... lived in a little farming community outside of East Lansing, a community where they were starting to build up a subdivision as was the American way after the war.

It's summertime in Southern California, school is out, and the living is easy - but not necessarily for 24 high school juniors, who are spending their vacation at UCLA residence halls and class rooms instead of the beach. Three are from the Valley. They are Michael G Aschbacher, 16346 Mayall Granana Hills of James Monroe High School ... The youngsters, split between boys and girls, are attending a special six-week mathematics training program, studying postulational development of algebra, truth tables, operations with sets and other subjects usually not taught until the college freshman or sophomore year.

I wanted to get away from home, so I wanted to go to MIT. But my mother had cancer in the summer before my senior year, and she said she wanted me to not go that far away. She wasn't sure that the cancer would not reoccur. So I agreed [and] ended up at Caltech.

... my instructor in the analysis course was Donald Knuth. He was a student of Marshall Hall, who was the biggest name in the mathematics department at that time. ... he was a very interesting instructor. And the other guy was pretty good, the algebraist. He was less exciting, but the course was interesting. I did well in those two courses and enjoyed them. I'd already said I was going to be a mathematics major because I wasn't going to be a physics or chemistry major.

It is the aim of this paper to investigate the automorphism groups of a certain class of combinatorial or geometric systems commonly known as symmetric block designs, symmetric balanced incomplete block designs, (v, k, λ) systems, or as we shall refer to them: designs. ...

While there are many group theoretical results in the literature on projective planes and certain other special classes of symmetric designs, and while there are a number of matrix theoretical theorems for more general symmetric designs, to our knowledge there are few general group theoretical results for arbitrary symmetric designs. In the early sections of this paper we state and prove a number of such theorems. In later sections our hypotheses become progressively restrictive.

While we are interested in gaining information about designs, we are also interested in using designs to obtain information about groups: particularly permutation groups. Thus in sections seven and eight we investigate group representations related to rank three permutation groups.

In the last few years the study of multiply transitive and rank three permutation groups has resulted in the discovery of a number of new simple groups. We had hoped the line of investigation in section eight would lead to new rank three, multiply transitive, or simple groups. Unfortunately our results are negative.

In the final section we utilise the results of the previous sections to single out the possible automorphism groups for designs with parameters (79,13, 2). We construct such a design using the candidate of largest order. The existence of a design with these parameters had been in doubt.

The reader is cautioned that in our discussion, all groups are finite and all designs are finite and symmetric.

This paper was prepared while the author was holding a National Science Foundation Graduate Fellowship.

My thesis was in combinatorics, but in my last year of graduate school I decided to switch specialties and become a finite group theorist. Thus, for a few years, I had to acquire the necessary background to work in my new specialty and to identify the important problems in finite group theory. During this time I worked on problems that the community had generated and deemed important, and I used some combination of existing strategies and techniques, together with ideas of my own that slightly extended existing approaches. But, after three or four years, I had a good enough feeling for the subject that I could find my own problems, and produce my own strategies and techniques for solving the problems.
...
By the time I received my degree in 1969, significant new results were appearing almost every day, so that finite group theory was in a state of flux. My lack of background was not as big a handicap as it should have been, since the knowledge base of the subject was changing rapidly. This allowed me to learn local group theory and algebraic Lie theory on the job, along with everyone else, so that I could transition into those communities relatively quickly and painlessly. But to do so, and indeed for more established finite group theorists to continue to function, it was necessary to learn the new mathematics in real time, and adapt to the changing field.

University of Wisconsin students traditionally have been active in political and social causes, and that was never more apparent than during the turbulent 1960s. During that time, students frequently led rallies and demonstrations, many of which protested U.S. involvement in the Vietnam War. Those activities succeeded in mobilising thousands in the name of social justice. The tensions and divisions on campus eventually devolved into violence, culminating with the bombing by four radicals of Sterling Hall, which housed the Army Math Research Center. On August 24, 1970, the explosion killed a graduate student, bringing the period of protest to a tragic end.

I walked around the university, and came to a place where the police were pushing the crowds back. I waited to see what was happening, and in a while they set off tear gas. People were running around the university, trying to escape from the tear gas. ... somebody set off a bomb in the Army Mathematics Research Center, I think next to the computer. People were killed by the bomb. I roomed with some astronomers, and one of the astronomers had his thesis on stellar interiors on this computer, and he lost his thesis.

The rather difficult proof of this theorem depends heavily on many of the recent major results in group theory. Some of the results used are the odd order and N-group theorems; the classifications of groups with abelian, dihedral, semi-dihedral or wreathed Sylow 2-subgroups; the classification of groups with strongly embedded subgroups and several others.

My husband is very succinct and logical while I use a much longer, less direct narrative structure. ... My husband is also excellent at calling out the talking heads on television who use language very loosely with ill-defined terms, imprecise language, and sloppy thinking.
...
For the month we lived in a Paris suburb when our daughter was $3\large\frac{1}{2}\normalsize$, she began to babble nonsense syllables with a French accent when playing with other children in the communal sandbox. Three years later when we were in Oxford for three months, she developed a temporary English accent.

Though Michael Aschbacher became interested in finite simple groups only as a post doc (having written his dissertation on combinatorics), his early contribution to the field took the community by surprise. Gorenstein described Aschbacher's entrance into the field as 'dramatic', and Solomon remarked that following Aschbacher's work in 1974 and 1975, 'belief mounted that nothing could stand between him and the completion of the Classification'. In recognition of his many accomplishments, Aschbacher won the prestigious Frank Nelson Cole Prize in Algebra in 1980. However, as Aschbacher's esteem within the community grew, his papers became notoriously difficult to comprehend. When Aschbacher's first important paper in the field appeared in print, Solomon was an instructor in the Department of Mathematics at the University of Chicago. Together with George Glauberman, he tried to read the proof, but found it incredibly difficult to follow Aschbacher's arguments. Specifically, Solomon complained that 'there were these clever counting arguments, but he never bothered to write them down'. Aschbacher's style made it notoriously difficult for other mathematicians to follow his proofs, and as his papers grew longer, the difficulties were exacerbated.

Group theorists no longer judged a proof as a self-contained document, but took into account its author, his previous work, and his standing within the community. When asked about the process of refereeing in the finite simple group community, Gorenstein characterised Aschbacher's papers as 'extremely difficult'. He recalled, 'Aschbacher is so smart .... Richard Lyons and I and Aschbacher had just written a joint paper .... I wrote a draft of this paper, Aschbacher rewrote it - I had enormous difficulty reading my own goddamn paper ... . He can see things so much better than anybody else.' He added, 'he's so quick that he misses things'. The impenetrability of Aschbacher's papers was taken as testimony of his mathematical prowess, rather than a challenge to the veracity of his proofs.

This is a delightful little book. For one thing, it contains no proofs whatever! It describes the bare bones of a programme for the classification of the finite simple groups.

This book is likely to become a standard text for graduate students beginning work in finite group theory. It will also be of interest to a wider audience interested in the foundations of the classification of finite simple groups, a great mathematical achievement completed several years earlier with many essential contributions by the author.

The goal of these talks is to give some insight into a program to, first, classify a large subclass of the class of simple 2-fusion systems, and then, second, to use the result on fusion systems to simplify the proof of the theorem classifying the finite simple groups. We will begin with an introduction to the theory of fusion systems, and then move on to an overview of the proof of the theorem classifying the finite simple groups of component type. We then discuss how to translate that proof into the category of 2-fusion systems, and the advantages that accrue from the change in category. Finally we describe how the result on fusion systems can be used to derive a corresponding theorem on simple groups.