§l. Convergent sequences and series
93
Let us return to the mathematicians. As in every very hierarchical community obeying strict rules, for about fifty years discipline has been imposed
by a sort of policing. Before publishing an article, and of course not only in
mathematics, every serious journal now submits it to specialists, the "referees" or "gate keepers of Science" as a sociologist has called them, or, if one
prefers a French term, the sentinels of Science. They do not fail to detect the
weaknesses, particularly when the results announced are so very important
that some of the referees are angry at not having found them themselves
before the author; this system has contributed to improving the level of publications considerably. Moreover, all the authors of scientific articles now send
"preprints" ("hard" or "virtual") to their colleagues, to arrive six or twelve
months before the printed article. This is useful to one's colleagues and frees
them from following the same path if they were on it - thus doubly assuring
one's priority -, but can also lead these to criticise more or less severely the
articles that they receive. Not everyone reacts like Legendre, the great expert
on the theory of elliptic functions under the Revolution and the Empire, who,
in his late days, about 1825, on learning the results of Abel and of Jacobi
which totally revolutionised the subject, was extremely delighted at such a
"great step forward" and only complained that these young people born with
the century advanced too fast for him at seventy still to be able to hope to
follow them ...
This is what happened a few years ago to Andrew Wiles with his proof,
seven years of work, of "Fermat's Last Theorem" which generations of mathematicians have ogled for three centuries, as generations of alpinists ogled
Everest before Edmund Hillary. One might well think that the referees set to
on Wiles' preprints, breaking off all other activities, fell onto the object in
the hope or fear, according to the degree of generosity of the person considered, of finding gaps or errors as had always been the case in the past; there
was indeed an error in the calculation which, apparently, vitiated it all. But
Wiles corrected it a year later with the help of one of the referees; those of
the gate keepers who were angry at having lost their "first" when they were
so close had their hopes dashed. It is better not to think of what would have
happened to Wiles if his proof had been irremediable, as happened recently
a propos another Everest. Some of the more prestigious authorities decided
that the author - although brilliant and, it is the least one can say, not lacking in courage - of this false proof that used mathematics other than their
OWn ''was not of the required level" to succeed. Neither were they, until proof
to the contrary ...
One can also meditate on the recent affair of the "memory of water" when
a French biologist in other respects well-reputed, having published a revolutionary theory depending on difficult or impossible to reproduce experiments,
was expelled with the ultimate brutality from the "community" by dozens
of pontiffs of Physics and of Biology, agitating against the spectres of irrationality, of homeopathy and fraud, and claiming that his publications were
93
Let us return to the mathematicians. As in every very hierarchical community obeying strict rules, for about fifty years discipline has been imposed
by a sort of policing. Before publishing an article, and of course not only in
mathematics, every serious journal now submits it to specialists, the "referees" or "gate keepers of Science" as a sociologist has called them, or, if one
prefers a French term, the sentinels of Science. They do not fail to detect the
weaknesses, particularly when the results announced are so very important
that some of the referees are angry at not having found them themselves
before the author; this system has contributed to improving the level of publications considerably. Moreover, all the authors of scientific articles now send
"preprints" ("hard" or "virtual") to their colleagues, to arrive six or twelve
months before the printed article. This is useful to one's colleagues and frees
them from following the same path if they were on it - thus doubly assuring
one's priority -, but can also lead these to criticise more or less severely the
articles that they receive. Not everyone reacts like Legendre, the great expert
on the theory of elliptic functions under the Revolution and the Empire, who,
in his late days, about 1825, on learning the results of Abel and of Jacobi
which totally revolutionised the subject, was extremely delighted at such a
"great step forward" and only complained that these young people born with
the century advanced too fast for him at seventy still to be able to hope to
follow them ...
This is what happened a few years ago to Andrew Wiles with his proof,
seven years of work, of "Fermat's Last Theorem" which generations of mathematicians have ogled for three centuries, as generations of alpinists ogled
Everest before Edmund Hillary. One might well think that the referees set to
on Wiles' preprints, breaking off all other activities, fell onto the object in
the hope or fear, according to the degree of generosity of the person considered, of finding gaps or errors as had always been the case in the past; there
was indeed an error in the calculation which, apparently, vitiated it all. But
Wiles corrected it a year later with the help of one of the referees; those of
the gate keepers who were angry at having lost their "first" when they were
so close had their hopes dashed. It is better not to think of what would have
happened to Wiles if his proof had been irremediable, as happened recently
a propos another Everest. Some of the more prestigious authorities decided
that the author - although brilliant and, it is the least one can say, not lacking in courage - of this false proof that used mathematics other than their
OWn ''was not of the required level" to succeed. Neither were they, until proof
to the contrary ...
One can also meditate on the recent affair of the "memory of water" when
a French biologist in other respects well-reputed, having published a revolutionary theory depending on difficult or impossible to reproduce experiments,
was expelled with the ultimate brutality from the "community" by dozens
of pontiffs of Physics and of Biology, agitating against the spectres of irrationality, of homeopathy and fraud, and claiming that his publications were