José Adem grew up in a family where harmony, love and tranquillity always reigned. Since he was a child he started fishing with a great interest that only increased with the years.

In 1944 I joined as a part-time connection the Instituto de Mathematicas at the National University of Mexico. This continued until 1966. At the Instituto I was as free as under my Princeton professorship. I conducted seminars in topology and differential equations, gave a couple of times a "volunteer" course on "general mathematical concepts" directed at beginners and, thanks to a good working library, was able to continue research. Conditions were of course quite different from ours, but as I became rapidly fluent in Spanish, it gave me many advantages. Through the years I found quite a number of capable young men, several of whom I directed to Princeton for further advanced training up to the doctorate and later. Among them I may mention Dr José Adem, Chairman of the Department of Mathematics of the newly founded Centro de Estudios Avanzados in Mexico City. My long connection with Mexico has been the occasion of many side trips (especially in connection with meetings of the Mexican Mathematical Society), so that I have a fair acquaintance with that wonderful country.

Although I began my professional studies at the National School of Engineers, it was in the professorships of maestro Alfonso Nápoles Gándara where I discovered my true vocation. In this way, when I finished my studies at the Faculty of Sciences in 1945, I attended the graduate courses and seminars offered at that time as they had been for several years. I remember the great influence that Roberto Vázquez's courses, the Topology seminar organised by Vázquez and Recillas, Enrique Valle's modern Algebra seminar, and Francisco Zubieta's Mathematical Logic seminar had on my formation.

During the visit that Lefschetz made to the Institute in the summer of 1949, I told him of my desire to go abroad for my doctorate. Days after his return to the United States, I received an offer from Princeton University, which I immediately accepted. In September of that same year, upon my arrival at Princeton, I began my research in algebraic topology under the direction of N E Steenrod. The preparation that I received in Mexico was satisfactory.

The author treats the problem of a semi-infinite anisotropic plate whose axes of symmetry coincide with the Cartesian axes, and which is subjected to a normal concentrated force at the origin. The solution is obtained by elementary methods ...

By the year 1950, the development of mathematics had extended beyond the classical formal areas and was growing rapidly in the interactions between geometry, algebra and analysis. In particular, algebraic methods were introduced to study topological situations. This principle, developed under the tutelage of Lefschetz, among others, represented an exceptional advance for mathematics. Among the most successful exponents of this new philosophy was Norman Steenrod, under whose direction Adem was fortunate to complete his doctoral thesis.

In this work it is proved that the Steenrod squares on cohomology classes satisfy certain identities. These identities are applied to solve particular homotopy problems. Full details will appear elsewhere.

The research summarised in the present note has been supported at various times by the following institutions: Instituto de Matematicas de la Universidad Nacional and Instituto Nacional de la Investigacion Cientifica, Mexico City, the Higgins Foundation, Princeton University and the Rockefeller and Guggenheim Foundations.

In this note we present the generalisation of the relations on iterated squares to the case of iterated cyclic reduced powers of arbitrary prime period p. As in the case p = 2, the new relations are used to solve some particular problems.

I have heard that H Cartan has obtained relations of the same type, using methods quite different from mine.

He had a great sense of humour, a noble soul that, together with his privileged intelligence and his enormous desire for knowledge, made him soon establish friendship with a large number of mathematicians from various countries of the world with whom he maintained correspondence throughout his life.

The author gives detailed proofs of the relations between iterated Steenrod operations which he had previously announced in ['The iteration of the Steenrod squares in algebraic topology' (1952), 'Relations on iterated reduced powers' (1953)]. In the meantime, the proof by H Cartan appeared [(1955)] which uses a completely different method. Adem adopts the point of view of Steenrod ...
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The calculations [by Adem] are delicate, and carried out with great care; in general, the exposition of this difficult subject is made with great clarity and precision. ... Topological applications of the theory are promised for future work.

With his great mathematical prestige and his hard editorial work, he managed to make it a journal of recognised international prestige, where many articles by mathematicians from various countries around the world have been published, including of course Mexican mathematicians. He kept it at that level until his death.

The paper describes secondary cohomology operations associated with the relations between iterated Steenrod squares which the author proved in an earlier paper ['Algebraic geometry and topology, A symposium in honor of S Lefschetz, 1957']; essentially the same method is used here, of which an outline is given (with less details than in the former paper) in the first part of this paper.

He discovered universal formulas, the "Adem Relations", in which the algebraic nature associated with each geometric object is established. In the field of algebraic topology he worked on the iteration of Steenrod's squares in their relation and application to geometry. He is the author of 'Algebraic Geometry and Topology' (1957), 'Lecture Notes in Mathematics' (1970), among other works. He co-founded the Department of Mathematics at Cinvestav. He was awarded the National Prize for Sciences and Arts 1967. He entered El Colegio Nacional on 14 June 1960.

I arrive today with a deep emotion to this welcoming House. My election as a Member of the National College has been the most pleasant and profound of surprises. Surprise not only for me, but also for my mathematical colleagues, with whom I have been so actively and fruitfully linked in recent years. The nature of our work apparently closes to us some doors more accessible to other specialists, but this does not mean that there is not a decided interest among us in everything related to culture in general and to the development of our country. The great honour that is now being given to me, I take as both an award and an incentive to a team of scientific workers of which I am a part.

I remember that before I returned to Mexico, Norman Steenrod, also my thesis advisor, told me that I was very lucky to go to work with José Adem, because I would learn from him how to do mathematics and how to write it. A fundamental part of mathematical research is how to write the results already obtained, because when you do, you find generalisations and many, many times, better results. Each article José Adem wrote went through many drafts, always searching for the best expression. I had the opportunity to collaborate in several of them and I learned a lot from this experience. His articles are a model of how to write mathematics; express the results in a precise way and in the demonstrations look for clarity and elegance.

He was an excellent teacher in the classroom. He had a special talent for explaining very complicated topics in a very understandable way, always with relevant examples that made understanding a concept much easier.
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José Adem had a photographic memory and great intelligence. He was a man of science who tried to understand the results in other areas of knowledge. His engineering training enabled him to understand many problems in physics. He had great pleasure in painting and literature. Conversing with him on any subject was always one of my most happy pleasures. I always came out richer.
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José Adem leaves us a scientific tradition and goals to achieve; do top-notch research in Mexico and publish it. Only by having first class science can we aspire to raise the levels of education to a higher level and thus be able to face the challenge that is presented to us to improve our quality as human beings and as Mexicans.