Michael Aschbacher | |
|---|---|
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| Born | (1944-04-08)April 8, 1944 (age 81) |
| Alma mater | California Institute of Technology University of Wisconsin–Madison |
| Known for | Group theory |
| Awards | Cole Prize (1980) Rolf Schock Prize (2011) Leroy P. Steele Prize (2012) Wolf Prize (2012) |
| Scientific career | |
| Fields | Mathematics |
| Institutions | California Institute of Technology |
| Doctoral advisor | Richard Hubert Bruck |
Michael George Aschbacher (born April 8, 1944) is an Americanmathematician best known for his work onfinite groups. He was a leading figure in the completion of theclassification of finite simple groups in the 1970s and 1980s. It later turned out that the classification was incomplete, because the case ofquasithin groups had not been finished. This gap was fixed by Aschbacher and Stephen D. Smith in 2004, in a pair of books comprising about 1300 pages. Aschbacher is currently the Shaler Arthur Hanisch Professor of Mathematics at theCalifornia Institute of Technology.
Aschbacher received his B.S. at theCalifornia Institute of Technology in 1966 and hisPh.D. at theUniversity of Wisconsin–Madison in 1969.[1] He joined the faculty of the California Institute of Technology in 1970 and became a full professor in 1976. He was a visiting scholar at theInstitute for Advanced Study in 1978–79.[2] He was awarded theCole Prize in 1980, and was elected to theNational Academy of Sciences in 1990. In 1992, Aschbacher was elected a Fellow of theAmerican Academy of Arts and Sciences.[3] He was awarded theRolf Schock Prize for Mathematics by theRoyal Swedish Academy of Sciences in 2011.[4] In 2012 he received theLeroy P. Steele Prize for Mathematical Exposition and theWolf Prize in Mathematics, and became a fellow of theAmerican Mathematical Society.[5]
In 1973, Aschbacher became a leading figure in theclassification of finite simple groups. Aschbacher considered himself somewhat of an outsider in the world of conventional group theory, claiming that he was not "plugged into the system at that point in time".[6] Although he had access to several preprints that were shared among the practitioners of the field, he reproduced many proofs that had already been discovered by other researchers and published them in his early papers. Aschbacher only became interested infinite simple groups as a postdoctorate. He wrote his dissertation incombinatorics and was able to utilize many techniques developed in this area to make early contributions to the study offinite simple groups, which surprised the community of researchers. In particular,Daniel Gorenstein, another leader of theclassification of finite simple groups, said that Aschbacher's entrance was "dramatic".[7]
While Aschbacher's ideas were held in esteem by the group theory community, his writing style drew complaints. Some commented that his proofs lacked explanations of very sophisticated counting arguments. The difficulty in reading his papers became more pronounced as the papers became longer, with even some of his coauthors finding their joint papers hard to read. The challenge in understanding Aschbacher's proofs was attributed not to a lack of ability, but rather to the complexity of the ideas he was able to produce. This was part of a general trend where researchers working on the Classification of Finite Simple Groups began to view papers as being reliable because of the reputation of their authors and their previous work, rather than as self-contained documents. As a result, responsibility of finding errors in the classification problem was up to the entire community of researchers rather than just peer-reviewers alone.[8]
