#### by Sheila Newbery

Managing Editor, Celebratio Mathematica

This collection is a compilation and transcription of the extant holograph letters from Ingrid Daubechies to Yves Meyer.1 Our aim in offering it to the public is to make its contents easy to peruse in their entirety: readers will find here our typeset versions of the original French texts juxtaposed with their English translations. Yves Meyer provides an introduction to explain the mathematical significance of the letters and to flesh out the circumstances of their writing.

The collection came to light when I asked Yves (who was then Professor
Meyer to me) about a particular letter from Ingrid (dated March 12,
1987) which he mentioned in some remarks addressed to the editor of
the *American Scientist* (see “Letters to the editor” in
vol. 85, no. 3, 1997, pp. 204–206). There Yves described the role of
Stéphane Mallat’s prior work and that of his own in what Ingrid
accomplished in January–February 1987: the construction of smooth
orthogonal wavelets of compact support.

Taking a historical perspective, Daubechies’s construction belongs […] to Mallat’s program. Although this statement may be construed to mean that Daubechies merely treated a special example that arose from someone else’s great vision, that was never my opinion. I always knew that a large gap existed between the formalism that I developed with Mallat and what Daubechies achieved. When one tries to apply this formalism, many problems occur immediately. The first one concerns the stability of the construction, and the second one is related to the desired regularity. These difficulties require a subtle and difficult analysis, which was achieved by Ingrid and could not be discovered by ordinary human beings.

I kept a beautiful seven-page letter that Daubechies wrote to me at the time she was working on her construction, explaining how she discovered the bases. Mallat’s algorithm was not the starting point, but it did play a role as an ingredient.

Yves’ remarks piqued my curiosity. I wrote to him and asked if he
would consider letting us include Ingrid’s letter in our
*Celebratio* volume on her work, assuming we could get her
agreement as well. I feared he would say no.
Yet he wrote back promptly (and with characteristic generosity, as I
would soon learn) to say that he would look
for the letter in question, but that he was traveling and away from his office, and
could only do so on his return.

Yves did look, and that’s how this collection came to light, for there
was not only the *lettre sublime*, as he called it (eight
handwritten pages, in fact), but a folder full of handwritten
correspondence: letters and notes from Ingrid spanning the years
1985–2002, the decades of the momentous shift from
postal mail to email.

I’m grateful to Yves and Ingrid for their extraordinary generosity in letting us share these letters with our readers. Yves freely gave of his time to review the English translations and correct our typeset versions (French and English), even as he was fully engaged in new mathematical research and was trying to complete publishing projects of his own. Ingrid trusted Yves and me both to handle the personal and visionary content of these letters with care.

I want to thank Silvio Levy, Director of Publishing at MSP, who
translated the letters from the French, and whose rigorous attention
to detail was invaluable; Hélène Barcelo, Deputy Director of
the Mathematical Sciences Research Institute (MSRI), who helped secure
critical financial support for *Celebratio*’s Daubechies volume
as MSRI’s Acting Director in 2018–19; Georgia Benkart, whose
leadership as the Chair of the Committee on Women in Mathematics at
MSRI has helped make possible a series of *Celebratio* volumes of
women mathematicians, including this one; and Elizabeth Weaver, Senior Editor at
MSP, who catalogued the Daubechies letters in preparation for this project.