kirkman was born 31 March 1806 in Bolton, in the north west of England, the son of a local cotton dealer.

[1][2][3] Next, in 1849, Kirkman studied the Pascal lines determined by the intersection points of opposite sides of a hexagon inscribed within a conic section.

[6] Generalizing the quaternions and octonions, Kirkman called a pluquaternion Qa a representative of a system with a imaginary units, a > 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 a = 3 but not a = 4.

[1][3] Kirkman was inspired to work in group theory by a prize offered beginning in 1858 (but in the end never awarded) by the French Academy of Sciences.

[1][3] In the early 1860s, Kirkman fell out with the mathematical establishment and in particular with Arthur Cayley and James Joseph Sylvester, 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 doggerel) in the problem section of the Educational Times and in the obscure Proceedings of the Literary and Philosophical Society of Liverpool.