70 Normat 60:2, 70–81 (2012)
Pierre Lelong 1912—2011
Christer O. Kiselman
Uppsala University,
Department of Mathematics,
Box 480,
SE-75106 Uppsala
kiselman@math.uu.se
Pierre Lelong died in Paris on October 12, 2011. He was born on March 14, 1912,
also in Paris. His mother and father lived long lives too. Closest to him are his
wife France Lelong, four children with his first wife Jacqueline Lelong-Ferrand, and
grandchildren. His family was, as he once told me, by tradition atheists for several
generations. Like his mother, he fe lt profoundly Alsacian, but his father was a
true Parisian boy with ancestors from the Massif central (France Lelong, personal
communication 2012-11-06, 2012-11-07).
Among mathematicians Lelong was best known as a pioneer in the theory of
several complex variables and above all as the one who had introduced the pluri-
subharmonic functions and wrote extensively about them. But in French politics
he was well known and highly respected as Charles de Gaulle’s advisor during
two important years just at the beginning of the Fifth Republic. This was c lear
for instance when he came to Sweden to sit on the jury for Leif Abrahamsson’s
PhD Thesis presentation in 1982, and had his flight ticket paid by the French Min-
istry of Foreign Affairs. For this reason I was in contact with French diplomats in
Stockholm, who incredulously wondered how I could have such an important guest.
Lelong was elected a corresponding member of the French Academy of Sciences in
1980 and as a member in 1985. That was of course a most important recognition.
Howe ver, it came rather late in his life. He had several orders, among them La
L´egion d’honneur (Legion of Honor), where he re ce ived the degree of chevalier
(Knight) in 1959, officier (Officer) in 1967, and finally commandeur (Commander).
Lelong’s mathematics
From Lelong’s very large production during more than sixty years, 1937–1999, I can
mention just a small part. In MathSciNet he is the author of 108 articles, to which
one should add one from 1937 and one from 1938 which are not mentioned there;
if we add Related Publications there are a total of 129 hits. He has made several
important contributions to science. Among these I consider the most significant to
be the introduction of the class of plurisubharmonic functions (1942); the Lelong
number (1950); closed positive currents and integration on an analytic set (1957a,
1957b). But these are far from the only ones.
Normat 2/2012 Christer O. Kiselman 71
Plurisubhar monic functions
The class of functions which are now known as plurisubharmonic was introduced
by Kiyoshi Oka (1942) and Pierre Lelong (1942), who worked independently of
each other in Japan and France, respectively. As a matter of fact, Oka did his re-
search already in 1935 (Toshio Nishino, personal communication 1997-10-03) at the
University of Hiroshima, where he was Assistant Professor during the period 1932–
1938, while Lelong was Charg´e de conf´erences in Mechanics in Paris. As Lelong
once told me, the two never met.
Oka used the term fonctions pseudoconvexes ‘pseudoconvex functions’—they
prefer to live in pseudoconvex domains—while Lelong coined the term now in use,
fonctions plurisousharmoniques ‘plurisubharmonic functions’, to emphasize their
relation to subharmonic functions: they are subharmonic in many ways. And that
is clear from the definition: a function defined in an open set in the space of sev-
eral complex variables is defined to be plurisubharmonic if its restriction to every
complex line is subharmonic, and in addition it is upper semicontinuous (the latter
requirement is the same as for subharmonic functions).
If h is a holomorphic function, then log |h| is plurisubharmonic, and this is a
first important relation to the holomorphic functions. But the plurisubharmonic
functions are easier to manipulate: for instance, the maximum of two plurisub-
harmonic functions is in the same class—no similar conclusion is allowed for the
holomorphic functions. This property shows that these functions are, as Lelong
put it, souples ‘supple’ compared with the classical objects, which are rigid and
more difficult to do carpentry on. In an article (1994) Lelong describes these objets
souples and how they have been developed during the twentieth c entury. The pluri-
subharmonic functions are the archetype for these supple objects. They resemble
in some respects the convex functions; in others the subharmonic.
An important property is that the class is invariant under holomorphic coordi-
nate changes: this implies that the functions are subharmonic not only on complex
lines but on every holomorphic curve as well, and allows us to define the class also
on a complex manifold.
I have understood that the mathematicians around Nicolas Bourbaki were of the
opinion that Lelong’s class of functions was a rather uninteresting generalization
of the subharmonic functions of one complex variable. But they had to change
their opinion when it turned out that this class of functions played an important
role in the theory for the
¯
ˆ operator which Lars H¨ormander developed (1965), and
which in a natural way came to be used as weight functions in the Hilbert spaces
of functions and differential forms that Lars constructed in order to solve a number
of classical problems in several complex variables.
The Lelong number, or le nombre densit´e
The mathematical object which is most associated with Lelong’s name is certainly
the Lelong numbe r of a plurisubharmonic function at a point. It is a generalization
of the multiplicity of a zero to a holomorphic function and can be defined in several
ways: as a density or as the slope of a convex function.
The Laplacian f of a plurisubharmonic function f is a measure, and this
measure has a well-defined mass
s
B(c,r)
f in the open ball B(c, r)withcenter
72 Christer O. Kiselman Normat 2/2012
at c and radius r; it is an increasing function of r. In his paper (1950), Lelong
showe d that even if you divide this mass by the volume of the ball B(0,r) fl C
n≠1
of dimension 2n ≠ 2, the result is an increasing function of r , i.e., the quotient
s
B(c,r)
f/vol(B(0,r) fl C
n≠1
), which is the mean density of f in the ball, is an
increasing function of r. (Density is mass per unit volume, but you have to take
the volume in the correct dimension.) Hence the limit
‹
f
(c)=lim
ræ0
⁄
B(c,r)
f
vol(B(0,r) fl C
n≠1
)
exists. This number, thus the pointwise density at c, Lelong called le nombre densit´e
‘the density number’, while everybody else calls it the Lelong number of f at the
point c. Lelong himself most often avoided the term le nombre de Lelong, and wrote
usually le nombre densit´e; sometimes he said le nombre vous savez ‘the number you
know’.
In another definition one considers the supremum g(t) of f over the ball B(c, e
t
)
with radius r = e
t
. It then turns out that g is an increasing convex function of t,
and the limit lim
tæ≠Œ
g(t)/t therefore exists. This limit is equal to ‹
f
(c).
The Lelong number has been shown to be a very important entity in complex
analysis and has been generalized in several ways, for instance to closed positive
currents. An important connection to analytic sets is that the set where the Lelong
number of a plurisubharmonic function is at least equal to a certain constant is an
analytic set: this is Siu’s theorem, proved by Yum-Tong Siu (1974).
Integration on an analytic set
An analytic set is locally the common zero set of a family of holomorphic functions:
one can describe it as an analytic manifold with singularities. A fundamental prob-
lem was to integrate a differential form which is defined on such a set even over
the singular points .
Lelong solved this problem (1957a, 1957b): he took integration ove r the regular
points, considered this operation as a current in the sense of Georges de Rham
(1903–1990), and then extended it in a suitable manner over the whole analytic
set. He introduced closed positive currents and proved results on how to extend
them. These currents later became much studied objects in complex analysis; they
belong to the supple ob jec ts I already mentioned.
The indicator of an entire function
An entire function grows at infinity; to measure this growth, mathematicians have
for a long time used the concept of order and type. But these say nothing about
how the function behaves in different directions: they take account only of the worst
direction. For example, we know that the cosine function cos z =
1
2
(e
iz
+ e
≠iz
), z œ
C, can be estimated by | cos z| 6 e
|Im z|
: it grows fast in the imaginary directions but
is bounded in the real ones. The logarithm can be estimated by log | cos z| 6 |Im z|,
a convex function of z. In the estimate |Im z| 6 |z| the left-hand side but not the
right-hand side is sensitive for the choice of direction.
Normat 2/2012 Christer O. Kiselman 73
In several variables one has for instance the entire function h(z) = cos
z
2
1
+ z
2
2
,
z =(z
1
,z
2
) œ C
2
, which satsifies
log |h(z)| = log
-
-
-
-
cos
Ò
z
2
1
+ z
2
2
-
-
-
-
6
-
-
-
-
Im
Ò
z
2
1
+ z
2
2
-
-
-
-
= Ï(z),
where the right-hand side no longer is a convex function: we have for instance
Ï(i, ±1) = 0, while Ï(i, 0) = 1. We do have an estimate
-
-
-
-
Im
Ò
z
2
1
+ z
2
2
-
-
-
-
6
|z
1
|
2
+ |z
2
|
2
= ÎzÎ
2
,
where the left-hand side but not the right-hand side is sensitive for the direction
in which one goes out to infinity.
To describe the growth in different directions, one defines the indicator p
h
of an
entire function h of exponential type by
p
h
(z)=limsup
tæŒ
1
t
log |h(tz)|,zœ C
n
.
It is an important result that the smallest upper se micontinuous majorant p
ú
h
of p
h
is plurisubharmonic, whe re
p
ú
h
(z)=limsup
wæz
p
h
(w),zœ C
n
.
Furthermore it is clear that p
ú
h
is positively homogeneous: p
ú
h
(tz)=tp
ú
h
(z) for t>0,
z œ C
n
. The question is now whether every positively homogeneous plurisubhar-
monic function f is the indicator of some entire function, i.e., whether there exists
h such that p
ú
h
= f. Lelong (1966) proved that this is so under an additional
condition, viz. that f is complex homogeneous, f (tz)=|t|f(z), t œ C, z œ C
n
.
Urban Cegrell, Pierre Lelong, Bengt Josefson (1981 June 06). Photo: Christer Kiselman.
Andr´e Martineau (1966, 1967) and I (1967) solved the general problem when f is
only positively homogeneous. Martineau did it even more generally for functions of
finite order and finite type. Lelong wrote in his Notice (1973:17): “j’ai ´et´e devanc´e
simultan´ement par le su´edois C.-O. Kiselman et le regrett´e A. Martineau” ‘I was
overtaken simultaneously by the Swede C. O. Kiselman and by A. Martineau,
unfortunately deceased’.
74 Christer O. Kiselman Normat 2/2012
S´eminaire Lelong
For many years, Lelong led a series of seminars known as the S´eminaire Lelong.
The seminar talks were published. The first s even volumes were from the years
1957/58 through 1966/67 and were published by the Faculty of Sciences in Paris
under the title S´eminaire d’Analyse dirig´e par Pierre Lelong. After that they came
out in Springer’s series Lecture Notes in Mathematics, in a total of 15 volumes.
The first nine (with the numbers 71, 116, 205, 275, 332, 410, 474, 524, 578) had the
title S´eminaire Pierre Lelong (Analyse); the next three (694, 822, 919) were called
S´eminaire Pierre Lelong – Henri Skoda (Analyse), and the final three (1028, 1198,
1295) S´eminaire d’Analyse P. Lelong – P. Dolbeault – H. Skoda. The total was
22 volumes from the years 1957/58 through 1985–1986. Together these volumes
provide us with an impressive survey of the development of several branches of
complex analysis during thirty years.
Lelong’s seminars always started at 13:45, while all other Paris se minars after
lunch started at 13:30. Lelong claimed that one did not have time to have lunch
when one had to go to a seminar which started that early. For that very reason, he
gave himself—and all other participants—these extra, obviously very important,
15 minutes.
Meetings with Pierre Lelong
I have met Pierre Lelong many times during forty years, 1966–2005, mostly in
France and Sweden, but also in other countries, and will mention here only a few
of these occasions.
The first time I met him was in 1966, when we both participated in a four-week
conference in La Jolla, American Mathematical Society 1966 Summer Institute on
Entire Functions and Related Parts of Analysis, June 27 – July 22, 1966. His wife at
the time, Jacqueline Lelong-Ferrand (before marriage Jacqueline Ferrand) was also
there. They later divorced, and Pierre married France Fages (now France Lelong).
1
Both Jacqueline Ferrand and France Lelong are mathematicians.
The second time was in March 1968, when he invited me to talk at his seminar
in Paris. At the time I was a visiting professor at Nice, invited by Andr´e Martineau
(1930–1972). I gave my lecture on March 13, and talked later three more times at
Lelong’s seminar.
Pierre Lelong served as Faculty Opponent when Urban Cegrell presented his
PhD Thesis in Uppsala on May 23, 1975.
In May 1981, G´erard Cœur´e and Henri Skoda organized a big conference in
Wimereux in northern France on the occasion of Lelong’s retirement. This con-
ference attracted many outstanding scientists; among them Eric Bedford, Henri
Cartan, Klas Diederich, Se´an Dineen, Pierre Dolbeault, Hans Grauert, Joseph
J. Kohn, Paul Malliavin, Reinhold Meise, Leopoldo Nachbin, Bernard Shiffman,
Nessim Sibony, J´ozef Siciak, Yum-Tong Siu, Wilhelm Stoll, and Vasili˘ı Sergeeviˇc
Vladimirov. According to some participants, the food was not so good (I did not
1
When I many years later told him that I had divorced and now was with another woman,
Iwasmetwithamarkedapproval:itisOKtodivorceandremarryonce,mais pas plus que ¸ca
‘but not more than once’.
Normat 2/2012 Christer O. Kiselman 75
notice). Towards the end of the conference, Lelong, pulled Larry Gruman into a
corner and said: “Gruman, on aurait mieux fait d’organiser ce colloque chez vous”
‘Gruman, it would have been better to organize this conference at your place’
(Larry Gruman, personal communication 2011-10-30). This did not refer at all to
the organization of the meeting, nor to the mathematics; it was all about the food.
Larry lived at the time in the Department of Gers in southern France, the cuisine
of which Pierre Lelong appreciated during his many visits there.
2
Lelong received the degree of Doctor Honoris Causa at Uppsala University on
June 5, 1981. He was appointed to give the acceptance speech for all the seventeen
honorary do c tors at the banquet in Uppsala Castle. His speech was a brilliant show
of French rhetoric. He started off by complaining about the pain he had suffered
from puttin’ on the Ritz—a complaint, however, which was so well hidden behind
polite words that very few of his hosts or fellow dinner guests understood it as a
complaint. Then there came a flood of high-strung praise for science in general and
mathematics in particular:
Puis-je dire que pour moi elle est la plus profond´ement humaine des sciences, la plus
universelle aussi et qu’elle est aussi celle o`u les d´esirs de l’imagination, et parfois
mˆeme sa fantaisie, trouvent le mieux `a s’accomplir, pr´ecis´ement fortifi´ees par la
pr´esence des r`egles de la logique ? ‘Am I allowed to say that it [mathematics] for
me is the most profoundly human of the sciences, and the most universal as well,
and that it is also the one where the wishes of our imagination, sometimes even
its fantasies, can be best realized, reinforced by the presence of the rules of logic?’
(Pierre Lelong, June 5, 1981)
But he then aired criticism against Sweden’s research policy:
Puis-je dire, Monsieur le Recteur, que cette e xcellence des recherches et cette place
que tiens votre pays dans le domaine des math´ematiques ne vous emp`echent pas
d’ˆetre bien s´ev`eres : on m’assure que vous maintenez longtemps dans l’attente d’un
poste de professeur de jeunes docteurs dont l’´etranger a reconnu le m´erite [?] ‘Am I
allowed to say, Mr President, that this excellence in research and the position that
your country occupies in the domain of mathematics do not prevent you from being
quite severe: I am being assured that you keep waiting for a long time for a pro-
fessorship young doctors w ho have been recognized in other countries as worthy[?].’
(Pierre Lelong, June 5, 1981)
The following day, we went on a boat excursion in the Swedish archip e lago, starting
at Spillersboda: Urban had a big boat, a renovated fishing boat from the northern
coast of the province of Uppland, and took Pierre Lelong, Dan Shea, Bengt Josefson
and me on a tour. We visited the National Park of
¨
Angs¨o, one of the well-preserved
islands not far from Uppsala and Stockholm.
As already mentioned, Lelong was a member of the jury for Leif Abrahams-
son when Leif presented his PhD Thesis on November 13, 1982. During the week
Novembe r 7–14, he combined this with a tour of Sweden: a visit to Lund (Lars
2
Gers is situated in the historical region Armagnac, which is part of the historical province and
duchy Gascogne. Goose liver (foie gras)andarmagnacareimportantproducts.OnGersLe petit
Larousse (1967) writes: “Le Gers est un d´epartement essentiellement agricole, o`u la population,
dispers´ee en hameaux et en fermes, pratique une polyculture complexe [. . . ]” ‘Gers is essentially
adepartmentforagriculture,wherethepopulation,whichisspreadoutinhamletsandfarms,
practice a complex polyculture [. . . ]’. Lelong’s life testifies to the fact that there is but a small
step from polyculture complexe to analyse pluricomplexe.
76 Christer O. Kiselman Normat 2/2012
G˚arding and Lars H¨ormander), Uppsala (Urban Cegrell, Christer Kiselman), Stock-
holm (Lars Inge Hedberg), Link¨oping (Bengt Josefson), and back to Uppsala again
for Leif’s PhD defense. All was paid for by the Ministry of Foreign Affaires of
France.
Christer Kiselman, Astrid Kiselman,
Bo Berndtsson, Pierre Lelong, Ola
Kiselman (1982 November 14). Photo:
Larry Gruman.
Christer Kiselman and Pierre Lelong in
Toulouse, May 2002.
In 1986, Lelong paid a visit to Sweden within the framework of an exchange program
betwe en the French and Swedish Academies of Science. He visited Ume˚a University,
Uppsala University and the Academy of Sciences in Stockholm during the week
October 2–9, 1986.
Lawrence Gruman (better known as Larry) worked with Lelong, and they wrote
a book (Lelong & Gruman 1986) on entire functions. It contains a lot about the
growth at infinity of these functions, functions of regular growth, solutions to the
equation iˆ
¯
ˆU = ◊, relations between the growth of a function and the growth of
the area of its zero set, etc.
The person who last worked with Lelong is Alexander Rashkovskii, now in
Stavanger. They published a joint paper in 1999, Alexander translated a text by
Lelong into English, and they discussed a lot.
On the occasion of Larry’s retirement, Paul Sabatier University in Toulouse
organized a conference in May 2002, where Lelong appeared in high spirits and
gave a mathematical lecture.
At a conference in Paris for Henri Skoda in September 2005, Lelong gave a long
speech for Henri at a reception on September 15, but no mathematical lecture.
The first day of the conference, September 12, he was present during the morning
session. I talked with him during the lunch, and accompanied him to his car, an
ostensibly damaged C itro¨en BX. He drove home alone in the Paris traffic, 93 years
old.
Normat 2/2012 Christer O. Kiselman 77
Pierre Lelong steps into his Citro¨en BX. Paris, September 2005. (The extensive
damage is on the right-hand side and therefore not visible.) Photo: Christer Kisel-
man.
Charles de Gaulle
General Charles de Gaulle (1890–1970) was installed as President of the Fifth Re-
public on January 8, 1959. The same day he appointed Pierre Lelong as Conseiller
technique au Secr´etariat g´en´eral de la Pr´esidence de la R´epublique ‘Technical Coun-
selor at the General Secre tatiat of the President of the Republic’. Lelong’s responsi-
bility was Recherche scientifique,
´
Education nationale et Sant´e publique ‘Scientific
Research, Public Education [at all levels, not only higher education], and Public
Health’, thus encompassing several ministries. Lelong had this function during two
years, up to January 8, 1961. He could then obtain that a biologist, R. Camus, a
professor at the University of Paris, took over the post as counselor. (It seems it
was not at all obvious that he could get a successor at that post.) When Camus
left in 1964, the post was suppressed, which meant that the s cience s no longer had
direct access to the General. (Lelong 1977:212.)
Lelong gives an insight into the working habits of the General, who left a lot of
initiative to his Technical Counselor during the two years of the latter’s tenure.
From time to time, a note from the Counselor sufficed to start a government
action—provided (of course!) that the note was short and well written. When the
note was approved and annotated in de Gaulle’s handwriting, it went to the General
Secretariat and from there to the relevant ministry with the understanding that a
“proposal” from the ministry along these lines would be welcomed by the president.
A strange procedure, writes Lelong, no doubt conditioned by the technical context,
but even more so by the General’s personality. (Lelong 1977:209–210.) An example
78 Christer O. Kiselman Normat 2/2012
is the Direction des recherches et des moyens d’essai (D.R.M.E.), created at the
end of 1960 and approved by the General following a report from the Scientific
Counselor, viz. Lelong, (1977:198).
The last years of the Fourth Republic, before de Gaulle and the Fifth Republic,
were characterized by weak, s hort-lived governments. A lot of public affairs got
stuck for years for lack of forceful national leadership.
When de Gaulle came to power many matters started to move and a series of
important decisions could be made. Lelong found himself in the middle of these,
actually already during the Fall of 1958 before de Gaulle had become president and
he himself had been formally appointed: The Constitution of the Fifth Republic
came into effect on October 4, 1958, following a referendum on September 28. An
ordinance of November 28, 1958, established a new structure for the government’s
handling of research (Lelong 1977:186). In a statement which I find typical, Lelong
mentions that it is easy to create a research institution but difficult to put an end
to it (1977:197).
In addition to the Comit´e consultatif mentioned below , de Gaulle created the
D´el´egation `a la recherche scientifique et technique (D.R.S.T.) attached to the office
of the Prime Minister (Le long 1979:180).
In his contribution to a book on de Gaulle’s collaborators, he describes how
de Gaulle paid a lot of attention to high-tech industries in four domains: nuclear
energy; civil aviation; space research; and computers and IT (Lelong 1979:179).
La Halle aux vins
One of the affairs that had got stuck during the Fourth Republic was the problem
around La Halle aux vins, a block devoted to the selling of wine since 1665, most
centrally located in the Fifth Arrondissement in Paris. The Paris University wished
to come to this district, but the wine merchants had blocked this aspiration for
many years.
With de Gaulle there came a solution, and the university could take over almost
the whole block. For a long time it was called “la Facult´e des Sciences de la Halle
aux vins.” Nowadays Paris VI and Paris VII are there, as well as the Institut du
monde arabe. I believe that Lelong played an important role for the decision to
liberate the block for education and research.
Advice to the president
One evening Lelong was correc ting students’ exams at his home when he received a
phone call from the
´
Elys´ee Palace. He drove there. The General explained the prob-
lem, which was about the Catholic schools: should they receive financial support
from the state?
For a long time, the French Republic has been secular: The state shall not be in-
volved in or support any religion. The la¨ıcit´e is inscribed in the French constitution
of 1958 as well as in a law of 1905.
Lelong thought about the problem—it could not have been for a long time, for de
Gaulle wanted an immediate answer. Lelong replied that he was of the opinion that
the private Catholic schools should receive support from the state. The General:
“Je suis de votre avis.” ‘I share your opinion.’ The me eting was over. The question
was res olved. Lelong drove home and continued to correct the students’ papers.
Normat 2/2012 Christer O. Kiselman 79
Planning of research
In a long article, Lelong (1964) describes his views on the evolution of science and
the planning of research. It is remarkable for its sheer length (62 pages) and the
fact that it appeared in a journal devoted to economics, but above all for the broad
and at the same time very detailed picture the author presents on the possibilities
for a state (France) to initiate, coordinate, plan, and steer scientific and technical
research, as well as the obstacles for this activity.
Pierre Lelong was during the four years December 1960 through December 1964
a member of the Comit´e consultatif de la Recherche scientifique et technique,which
had twelve members, and he was its chairman during two years, December 1961
through December 1963 (Lelong Notice 1973:4; cf.
ÈÈ
L’Entourage
ÍÍ
et de Gaulle
1979:370). The article (1964), written when he still chaired the committee, is clearly
an attempt to influence the authors behind the upcoming Fifth Plan based on the
experience he had had concerning the Fourth Plan (1961–1965) and its shortcom-
ings (e.g., 1964:48). In the paper several pages (1964:10–16) are devoted to a de-
scription of the financing of research in the United States, which is presented as a
model for French research policy.
The article is obviously not written for s cientists; it is aimed at politicians. He
mentions even twice the basic conditions for research, well known to scientists but
perhaps not to politicians: le m´ecanisme de l’invention est complexe, peu explor´e
et, n e l’oublions pas, il n’existe pas de recherche v´eritable sans chercheurs ni al´eas
inh´erents `a la recherche ‘the mechanism of invention is complex, little explored,
and, let us not forget it, there is no real research without researchers and the
hazards inherent in research’ (1964:2); and again: On ne fait pas de recherche sans
chercheur qualifi´e ‘One cannot do research without a qualified researcher’ (1964:27).
He admits that it is probably not possible to plan scientific activity (1964:4). He
describes eloquently the obstacles to an orderly development, Nombre de freins ‘A
number of brakes’, that are of several different kinds (1964:37–40).
This long article, which curiously is not mentioned in the bibliography in Lelong’s
Notice (1973), is indeed remarkable for its political and philosophical contents. It
also provides an explanation of the fact that its author could reach positions of
great political importance, e.g., as a technical counselor to the first President of
the Fifth Republic.
Georges Pompidou
Also after he had left the function as Counselor to de Gaulle, Lelong had many
commissions from the highest offices of the French Republic. Georges Pompidou
(1911–1974) was Prime Minister during the years 1962–1968, and President of the
Republic during 1969–1974. After the period of counselor to de Gaulle, Lelong was
charged with preparing the budget for all research in France for Pompidou when
the latter was Prime Minister (1993:2). He writes:
Je puis dire aujourd’hui que le pro jet spatial fut par mes soins retard´e d’un an
pour faire passer le projet de la biologie mol´eculaire. ‘I can say today that space
research was delayed by one year because of my actions, to allow molecular biology
to advance.’ (Lelong 1993:2)
80 Christer O. Kiselman Normat 2/2012
Lelong and Pompidou said tu to each other. Pompidou was less than one year older
than Lelong and entered the
´
Ecole normale sup´erieure in 1931, the s ame year as
Lelong. They were school mates and therefore used the informal way of addressing
each other for the re st of their lives.
3
To make this clear to me, Lelong, when he
recounted something Pompidou had s aid, never used indirect quotes (And then
Pompidou said to me that I should do this or that) but always direct quotes: And
then Pompidou said to me: “Tu dois faire ceci et cela.”
Also in writing, Lelong used direct quotes to make the intimacy of their relation
evident. He quotes Pompidou like this:
ÈÈ
Penses-tu qu’il faut vraiment faire l’Espace ?
ÍÍ
me disait-il alors qu’il ´etait Premier
Ministre. ‘ “Do you think that we really have to do Space?” [That is, to accept a
large space research program] he said to m e when he was Prime Minister.’ (Lelong
1993:2)
So the resistance against space research was perhaps there with Pompodou already
before Lelong presented the budget.
Words of wisdom
Without having been asked, Pierre Lelong gave me and others advice on how to view
one’s retirement: one should pretend that nothing has happened and go on doing
research just as usual. And actually, more than a quarter of Lelong’s mathematical
papers were published after he had reached the age of 69.
The other word of wisdom that comes to my mind is this: The highest honor a
mathematician can get in this world is that his or her results become so well known
and generally accepted that everybody thinks that they are completely self-evident
and trivial. And this is probably so: you cannot understand mathematics, you can
only get used to it, and what you are used to, you consider as self-evident. Your
brain has been re-programmed.
In writing he comes close to this idea in a speech in Wimereux in May 1981:
En math´ematiques l’indispensable processus d’assimilation est un processus de tri-
vialisation. ‘In mathematics the unavoidable pro ces s of assimilation is one of triv-
ialization.’ (Lelong 1982:191)
The plurisubharmonic functions are perhaps just such a self-evident structure.
3
It is perhaps unnecessary to add that something similar cannot be imagined concernin g de
Gaulle, who was reported to say vous to his own wife, Yvonne.
Normat 2/2012 Christer O. Kiselman 81
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