Lars Hörmander: Unpublished Manuscripts from 1951 to 2007

The late Lars Hörmander (1931–2012) was a titan among analysts, who was described at one point as the world’s leading expert in partial differential equations. The book under review contains manuscripts of his that were never launched in the normal scheme of things, and thus gives testimony to not only his scholarship and its breadth and depth, but his disciplined character.

As his daughter points out in the book’s Foreword, in his last years Hörmander set himself the substantial undertaking of reviewing his mathematical life. This included the task of going through the entirety of his mathematical correspondence (kept in twenty-three binders) and his mathematical production.

He compiled a complete bibliography of all published materials … but also carefully went through all unpublished manuscripts, checking them with his very critical eye and deciding what should be kept for posterity and what should be thrown out. Every paper he felt should be kept was carefully retyped in AMS-TeX, unless already in that format, sometimes with added comments, and in at least two cases … translated into English.

She goes on to say, “He did all this with the University [of Lund’s] Library in mind — not intending a publication — but shortly before his death … suggested I seek advise from his colleagues and do as I please.” Hence the present book.

The over two dozen papers in this collection evince Hörmander’s masterful scholarship, as well as the remarkable scope of his interests. There is of course a wealth of what is generally called “hard” analysis (as opposed to “soft” analysis, I guess: certainly not as opposed to “easy” analysis since no such thing exists), but also a paper on neuron transport theory, a paper on electromagnetic wave propagation, and (perhaps most remarkably) a “Guide to the Mathematical Models in the Department of Mathematics in Lund.” His daughter provides a very poignant description of how much joy it gave Hörmander to carry out the latter project.

Hörmander’s Unpublished Manuscripts are now published, and they clearly should be.

Michael Berg is Professor of Mathematics at Loyola Marymount University in Los Angeles, CA.