digplanet beta 1: Athena
Share digplanet:


Applied sciences






















"Aschbacher" redirects here. For the similar name Äschbacher, see Aeschbacher.
Michael Aschbacher
Michael Aschbacher.jpg
Born (1944-04-08) April 8, 1944 (age 70)
Little Rock, Arkansas
Residence United States
Nationality American
Fields Mathematics
Institutions California Institute of Technology
Alma mater California Institute of Technology
University of Wisconsin–Madison
Doctoral advisor Richard Hubert Bruck
Known for Group Theory
Notable awards Cole Prize (1980)
Rolf Schock Prize (2011)
Leroy P. Steele Prize (2012)
Wolf Prize in Mathematics (2012)

Michael George Aschbacher (born April 8, 1944) is an American mathematician best known for his work on finite groups. He was a leading figure in the completion of the classification of finite simple groups in the 1970s and 1980s. It later turned out that the classification was incomplete, because the case of quasithin 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 the California Institute of Technology.

Education and career[edit]

Aschbacher received his B.S. at the California Institute of Technology in 1966 and his Ph.D. at the University 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 the Institute for Advanced Study in 1978-79.[2] He was awarded the Cole Prize in 1980, and was elected to the National Academy of Sciences in 1990. In 1992, Aschbacher was elected a Fellow of the American Academy of Arts and Sciences.[3] He was awarded the Rolf Schock Prize for Mathematics by the Royal Swedish Academy of Sciences in 2011.[4] In 2012 he received the Leroy P. Steele Prize for Mathematical Exposition and the Wolf Prize in Mathematics, and became a fellow of the American Mathematical Society.[5]

Classification of finite simple groups[edit]

In 1973, Aschbacher became a leading figure in the classification of finite simple groups. Interestingly, 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 in finite simple groups as a postdoctorate. He wrote his dissertation in combinatorics and was able to utilize many techniques developed in this area to make early contributions to the study of finite simple groups which surprised the community of researchers. In particular, Daniel Gorenstein, another leader of the classification of finite simple groups, said that Aschabacher's entrance was "dramatic." [7]

In fact, the rate of Aschbacher's results proved so astounding that many other mathematicians decided to leave the field to pursue other problems. Aschbacher was proving one major result after another and when he announced his progress at the Duluth conference, mathematicians were convinced that the problem was almost solved. This conference represented a turning point for the problem as many mathematicians (in particular those relatively new to the field) decided to leave the field to pursue other problems.[8]

However, Aschbacher's entrance into the field did not come without difficulties. Aschbacher's papers, beginning with the first he wrote in the field for publication, were very difficult to read. Some commented that his proofs lacked explanations of very sophisticated counting arguments. As Aschbacher's proofs became longer, it became even more difficult for others to understand his proofs. Even some of his own coauthors had trouble reading their own papers. From that point on, researchers no longer read papers as independent documents, but rather ones that required the context of its author. 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. That Aschbacher's proofs were hard to read was not due to a lack of ability, but rather to the astounding complexity of the ideas he was able to produce.[9]



  1. ^ Michael Aschbacher at the Mathematics Genealogy Project
  2. ^ Institute for Advanced Study: A Community of Scholars
  3. ^ "Book of Members, 1780-2010: Chapter A". American Academy of Arts and Sciences. Retrieved 25 April 2011. 
  4. ^ Michael Aschbacher is being awarded The Rolf Schock Prize in Mathematics, Royal Swedish Academy of Sciences press release, March 23, 2011.
  5. ^ List of Fellows of the American Mathematical Society, retrieved 2012-11-03.
  6. ^ Steingart, Alma (2012). "A group theory of group theory". Social Studies of Science (sagepub) 42 (2): 197. doi:10.1177/0306312712436547. 
  7. ^ Steingart, Alma (2012). "A group theory of group theory". Social Studies of Science (sagepub) 42 (2): 200. doi:10.1177/0306312712436547. 
  8. ^ Steingart, Alma (2012). "A group theory of group theory". Social Studies of Science (sagepub) 42 (2): 203. doi:10.1177/0306312712436547. 
  9. ^ Steingart, Alma (2012). "A group theory of group theory". Social Studies of Science (sagepub) 42 (2): 201. doi:10.1177/0306312712436547. 

External links[edit]

Original courtesy of Wikipedia: http://en.wikipedia.org/wiki/Michael_Aschbacher — Please support Wikipedia.
This page uses Creative Commons Licensed content from Wikipedia. A portion of the proceeds from advertising on Digplanet goes to supporting Wikipedia.
59 videos foundNext > 

It Rains - Tressa Harings

Original song written and performed by the beautiful voice of Tressa Harings! Instrumentation and production by Michael Aschbacher.

Motorcycle sequential taillights with Arduino

Making animated rear lights on my motorcycle with an Arduino Mega (eventually micro) and a couple tlc5940 chips.

Kriegerkirchen u. Jahreshauptversammlung der Aschbacher Schützen


With Everything - Captain Freeze

This is Captive Free East Lakes (Captin Freeze) 10-11 playing With Everything, originally written by Hillsong. Miss all you YE people!

This Is The Stuff Cover

Cover of myself singin' and playin' 'This Is The Stuff' by Francesca Battistelli.

Captive Free East Lakes '10-'11 Year Memories

Our Teams end of the year video.

You Never Let Go - Captain Freeze

Captive Free East Lakes playing You Never Let Go, originally written by Matt Redman,

The Incredible Strange SLASH Sideshow of Horros - FRAUENARZT DR.PRAETORIUS


1.Wiener Bluttheater mit WIZARD OF GORE

Das 1. Wiener Bluttheater im OBSKURITARIUM vom 12.1.2012 im VIPER ROOM Vienna. mit Michael Operschall ( Wizard ), Christian Steiner ( Groton ), Apollonya Morgenstern ( Volonteur ) und ...

Ann Ostermann, James Aschbacher and Mickey Singer

On October 2, 2013, the Santa Cruz Open Studio Team came onto Artist on Art to talk about their art work and the 28th Open Studio by the Arts Council of Santa Cruz. As the Director, this is...

59 videos foundNext > 

11 news items

Volume One

Volume One
Thu, 30 Oct 2014 15:07:30 -0700

A little banjo twang, a little moonlight, a couple of new members – Soren's brother Jens Staff on mandolin and Michael Aschbacher on bass – and soon the Boys had a seven-track demo under their belts and starting playing all over the state of Wisconsin.
New Scientist
Fri, 09 Sep 2011 06:44:46 -0700

In early November, Michael Aschbacher, an innovator in the abstract field of group theory at the California Institute of Technology in Pasadena will receive the $75,000 Rolf Schock prize in mathematics from the Royal Swedish Academy of Sciences for his ...
BBC News
Tue, 10 Jan 2012 08:52:30 -0800

Israeli physicist Jacob D Bekenstein won the physics prize and the other awards went to US based scientists, including A Paul Alivisatos, Charles M Lieber, Michael Aschbacher, Luis Caffarelli and Ronald M Evans. Previous winners have gone on to receive ...
University of Texas at Austin News
Fri, 13 Jan 2012 07:29:57 -0800

Caffarelli will share the 2012 prize for mathematics with Michael Aschbacher, a professor at the California Institute of Technology. "I feel deeply honored," says Caffarelli, who is a professor of mathematics, the holder of the Sid W. Richardson ...
Arutz Sheva
Sun, 13 May 2012 20:05:20 -0700

Michael Aschbacher received a prize in the mathematics category for his work on the theory of finite groups. He shared the prize with University of Texas at Austin's Prof. Luis A. Caffarelli, who received the prize for his work on partial differential ...
Thu, 26 Jan 2012 14:45:48 -0800

The Buenos Aires-born Luis Caffarelli, a math professor at UT, will share this year's Wolf Prize in mathematics with Michael Aschbacher. Caffarelli's work includes "nonlinear analysis, partial differential equations and their applications, calculus of ...
Stanford Report
Tue, 21 Feb 2006 22:48:22 -0800

The Changing Nature of Mathematical Proof," that included Michael Aschbacher of the California Institute of Technology, Thomas Hales of the University of Pittsburgh and Steven Krantz of Washington University. "Mathematics was built on this comforting ...
Mon, 15 Dec 2014 14:30:00 -0800

... 路易斯·卡法雷利),邵逸夫奖得主、美国麻省理工学院教授George Luszting(乔治·鲁滋提),沃尔夫奖得主、美国加州理工学院教授Michael Aschbacher(迈克尔·艾施巴赫)以及麻省理工学院数学家、美国数学学会主席David ...

Oops, we seem to be having trouble contacting Twitter

Support Wikipedia

A portion of the proceeds from advertising on Digplanet goes to supporting Wikipedia. Please add your support for Wikipedia!

Searchlight Group

Digplanet also receives support from Searchlight Group. Visit Searchlight