x TRANSLATOR’S PREFACE
Does he make the English elegant and accessible? Or does he convey to the reader
the flavor of the original? I have resolved this problem on a case-by-case basis,
hoping that the result reads smoothly without distorting the spirit of the original.
In this work, I have received invaluable help from an initial translation prepared
by Hari Bercovici, of Indiana University. While most of his work has been altered
and ﬁne-tuned, the core of it remains, and Bercovici made signiﬁcant contributions
to the resolution of a number of diﬃcult problems of translation. In addition, the
illustrations—faithful copies of Hadamard’s own—are almost entirely the work of
Bercovici. I am grateful for this opportunity to thank him for generously allowing
me access to his work. In return, I take on myself the responsibility for any errors
that may have crept in, and that the patient reader will doubtless ﬁnd.
Others to whom I am grateful for help in this work include Wing Suet Li,
Florence Fasanelli, Al Cuoco, Larry Zimmerman, and Sergei Gelfand. My wife,
Carol Saul, a great supporter of everything I do, has been immeasurably tolerant
of my preoccupation with this work.
This translation was supported by grant number NSF ESI 0242476-03 from the
National Science Foundation.
Hadamard’s career as a high school teacher does not seem to have ended suc-
cessfully. He did not stay long in the profession, and there exist notes by his
superiors testifying to his diﬃculties in getting along with his
he seems to have learned from his experiences how to approach them intellectually,
thus allowing other teachers, with other skills, the beneﬁt of his own genius.
It is in this spirit of combining the skills of the teacher and the mathematician
that I oﬀer these materials to the ﬁeld.
Mark Saul May 2008
mentoring of Maurice Fr´ echet, which started in the latter’s high school years,
is a notable exception to this circumstance.