# Michael Aschbacher Awards

We list information about five prestigious awards made to Michael Aschbacher.

**Click on a link below to go to that award**- Alfred P Sloan Foundation (1973)

- Frank Nelson Cole Prize in Algebra (1980)

- Rolf Schock Prize (2011)

- Leroy P Steele Prize (2012)

- Wolf Prize (2012)

**1. Alfred P Sloan Foundation (1973).**

**1.1. Sloan Picks Told at Caltech.**

Four young California Institute of Technology faculty members have been selected by the Alfred P Sloan Foundation for the 1973 research fellowships, the foundation announced.

This was the largest number of fellowships awarded to any California University. UCLA was second with three. Stanford had two and UC Berkeley two.

Nationally, 79 young scientists were chosen from the faculties of 49 colleges and universities for fellowships in the $1.4 million-per-year Sloan Research Fellowship programme.

The Caltech recipients are:

Michael Aschbacher, 29, assistant professor of mathematics; Jeffrey E Mandula, 31, assistant professor of theoretical physics; Robert W Vaughan, 31, assistant professor of chemical engineering; and Michael W Werner, 30, assistant professor of physics.

Sloan fellows are selected on the basis of nominations from senior colleagues for their capacity to perform outstanding and creative basis research.

They will be supported for two years at an average of $8,750 per year.

The Sloan Fellowships are designed to make possible advances in fundamental research by young scientists at an early stage of their careers in fields of science which include physics, mathematics, chemistry, neuroscience and certain connected fields such as geochemistry and astrophysics.

**2. Frank Nelson Cole Prize in Algebra (1980).**

**2.1. About the Frank Nelson Cole Prize in Algebra.**

The Frank Nelson Cole Prize in Algebra (and the Frank Nelson Cole Prize in Number Theory) was founded in honour of Professor Frank Nelson Cole upon his retirement after twenty-five years as Secretary of the American Mathematical Society. Cole also served as Editor-in-Chief of the Bulletin for twenty-one years. The original fund was donated by Professor Cole from moneys presented to him on his retirement, and was augmented by contributions from members of the Society. The fund was later doubled by his son, Charles A Cole, and supported by family members. It has been further supplemented by George Lusztig and by an anonymous donor.

The award is for a notable research memoir in analysis that has appeared during the past six years in a recognised North American journal and only members of the American Mathematical Society are eligible.

**2.2. Tenth award of the Frank Nelson Cole Prize in Algebra.**

The 1980 Frank Nelson Cole Prize in Algebra was awarded to Michael Aschbacher for his paper, 'A characterization of Chevalley groups over fields of odd order',

*Annals of Mathematics*(2)

**106**(1977), 353-398.

**3. Rolf Schock Prize (2011).**

**3.1. News from the AMS.**

The 2011 Rolf Schock Prize in Mathematics will be awarded in November to Michael Aschbacher:-

... for his fundamental contributions to one of the largest mathematical projects ever, the classification of finite simple groups, notably his contribution to the quasi-thin case.Aschbacher is the Shaler Arthur Hanisch Professor of Mathematics at Caltech. He was awarded the Cole Prize by the AMS in 1980 and was elected to the National Academy of Sciences in 1990. Hilary Putnam will receive the 2011 Schock Prize in Logic and Philosophy. Each prize amount is SEK 500,000 (approximately US$75,000). The prizes will be awarded by the Royal Swedish Academy of Sciences in a ceremony in Stockholm on 2 November.

**3.2. The Rolf Schock Prize Symposium.**

A symposium in the honour of the Rolf Schock Prize Laureate in Mathematics Prof Michael Aschbacher was held in the Beijer Hall, the Royal Swedish Academy of Sciences, Lilla Frescativägen 4A, Stockholm on 3 November 2011. It was chaired by Torsten Ekedahl and Jan-Erik Roos. After an Opening Address by Staffan Normark, Permanent Secretary of the Royal Swedish Academy of Sciences, there were four lectures:

(i)

*The general background and history of the classification of finite simple groups*by Prof John Griggs Thompson, University of Cambridge, UK.

(ii)

*Applying the classification in other areas of mathematics*, by

The Rolf Schock Prize Laureate in Mathematics Prof Michael Aschbacher, California Institute of Technology, CA, USA.

**Abstract:**There are many applications of the classification of the finite simple groups in many areas of mathematics. I'll briefly mention a few examples, but most of the time will be spent giving some idea of how a problem on finite groups can be reduced to the simple case, and what information about simple groups is then needed to complete the solution.

(iii)

*Michael Aschbacher's work and the Classification of Finite Simple Groups*, by Prof Stephen Smith, University of Illinois at Chicago, IL, USA.

**Abstract:**An attempt is made to survey how the classification was finished. A more detailed abstract is given on the enclosed sheet of paper.

(iv)

*A glimpse into the future*, by Prof Ron Solomon, The Ohio State University, OH, USA.

**Abstract:**The classification of the finite simple groups leaves open many fascinating questions concerning finite groups, and points toward numerous directions for future investigation. I will highlight some questions in the modular representation theory of groups, notably the Weight Conjecture of Alperin, which in turn focus interest on the category of saturated fusion systems, establishing a new interface between group theory and topology, which is actively being explored by Aschbacher, Chermak, Oliver, and others.

**3.3. A Schock Prize for an enormous theorem.**

The Rolf Schock Prize in Mathematics 2011 has this week [March 2011] been awarded to Michael Aschbacher:-

... for his fundamental contributions to one of the largest mathematical projects ever, the classification of finite simple groups.Finite simple groups are the basic building blocks of the mathematical description of symmetry. At over 10,000 pages, spread across 500 or so journal articles, by over 100 different authors from around the world, the proof of the classification was without precedent, and must be counted the longest in history.

Michael Aschbacher is the Shaler Arthur Hanisch Professor of Mathematics at the California Institute of Technology. He has made fundamental contributions to group theory, especially regarding the classification of finite simple groups. He was awarded the Cole Prize by the American Mathematical Society in 1980, and became a member of the United States National Academy of Sciences in 1990.

The Rolf Schock Prizes are triennial and are awarded in the fields of logic and philosophy, mathematics, the visual arts and the musical arts. Each prize amounts to USD 75,000. The prizes are awarded by The Royal Swedish Academy of Sciences, The Royal Swedish Academy of Fine Arts and The Royal Swedish Academy of Music. The prize award ceremony will take place in Stockholm, Sweden, on 2 November 2011.

The three other laureates 2011 are the violinist and conductor Andrew Manze, who is awarded The Rolf Schock Prize in the Musical Arts, the painter Marlene Dumas, who is awarded the prize in the visual arts and Professor Hilary Putnam, who is awarded the prize in logic and philosophy, as has been previously announced.

**3.4. Michael Aschbacher - 2011 Schock Prize for Mathematics.**

Michael Aschbacher was awarded the 2011 Schock Prize for Mathematics:-

... for his fundamental contributions to one of the largest mathematical projects ever, the classification of finite simple groups, notably his contribution to the quasi-thin case.Symmetries have long captured mathematicians' interest. An equilateral triangle that is rotated one or two thirds of a full turn, for example, has the same orientation as the original figure. This kind of triangle thus has three rotational symmetries (the first position, before it is moved at all, counts as one symmetry). Similarly, there are 60 rotations that preserve a dodecahedron. The symmetries for a geometrical figure make up what are called a 'group of symmetries' (or 'symmetry group'). In the 19th century, the 'group' notion was found interesting in many other contexts, and abstract group theory was developed.

Each group with a finite number of elements can be divided into components known as 'simple groups'. This is analogous to how an integer (whole number) can be written as the product of prime numbers; here, the simple groups play the role of prime numbers. Both the above examples (the triangle and the dodecahedron) are simple groups, with three and 60 elements respectively. Trying to find or classify all simple groups was a natural problem to address. The task of classifying all the finite simple groups came to be the largest single project in mathematical history. It also revealed intriguing patterns with several infinite series, along with a total of 26 'sporadic groups', mostly discovered in the course of the work. The most complex of these sporadic groups, containing

808017424794512875886459904961710757005754368000000000

elements, is known as the 'Monster group' owing to its enormous size. This group has proved to have startling connections with other disciplines, such as number theory and mathematical physics.

Michael Aschbacher made several essential contributions in this project, and by approximately 1980 the work was almost entirely finished. A gap, which came to be known as the 'quasi-thin' case, remained before the classification could be completed. The missing case proved highly challenging and the project was not concluded until two books written by Michael Aschbacher and Stephen Smith, with a total length of more than 1200 pages, were published in 2004.

Michael Aschbacher was born in 1944. He received his BS degree at the California Institute of Technology, to which he returned in 1970 (after gaining a PhD at the University of Wisconsin-Madison), and where he is now the Shaler Arthur Hanisch Professor of Mathematics. He has made fundamental contributions to group theory, especially regarding the classification of finite simple groups. He was awarded the Cole Prize by the American Mathematical Society in 1980, and became a member of the United States National Academy of Sciences in 1990.

**3.5. The Enormous Theorem by Nitsa Movshovitz-Hadar.**

On 2 November 2011, at a ceremony in Stockholm, Sweden, the Rolf Schock Prize in mathematics was awarded to Professor Michael Aschbacher of Caltech - the California Institute of Technology, "... for his fundamental contributions to one of the largest mathematical projects ever, the classification of finite simple groups ...."

The programme for the classification of simple finite groups project, undoubtedly one of the most ambitious projects in pure mathematics that have ever been conceived, was outlined in 1972 by Prof Daniel Gorenstein, a mathematician at Rutgers University, USA. His idea was to tie together various disparate strands of mathematical studies published from the mid-20th century on, rooted in the work that began as early as the 19th century, and turn them into a concerted classification programme.

Nine years later, in 1981, Robert Greiss constructed "The Monster Group", which is a simple finite group with as many as $8\times 10^{53}$ elements. This discovery led Gorenstein to his proclamation made in 1983: "In February 1981, the classification of simple finite groups was completed."

The announcement of the completion of the classification, which is nowadays considered a landmark in contemporary mathematics, was met with scepticism from the outset and did not receive any special public attention. Why? - Because its proof was controversial. It spanned more than 10,000 pages and was spread across some 500 articles published in various journals and written by over 100 different authors from all over the world. This was an unprecedented case in the history of mathematics. Some sceptics were right - indeed, the proof turned out to require corrections here and there, mostly done between 1995 and 2004.

Michael Aschbacher's great contribution was the result of seven years of work, during which he and his colleague Stephen Smith published two additional voluminous books on solving the issue, until in 2004, Aschbacher wrote: "to my knowledge the main theorem [of our recent work] closes the last gap in the original proof, so (for the moment) the classification theorem can be regarded as a theorem."

**3.6. Prize awarded for largest mathematical proof.**

The largest proof in mathematics is colossal in every dimension - from the 100-plus people needed to crack it to its 15,000 pages of calculations. Now the man who helped complete a key missing piece of the proof has won a prize.

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 pivotal role in proving the Classification Theorem of Finite Groups, aka the Enormous Theorem.

If it were not for Aschbacher, the behemoth might still contain a gaping hole. In 2004, he and Stephen Smith of the University of Illinois in Chicago published a 1200-page guide through the last piece of the puzzle.

That 2004 tome brought together some of Aschbacher's early works, and completed the proof. His contributions to the overall proof were "absolutely monumental", says Ronald Solomon, a group theorist at Ohio State University in Columbus.

The Enormous Theorem concerns groups, which in mathematics can refer to a collection of symmetries, such as the rotations of a square that produce the original shape. Some groups can be built from others but, rather like prime numbers or the chemical elements, "finite simple" groups are elemental.

There are an infinite number of finite simple groups but a finite number of families to which they belong. Mathematicians have been studying groups since the 19th century, but the Enormous Theorem wasn't proposed until around 1971, when mathematician Daniel Gorenstein of Rutgers University in New Jersey devised a plan to identify all the finite simple groups, divide them into families and prove that no others could exist.

Gorenstein and his hundreds of collaborators spent a decade working on the proof. By 1981, Gorenstein could see the light at the end of the tunnel, though a few hurdles remained. The proof remained incomplete until the 2004 publication by Aschbacher and Smith, which completed the proof. It identified all the families - and showed no others could exist.

It also identified all the known "sporadic groups", 26 (or 27, according to some) outlying simple finite groups that get pooled as one family because they do not fit neatly into the other families.

Solomon estimates that only a few mathematicians in the world (including Aschbacher) understand the complete proof. It was a punishing read, says Mark Ronan, an honorary professor of mathematics at University College London. "Some of Aschbacher's proofs were just diabolically difficult," he adds.

Mathematicians cannot predict how the proof will influence the future of mathematics or the sciences. Ronan says that like many mathematical results, the applications may not surface any time soon. "Whatever it's telling us, we haven't yet found out," he says. "I'd be willing to bet a million dollars that it has an application, but there's no point in making the bet because I'll be dead before I can collect."

**4. Leroy P Steele Prize (2012).**

The 2012 AMS Leroy P Steele Prizes were presented at the 118th Annual Meeting of the AMS in Boston in January 2012. The Steele Prizes were awarded to Michael Aschbacher, Richard Lyons, Steve Smith, and Ronald Solomon for Mathematical Exposition; to William Thurston for a Seminal Contribution to Research; and to Ivo M. Babuska for Lifetime Achievement.

The 2012 Leroy P Steele Prize for Mathematical Exposition is awarded to Michael Aschbacher, Richard Lyons, Steve Smith, and Ronald Solomon for their work, The Classification of Finite Simple Groups: Groups of Characteristic 2 Type, Mathematical Surveys and Monographs, 172, American Mathematical Society, Providence, RI, 2011. In this paper, the authors, who have done foundational work in the classification of finite simple groups, offer to the general mathematical public an articulate and readable exposition of the classification of characteristic 2 type groups.

Michael Aschbacher was born in Little Rock, Arkansas, in 1944. He received his undergraduate degree from Caltech in 1966 and his Ph.D. from the University of Wisconsin in 1969 under the direction of Richard Bruck. He was a postdoctoral fellow at the University of Illinois in 1969-70, and since then he has been at Caltech, where he is the Shaler Arthur Hanisch Professor of Mathematics. He received the Cole Prize in Algebra from the AMS in 1980 and the Rolf Schock Prize from the Royal Swedish Academy of Sciences in 2011. He was an invited speaker at the International Congress of Mathematicians in 1978 and a vice president of the AMS from 1996 to 1998. He is a member of the National Academy of Sciences and the American Academy of Arts and Sciences. Aschbacher's research focuses on the finite simple groups.

We are deeply grateful to the Society for honouring us with this Steele Prize for Mathematical Exposition. For decades Danny Gorenstein was the voice of the Classification Project, providing the community with a vivid narrative of our travails and accomplishments. Unfortunately, he departed this life before the task was completed and the tale fully told. Our book serves in part as a sequel to his 1983 volume, providing a detailed reader's guide to the major papers composing the second ("even") half of the Classification proof, but we have prefaced it with an outline and synopsis of the entire proof, updating Danny's references and giving our personal view of the entire enterprise. In writing a book it always helps to have a great story to tell, and few mathematical projects have played out on such an epic scale and reached such a gratifying culmination as the Classification of the Finite Simple Groups. We appreciate that, in awarding us this prize, the Society acknowledges the importance of this work.

Michael Aschbacher, the Shaler Arthur Hanisch Professor of Mathematics, has been awarded the 2012 Leroy P Steele Prize for Mathematical Exposition by the American Mathematical Society (AMS). Aschbacher, along with coauthors Richard Lyons of Rutgers University, Steve Smith of the University of Illinois at Chicago, and Ronald Solomon of Ohio State University, were recognised for a paper on the classification of certain types of groups, which are fundamental mathematical objects.

"AMS prizes are big honours, and we are proud that Michael has gotten this prize," says Barry Simon, the IBM Professor of Mathematics and Theoretical Physics." Over the last few decades, Aschbacher has played a leading role in the classification of so-called finite simple groups-an achievement that, Simon says, is one of the major mathematical accomplishments of the last 50 years, earning Aschbacher the Rolf Schock Prize from the Royal Swedish Academy of Sciences last year. "The mathematical proof involved in that work is so complicated that even experts in the specialty haven't absorbed it all," Simon says. "What Aschbacher and his co-authors got the Steele Prize for is an exposition for professional mathematicians that's one part of a wider program. Making this material accessible to mathematicians in different fields of mathematics is an important accomplishment."

In addition to the Schock Prize, Aschbacher has also received the Cole Prize in Algebra from AMS, and he is a member of the National Academy of Sciences and the American Academy of Arts and Sciences. The Steele Prize was awarded for the paper titled "The classification of finite simple groups: groups of characteristic 2 type," published in Mathematical Surveys and Monographs, Vol. 172.

**4.1. Citation: Mathematical Exposition: Michael Aschbacher, Richard Lyons, Steve Smith, and Ronald Solomon.**The 2012 Leroy P Steele Prize for Mathematical Exposition is awarded to Michael Aschbacher, Richard Lyons, Steve Smith, and Ronald Solomon for their work, The Classification of Finite Simple Groups: Groups of Characteristic 2 Type, Mathematical Surveys and Monographs, 172, American Mathematical Society, Providence, RI, 2011. In this paper, the authors, who have done foundational work in the classification of finite simple groups, offer to the general mathematical public an articulate and readable exposition of the classification of characteristic 2 type groups.

**4.2. Michael Aschbacher Biographical Sketch.**Michael Aschbacher was born in Little Rock, Arkansas, in 1944. He received his undergraduate degree from Caltech in 1966 and his Ph.D. from the University of Wisconsin in 1969 under the direction of Richard Bruck. He was a postdoctoral fellow at the University of Illinois in 1969-70, and since then he has been at Caltech, where he is the Shaler Arthur Hanisch Professor of Mathematics. He received the Cole Prize in Algebra from the AMS in 1980 and the Rolf Schock Prize from the Royal Swedish Academy of Sciences in 2011. He was an invited speaker at the International Congress of Mathematicians in 1978 and a vice president of the AMS from 1996 to 1998. He is a member of the National Academy of Sciences and the American Academy of Arts and Sciences. Aschbacher's research focuses on the finite simple groups.

**4.3. Joint Response from Michael Aschbacher, Richard Lyons, Steve Smith, and Ronald Solomon.**We are deeply grateful to the Society for honouring us with this Steele Prize for Mathematical Exposition. For decades Danny Gorenstein was the voice of the Classification Project, providing the community with a vivid narrative of our travails and accomplishments. Unfortunately, he departed this life before the task was completed and the tale fully told. Our book serves in part as a sequel to his 1983 volume, providing a detailed reader's guide to the major papers composing the second ("even") half of the Classification proof, but we have prefaced it with an outline and synopsis of the entire proof, updating Danny's references and giving our personal view of the entire enterprise. In writing a book it always helps to have a great story to tell, and few mathematical projects have played out on such an epic scale and reached such a gratifying culmination as the Classification of the Finite Simple Groups. We appreciate that, in awarding us this prize, the Society acknowledges the importance of this work.

**4.4. Aschbacher Receives Steele Prize for Mathematical Exposition.**Michael Aschbacher, the Shaler Arthur Hanisch Professor of Mathematics, has been awarded the 2012 Leroy P Steele Prize for Mathematical Exposition by the American Mathematical Society (AMS). Aschbacher, along with coauthors Richard Lyons of Rutgers University, Steve Smith of the University of Illinois at Chicago, and Ronald Solomon of Ohio State University, were recognised for a paper on the classification of certain types of groups, which are fundamental mathematical objects.

"AMS prizes are big honours, and we are proud that Michael has gotten this prize," says Barry Simon, the IBM Professor of Mathematics and Theoretical Physics." Over the last few decades, Aschbacher has played a leading role in the classification of so-called finite simple groups-an achievement that, Simon says, is one of the major mathematical accomplishments of the last 50 years, earning Aschbacher the Rolf Schock Prize from the Royal Swedish Academy of Sciences last year. "The mathematical proof involved in that work is so complicated that even experts in the specialty haven't absorbed it all," Simon says. "What Aschbacher and his co-authors got the Steele Prize for is an exposition for professional mathematicians that's one part of a wider program. Making this material accessible to mathematicians in different fields of mathematics is an important accomplishment."

In addition to the Schock Prize, Aschbacher has also received the Cole Prize in Algebra from AMS, and he is a member of the National Academy of Sciences and the American Academy of Arts and Sciences. The Steele Prize was awarded for the paper titled "The classification of finite simple groups: groups of characteristic 2 type," published in Mathematical Surveys and Monographs, Vol. 172.

**5. Wolf Prize (2012).**

**5.1. The Wolf Prize: Israel Society and Culture.**

The Wolf Prize is awarded to outstanding scientists and artists, "for achievement in the interest of mankind and friendly relations among peoples." The annual prizes of $100,000 are given in four out of five scientific fields in rotation: Agriculture, Chemistry, Mathematics, Medicine and Physics. In the Arts, the prize rotates among Architecture, Music, Painting and Sculpture.

The Wolf Prize was established in 1978 by German-born Ricardo Wolf and his wife Francisca Subirana-Wolf. Dr Wolf, an inventor, diplomat and philanthropist, lived in Cuba for many years and served as Fidel Castro's ambassador to Israel from 1961-1973. When Cuba severed ties with Israel in 1973, Dr. Wolf decided to stay in Israel where he spent his final years.

The Wolf Prizes in Physics and Chemistry are often considered the most prestigious awards in those fields after the Nobel Prize. The prize in physics has gained a reputation for identifying future winners of the Nobel Prize - from the 26 prizes awarded between 1978 and 2010, fourteen winners have gone on to win the Nobel Prize, five of those in the following year.

In medicine, the prize is probably the third most prestigious, after the Nobel Prize and the Lasker Award. Until the establishment of the Abel Prize, the Wolf Prize was probably the closest equivalent of a Nobel Prize in Mathematics, since the more prestigious Fields Medal was only awarded every four years to mathematicians under forty years old. The Prize in Agriculture has likewise been equated to a Nobel Prize in Agriculture.

**5.2. Scientists honoured with prestigious Wolf Prize.**

Six renowned scientists and music greats win this year's Wolf Prize - considered second only to the Nobel Prize in prestige and one that has often served as predictor of the Nobel - on Sunday at the Knesset.

Jacob Bekenstein of the Hebrew University of Jerusalem received his prize in the physics category; California Institute of Technology Prof Michael Aschbacher, and University of Texas at Austin's Prof Luis Caffarelli were Wolf Prize laureates in the mathematics category; Prof Ronald M Evans of the Salk Institute for Biological Studies in La Jolla, California, in medicine; University of California at Berkeley Prof A Paul Alivisatos, and Harvard University's Prof Charles Leiber shared the chemistry prize.

Berlin Philharmonic conductor Sir Simon Rattle and renowned tenor and conductor Placido Domingo - both of whom could not attend due to previous commitments - received the 2012 Wolf Prize for the Arts.

Knesset Speaker MK Reuven Rivlin and Education Minister MK Gideon Sa'ar, who is chairman of the Wolf Foundation, attended the ceremony.

President Shimon Peres, who was supposed to present the awards, was at home recovering from minor surgery.

**5.3. 2012 Wolf Prizes Handed Out in Special Ceremony.**

Education Minister Gideon Sa'ar and Knesset Speaker Reuven Rivlin hand out Wolf Prize at the Knesset.

Education Minister Gideon Sa'ar and Knesset Speaker Reuven Rivlin handed out the 2012 Wolf Prize in an official ceremony at the Knesset on Sunday evening.

Four awards of $100,000 each were divided among six winners in four areas - physics, medicine, chemistry and mathematics - for their contributions to the advancement of science for humanity. The Wolf Prize is considered second in prestige to the Nobel Prize. One out of every three scientists to win the award eventually goes on to win the Nobel Prize.

This year's winners were Jacob Bekenstein of the Hebrew University of Jerusalem, who received his prize in the physics category for his work on black holes.

California Institute of Technology Prof 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 equations.

Prof Ronald M Evans of the Salk Institute for Biological Studies in La Jolla, California received a prized in medicine for his discovery of the gene super-family encoding nuclear receptors and elucidating the mechanism of action of this class of receptors.

The chemistry prize was shared by University of California at Berkeley Prof A Paul Alivisatos, who won for his development of the colloidal inorganic nanocrystal as a building block of nanoscience and for making fundamental contributions to controlling the synthesis of these particles, to measuring and understanding their physical properties. The second winner was Harvard University's Prof Charles Leiber, who won for his seminal contributions to nanochemistry and particularly the synthesis of single-crystalline semiconductor nanowires, characterization of the fundamental physical properties of nanowires, and their application to electronics, photonics and nanomedicine.

In addition to the above, Berlin Philharmonic conductor Sir Simon Rattle and renowned tenor and conductor Placido Domingo received the 2012 Wolf Prize for the Arts.

Minister of Education Gideon Sa'ar said during the ceremony, "To this day, the Wolf Prize has been awarded to well-known people from the fields of science and humanities who have shaped science and modern culture. The prize is an expression of the respect we have to those who choose to dedicate their lives to the advancement of science and art."

Turning to the six science-related winners, Sa'ar said, "You have been chosen for your achievements in physics, mathematics, chemistry and medicine. These achievements are the result of a mission, of the love of the field, of constant curiosity and mostly of the uncompromising pursuit of excellence."

Sa'ar added, "Israel does not have the privilege of not investing in education, in higher education, science and advanced research. It is vital to ensuring the future of Israel, as well as achieving its destiny. The future of Israel depends on our ability to maintain our qualitative edge. We can only maintain this advantage if we encourage and nurture excellence at all stages of education and place the necessary emphasis on advanced research."

**5.4. Michael Aschbacher: Wolf Prize Laureate in Mathematics 2012.**

Michael Aschbacher, California Institute of Technology, USA, is awarded the 2012 Wolf Prize. He shared the prize with Luis Caffarelli.

Michael Aschbacher was awarded the Wolf Prize:-

... for being a principal architect of the classification of finite simple groups. His impact on the theory of finite is extraordinary in its depth, breadth and beauty.Michael Aschbacher and John Thompson (Wolf prize Laureate of 1992) are the two great modern masters of the theory of finite groups, in an era that brought to fruition a line of research going back to Galois in the 1830's. The breadth and depth of Aschbacher's understanding of finite groups in general, and finite simple groups in particular, and the power he brought to bear on their analysis, are astonishing.

Aschbacher astounded the finite group theory community with a series of papers that raised the classification project for finite simple groups from a distant dream to the reality it is today.

In a series of papers in the 1970's Aschbacher developed the theory of standard components and tightly embedded subgroups, and brought the theory of groups of odd characteristic type close to the completion.

Turning next to groups of characteristic type, Aschbacher handled all of the most difficult cases, notably the Thin Group case, the $p$-Uniqueness Case, and finally the Quasithin Case. This last result, contained in two massive monographs written jointly with S D Smith, completed the classification of finite simple groups. In the process, he significantly advanced the theories of $GF(2)$ representations, Thompson factorisation, and pushing-up.

Also worthy of mention are Aschbacher's work on maximal subgroups of finite simple groups, his joint work with Y Segev on the uniqueness of the sporadic groups, and his joint work with S D Smith on the Quillen conjecture.

**5.5. Aschbacher and Caffarelli Awarded 2012 Wolf Prize.**

The 2012 Wolf Prize in Mathematics has been awarded to: Michael Aschbacher, California Institute of Technology, for his work in classifying finite simple groups; and Luis Caffarelli, University of Texas, Austin, for his work on partial differential equations. The prize of US$100,000 was divided equally between the prizewinners.

Michael Aschbacher was born in 1944 in Little Rock, Arkansas. He received his B.S. from the California Institute of Technology in 1966 and his Ph.D. from the University of Wisconsin, Madison, in 1969. He joined the faculty of the California Institute of Technology in 1970 and is currently Shaler Arthur Hanisch Professor of Mathematics at Caltech. He was a visiting scholar at the Institute for Advanced Study in 1978-1979. He was awarded the Cole Prize in Algebra (1980), the Rolf Schock Prize of the Royal Swedish Academy of Sciences (2011), and the Leroy P Steele Prize for Mathematical Exposition (2012). He has been elected to the National Academy of Sciences (1990) and is a fellow of the American Academy of Arts and Sciences (1992) and of the American Mathematical Society (2012).

**5.6. Michael Aschbacher Wins Wolf Prize in Mathematics.**

Michael Aschbacher, the Shaler Arthur Hanisch Professor of Mathematics, will share the 2012 Wolf Prize in mathematics. The award recognises his role in classifying types of mathematical objects called finite simple groups. According to the prize citation, "His impact on the theory of finite groups is extraordinary in its breadth, depth, and beauty."

"The classification of finite simple groups is one of the crowning achievements of modern mathematics," says Hirosi Ooguri, the Fred Kavli Professor of Theoretical Physics and Mathematics at Caltech. "It's wonderful that Michael is recognised as the principal architect of this work."

Aschbacher will share the prize, which includes $100,000, with Luis Caffarelli at the University of Texas, Austin, who was recognised for work on partial differential equations. They will receive the award from Israeli President Shimon Peres at a ceremony on May 13 at the Knesset in Jerusalem.

"Receiving an award such as the Wolf Prize is of course personally very satisfying," Aschbacher says. "The finite simple groups are the building blocks of finite group theory, playing a role somewhat analogous to that of prime numbers in arithmetic. As a result, the classification theorem is not only a beautiful and natural result, but it's also very useful."

Since 1978, The Wolf Prize is awarded annually in the fields of agriculture, chemistry, mathematics, medicine, physics, and the arts. Among this year's winners is singer Placido Domingo. Past winners have included notable names such as Stephen Hawking in physics, violinist Isaac Stern and architect Frank Gehry in the arts. Previous winners from Caltech include Harry Gray, Ahmed Zewail, and Rudy Marcus in chemistry; Alexander Varshavsky, and the late Seymour Benzer, Edward Lewis, and Roger Sperry in medicine.

Aschbacher has recently garnered several awards for his work on finite simple groups. He was awarded the 2012 Leroy P. Steele Prize for Mathematical Exposition, and last year, he won the Rolf Schock Prize from the Royal Swedish Academy of Sciences. He also received the Cole Prize in Algebra and is a member of the National Academy of Sciences and the American Academy of Arts and Sciences.

**5.7. Invited Talks by the Recipients of the 2012 Wolf Prize in Mathematics.**

Invited Talks by the Recipients of the 2012 Wolf Prize in Mathematics were held in the Weizmann Institute of Science on Tuesday, 15 May 2012 in Room 115 of the Ziskind Building.

Prof Michael Aschbacher, Caltech, delivered the talk

*Finite simple groups*.

**Abstract:**The classification of the finite simple groups supplies us with a list of the simple groups. I'll describe those groups as automorphism groups of various interesting objects, and give some history of their discovery. The talk will be expository and accessible to anyone who has taken a good undergraduate algebra course.

Last Updated March 2024