Preface
IX
began addressing rigour of proof and generality of formulations, rather than
formulae.
This does not mean that numerical calculations have become pointless:
thanks to computers, one can do more and more of them, for better or worse,
in all scientific and technical areas that, from medical imaging to the perfecting of nuclear weapons 5 , use mathematics. One does the same in certain
branches of mathematics too; for example, displaying a large number of curves
may open the way to a general theorem or to understanding a topological
situation, not to speak of the traditional number theory where numerical
experiment always was, and still is, used to formulate or verify conjectures.
This only means that the aim of an exposition of the principles of analysis is not to teach numerical techniques. Moreover, the partisans of applied
mathematics, of numerical analysis and of computer science in all the universities of the world manifest their imperialist tendencies far too clearly for
real mathematicians to take on in their stead a task for which they generally
lack both taste and competence.
* * *
The innocent reader and many confirmed mathematicians will probably be
surprised, possibly even shocked, to find in my book some very heavy allusions to extramathematical subjects and particularly to the relations between
science and weaponry. This is neither politically nor scientifically correct: Science is politically neutral 6 , even when someone lets it fall inadvertently on
Hiroshima while the future winner of a Nobel Prize in physics is recording the
results in a B-29 trailing the Enola Gay 7 . Nor is it part of the curriculum: a
5 Nuclear powers agreed a dozen years ago to stop testing. The reason why was
that testing was made unnecessary by the improvement of numerical analysis.
The most immediate consequence of this "progress" is that everything is now
done in full secrecy, which was not the case when they had to propel into the
stratosphere two million tons of radioactive rock and sand in order to check their
"gadgets".
6 An assertion long since demolished by countless studies, notably American, either of particular facets of scientific activity, or of Science in a general way,
e.g. in Bernard Barber, Science and the Social Order (Collier Books, 1952) and
Jean-Jacques Salomon, Science et Politique (Paris, Ed. du Seuil, 1970, reed.
Economica). Disclosing the influence of politics, for instance of WW II and the
Cold War, upon Science and Technology is not the same as going in politics as
so many scientists believe without ever having read any serious historical work.
And I do not see why being opposed to the military exploitation of mathematics
and science should be considered as a more political stand tha~, for instance,
helping Los Alamos or Arzamas to develop their "weapons of genocide" was.
7 In Alvarez: Adventures of a Physicist (Basic Books, 1987), Luis Alvarez's trip
to Hiroshima is the very first thing he relates in his book. He was also one of
the main proponents of the H-bomb and, at the end of October, 1949, went to
Washington to lobby in favor of it. In 1954, he testified at the Oppenheimer
security hearing that Oppenheimer's opposition to the H-bomb was proof of an
exceedingly poor judgment. Alvarez is one of many similar counterexamples to
the "neutrality of Science" theory.
IX
began addressing rigour of proof and generality of formulations, rather than
formulae.
This does not mean that numerical calculations have become pointless:
thanks to computers, one can do more and more of them, for better or worse,
in all scientific and technical areas that, from medical imaging to the perfecting of nuclear weapons 5 , use mathematics. One does the same in certain
branches of mathematics too; for example, displaying a large number of curves
may open the way to a general theorem or to understanding a topological
situation, not to speak of the traditional number theory where numerical
experiment always was, and still is, used to formulate or verify conjectures.
This only means that the aim of an exposition of the principles of analysis is not to teach numerical techniques. Moreover, the partisans of applied
mathematics, of numerical analysis and of computer science in all the universities of the world manifest their imperialist tendencies far too clearly for
real mathematicians to take on in their stead a task for which they generally
lack both taste and competence.
* * *
The innocent reader and many confirmed mathematicians will probably be
surprised, possibly even shocked, to find in my book some very heavy allusions to extramathematical subjects and particularly to the relations between
science and weaponry. This is neither politically nor scientifically correct: Science is politically neutral 6 , even when someone lets it fall inadvertently on
Hiroshima while the future winner of a Nobel Prize in physics is recording the
results in a B-29 trailing the Enola Gay 7 . Nor is it part of the curriculum: a
5 Nuclear powers agreed a dozen years ago to stop testing. The reason why was
that testing was made unnecessary by the improvement of numerical analysis.
The most immediate consequence of this "progress" is that everything is now
done in full secrecy, which was not the case when they had to propel into the
stratosphere two million tons of radioactive rock and sand in order to check their
"gadgets".
6 An assertion long since demolished by countless studies, notably American, either of particular facets of scientific activity, or of Science in a general way,
e.g. in Bernard Barber, Science and the Social Order (Collier Books, 1952) and
Jean-Jacques Salomon, Science et Politique (Paris, Ed. du Seuil, 1970, reed.
Economica). Disclosing the influence of politics, for instance of WW II and the
Cold War, upon Science and Technology is not the same as going in politics as
so many scientists believe without ever having read any serious historical work.
And I do not see why being opposed to the military exploitation of mathematics
and science should be considered as a more political stand tha~, for instance,
helping Los Alamos or Arzamas to develop their "weapons of genocide" was.
7 In Alvarez: Adventures of a Physicist (Basic Books, 1987), Luis Alvarez's trip
to Hiroshima is the very first thing he relates in his book. He was also one of
the main proponents of the H-bomb and, at the end of October, 1949, went to
Washington to lobby in favor of it. In 1954, he testified at the Oppenheimer
security hearing that Oppenheimer's opposition to the H-bomb was proof of an
exceedingly poor judgment. Alvarez is one of many similar counterexamples to
the "neutrality of Science" theory.