Purkert received his doctorate (
Promotion) in 1972 from
Leipzig University. His thesis
Die Entwicklung des abstrakten Körperbegriffs (The development of the abstract concept of the
algebraic structure called a
field) was supervised by
Hans Wußing. From 1972 to 1979 Purkert was employed in the mathematics section of Leipzig University's mathematics/natural sciences department. In the mathematics section of Leipzig University's department of the history of medicine and the natural sciences, he was from 1979 to 1987 a lecturer (
Dozent), from 1987 to 1991 a professor extraordinarius, and from 1988 to 1990 the director of the mathematics section. Purkert was a visiting professor in the summer of 1988 at
Pace University and for the academic year 1992–1993 at the
University of Wuppertal. He has been a research assistant and professor at the
University of Bonn since the mid-1990s. There he was coordinating editor of the
Hausdorff Edition.
Friedrich Hirzebruch,
Reinhold Remmert, and
Erhard Scholz. There is a first edition done by editors from Germany and four other countries. There is also a supplemented edition. More than twenty mathematicians, historians, philosophers and literary scholars worked together. The edition was carried out as a long-term project by the
Nordrhein-Westfälische Akademie der Wissenschaften und der Künste (North Rhine-Westphalia Academy for Sciences and Arts). The edition comprises 10 separate volumes (IA, IB, and II through IX). The volumes were published between 2001 and 2020 by
Springer Verlag. Purkert completed (during 2013–2018) the biography of Hausdorff (Volume IB of the edition) begun by Egbert Brieskorn (1936–2013) and also edited Hausdorff's correspondence (Volume IX of the edition). Purkert was the co-author, with Hans-Joachim Ilgauds, of a well-regarded biography of
Georg Cantor. Purkert also edited
Felix Klein's 1891–1892 lectures in Göttingen on Riemann surfaces. In addition to his historical and editorial research, Purkert published mathematical research on
stochastic analysis. ==Honors==