I still remember with pleasure our hours of mathematics in school, and am so grateful to you for interesting me in mathematics.

Gerhard must have felt at home among these free thinkers, people of all races and political persuasions, meeting in defiance of the rigid social conventions of Cape Town.

I plan to specialise in tensor calculations and in the basis of modern relativity theory and 'geometrised mechanics' and then pure mathematics, differential geometry and certain parts of the theory of differential equations. I think the ideal middle ground for me is pure and applied mathematics in which I am equally interested.

Later in his life, Gerhard spoke of the great debt he owed Stanley Skewes, a lecturer (and later professor) in the mathematics department at Cape Town, who taught him in his undergraduate years and subsequently became his primary advisor and supporter. Skewes recommended him for a position as a junior lecturer in pure mathematics, which enabled him to continue his studies from 1937 to 1938, and encouraged him to apply to the mathematics department at Princeton for further graduate work. When Gerhard sailed for America in the summer of 1938, Skewes saw him off. Gerhard remembered Skewes standing at the pier, calling out his final words of advice: "Never doubt your own abilities."

The thesis deals with certain important problems in Lie algebras and related questions in associative algebras. It contains in particular a highly interesting characterisation of semisimple Lie algebras in terms of the operation of formal derivation. The thesis is highly worthy of publication as it contains many new results in addition to those indicated above. Furthermore, Hochschild set the problem himself and also did the research in an essentially independent way.

Roughly speaking, a derivation of an algebra is the infinitesimal operation corresponding to an automorphism. This notion plays an important part in the study of the structure of Lie algebras and associative algebras, and its structural significance will be understood best by first recalling the connections between derivations and automorphisms in general.

I have found it necessary to include proofs of a number of known results on representations of semi-simple Lie algebras, some of which (like the proofs of Whitehead's lemmas) cannot be found in the literature. For these proofs, which served me as a guide in the present investigation, I am indebted to Professor C Chevalley of Princeton University.

Memories dating back to 1942 are of spending hundreds of days calculating military firing tables with the help of a Friden desk calculator.

One cannot write about Gerhard comprehensively without mentioning his charisma. Some of his charisma resulted from his colourful criticism of the hypocrisies that abound in all large organisations. In the army, even though he was a recent immigrant to the United States, he impressed his fellow soldiers with the virtuosity of his profanity. I learned this from the famous geometric measure theory mathematician Herbert Federer, who served in Gerhard's unit at Aberdeen Proving Ground.

I was in Berkeley and participated in a Festschrift for Gerhard on the occasion of his sixty-fifth birthday. As it happened, that was exactly the time he was made a member of the National Academy of Sciences. He asked me "Is there any way to get out of this?" and I responded, "the only way is to die."

Citation for the Steele Prize for Work of Fundamental or Lasting Importance:

The Steele Prize for fundamental work is awarded to Gerhard P Hochschild of the University of California, Berkeley, for his significant work in homological algebra and its applications as exemplified by five papers:

Hochschild is one of the originators of homological algebra. The first two papers cited are the beginning of the cohomology of associative algebras where the so-called Hochschild cohomology, now ubiquitous in the theory of algebras, was introduced. The third and fourth papers mentioned are fundamental contributions to other areas of homological algebra, namely the cohomology of groups and Lie algebras. They construct what are now known throughout the literature as the Hochschild-Serre spectral sequences. The fifth paper is the first place where class field theory is given a homological treatment. This point of view now dominates that subject and has led to generalisations impossible with the older points of view. The Cole Prize winning work of John Tate is based in part on the contributions found in the last cited paper.

Taken all in all, these papers form a consistent and deep application of homological methods to wide and interesting areas of algebra and number theory. They are in no small part responsible for the lasting influence of homology and cohomology on algebraic questions.

While deeply honoured by the Society's consideration of his work for a prize, Professor Hochschild reported that for personal reasons he is unable to accept the Steele award. Nevertheless the selection committee has reaffirmed its view that Hochschild's work cited above fully merits the Steele Prize.

Note. A friend has commented that the reason was simply that Gerhard did not believe in prizes.

It is remarkable to what extent the author succeeds in providing a self-contained text for a reader familiar with the fundamentals of multilinear algebra, group theory, point-set topology, and calculus.

Hochschild frequently played the role of advisor of many junior members of the department, especially but not limited, to those in his areas of main interest. Even though he played a crucial academic role all along his tenure, he deeply disliked the bureaucratic organisation of academic institutions - for example he championed systematically and unsuccessfully, for the separation of sports and academics - and for that reason he never accepted to take responsibilities in the administrative tasks of the University.

He served for a short time in a committee to select the new Instructors at Berkeley and the administration gave him guidance as to consider Affirmative Action policies. As soon as he received the information he told the Dean that he was unable to stay in the committee as he had personally seen the Nazis making a difference between "Jewish" and "Aryan" mathematics. He did not accept the Dean's arguments about the difference between "negative" racism as in the Nazi era and the policy they were implementing of "positive" racism. In a conversation with the author of this note, he mentioned that what was considered positive today, could easily become negative tomorrow and that the only safe attitude was to be blind to racial distinctions to the point of never registering any information about the issue, specially in official documents. He resigned from the committee.

Gerhard had certain fixed standards that nothing could change. For example, in the many visits that I made to his photography lab, he showed me pictures of landscapes principally consisting of interestingly shaped stones coloured grey. Never once did he show me a picture that included a person or that included colour. He took many such pictures that I thought were repetitious, but to him they represented an effort to capture perfection. Anything short of that was a compromise that would disappoint him.

After his retirement, Gerhard engaged heavily in photography, taking beautiful images during his many trips to the deserts and forests in Canada, Arizona, New Mexico, and elsewhere. He also got involved in computer-generated images. Among these were fractals.

Gerhard Hochschild, professor emeritus of mathematics, died peacefully at home after a long and satisfying life on 8 July 2010, at the age of 95. His daughter Ann was at his bedside. He is survived by his daughter Ann, his son Peter, and two grandchildren. His beloved wife Ruth predeceased him on 2 June 2005.