Letter-writing has always been an important part of mathematical research. Experts write to each other to discuss ideas and thoughts, explore questions, and attempt proofs. Singularités Irrégulières preserves just such a correspondence from the years 1976–1991. The topic is irregular singularities of linear differential equations and the links between that subject and others, notably algebraic geometry and Hodge theory.
In addition to the letters themselves, the volume includes several other goodies. By way of introduction, we get two pages from Deligne on why he was interested in irregular singularities, "quelques souvenirs" from Malgrange, and four pages from Ramis on why the path from Gevrey estimations to Galois theories is a natural one. After the correspondence, four unpublished texts are included as well.
For historians of recent mathematics, this is primary source material. It should be available in libraries for that reason alone. For mathematicians interested in this circle of ideas, this is a treasure-trove, a chance to see how the great ones think, an entry into the charmed circle of those among whom copies of these letters and texts originally circulated.
This is the fifth volume in the series Documents Mathématiques, in which the Société Mathématique de France has set out to preserve important documents from the recent history of mathematics. Other books in the series include an edition of the correspondence between A. Grothendieck and J.-P. Serre and volumes one and two of the notes from Grothendieck's Séminaire de Géométrie Algébrique. The DM series is a perfect example of what professional societies do so well, preserving materials of great historical and mathematical importance. We owe SMF a debt of gratitude.
Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College.