I absorbed little family cultural influence during my childhood, apart from my father's orthodox Judaism, and the heated family discussions of national and world politics.

... came home on leave speaking excitedly to me and my younger brother Isaac about the science courses he was taking. It was these conversations that first awakened my awareness of and interest in science.

This was a rigorous course in analysis, with everything proved. More than that, Artin's lectures, which were like pieces of theatre, made you understand the crux of a proof, the moments where some essential new idea or invention makes its appearance. ... I had no reason to believe that this course was substantially different from any other college calculus course. I later learned otherwise, not only because of its remarkable teaching staff, but also for the students then enrolled. Our class included several students who later became prominent mathematicians ...

Kaplansky gave an inspiring series of courses on homological methods in commutative algebra. Faithful to his expository style, Kaplansky aimed not to lead us deeply into the whole forest, but rather to show us a few magnificent trees. He would target a few central theorems, and then track a logical geodesic to them, using the greatest economy of means, eschewing any avoidable extrinsic machinery. These lectures, attended by both students and young faculty, initiated a generation of Chicago students, myself included, into this new and blossoming field.

Since great teachers had been much of my mathematical inspiration, I looked forward to teaching, so it was not a hard sell.

... there was no one directly engaged with the kind of mathematics I had been thinking about. So I tried to learn what others were doing, attending many of the graduate courses: number theory and algebraic geometry from Lang, Lie groups and class field theory from Harish-Chandra, differential algebra from Kolchin, category theory from Eilenberg, and fiber bundles from Albrecht Dold.

Serre has established the rudiments of a dictionary for translating the language of projective modules into that of vector bundles. With this point of departure we have attempted to adapt some of the results and methods of homotopy theory to certain purely arithmetic and even noncommutative settings. Detailed proofs of our results will appear elsewhere.

Algebraic K-theory flows from two sources. The (J H C) Whitehead torsion, introduced in order to study the topological notion of simple homotopy type, leads to the groups $K_{1}$. The Grothendieck group of projective modules over a ring leads to $K_{0}$. The latter notion was applied by Atiyah and Hirzebruch in order to construct a new cohomology theory which has been enormously fruitful in topology. The observation that these two ideas could be unified in a beautiful and powerful theory with widespread applications in algebra is due to the author, who is also responsible for a major portion of those applications. The author of this book is thus uniquely qualified to produce a fundamental document in this new and expanding field; he has also produced an admirable exposition of its methods and results.

These informal reminiscences, presented at the ICTP 2002 Conference on algebraic K-theory, recount the trajectory in the author's early research, from work on the Serre conjecture (on projective modules over polynomial algebras), via ideas from algebraic geometry and topology, to the ideas and constructions that eventually contributed to the founding of algebraic K-theory. The solution of the congruence subgroup problem is presented as a pivotal event.

Mathematicians tend to think of educational matters almost exclusively in terms of content; what material should be taught. They thus approach teachers and educators in the guise of experts with the answers in hand, ready to contribute their authorative advice. They often convey disdain (even if unintended) to the teachers and educators with whom they speak, and inspire defensiveness and resentment in return. One result of this history is that the important conversations that now need to take place between mathematicians and educators are burdened with suspicion and cultural prejudices.

There are two perennial issues. One has to do with resources to support the research enterprise. That is a constant campaign with federal and public agencies. And the other is whether we are drawing enough talent into the field to maintain quality and productivity.