ВОт что умные товарищи говорят про приладную математику и математику:

It seems that there is not
enough mediation between science and mathemat-
ics.
Gromov: Absolutely, I completely agree. To say
“not enough” is an understatement. It is close to
zero. The communities have become very segre-
gated due to technical reasons and far too little
communication. A happy exception is the Courant
Institute. We still have many people interacting,
and it happens that mathematicians fall in love
with science. To see these young people at Cou-
rant is extremely encouraging because you don’t
see this kind of applied mathematicians anywhere
else. But they are well aware of the body of pure
mathematics where they can borrow ideas and then
apply them. Typically, applied mathematicians are
separated from the pure ones. They, kind of, don’t
quite like each other. That’s absurd. This has to be
changed because we have the same goals. We just
understand the world from different sides.
Raussen and Skau: Do you have any ideas of
how to improve this situation?
Gromov: No. But I think in any subject where
you have this kind of problem, the only suggestion
is that you have to start by studying the problem. I
don’t know enough about this; I just have isolated
examples. We have to look at where it works, where
it doesn’t work and just try to organize things in a
new way. But it has to be done very gently because

you cannot force mathematicians to do what they
don’t like. The obvious way to do it is to design
good combined educations in mathematics and
science. Actually, there is a very good initiative
by François Taddei in Paris who organizes classes
with lectures on biology for nonbiologists—for
young people in mathematics and physics. He
is extremely influential and full of enthusiasm. I
attended some of those classes, and it was fantas-
tic. He was teaching biology at Ecole Normale for
mathematicians and physicists, and he manages to
make those ideas accessible for everybody. That is
what I think should be done at the first stage. We
have to have this special kind of education that
is not in any curriculum; you cannot formalize
it. Only people who have enough enthusiasm and
knowledge can project this knowledge to young
people. An institutionalized system is much harder
to design, and it is very dangerous to make it in
any way canonical, because it may just misfire.
Forcing mathematics on nonmathematicians only
makes them unhappy.

И за образование:

Education is apparently a
key factor. You have earlier expressed your distress
about realizing that the minds of gifted youths are
not developed effectively enough. Any ideas about
how education should change to get better adapted
to very different minds?
Gromov: Again I think you have to study it.
There are no absolutes. Look at the number of
people like Abel who were born two hundred
years ago. Now there are no more Abels. On the
other hand, the number of educated people has
grown tremendously. It means that they have not
been educated properly because where are those
people like Abel? It means that they have been
destroyed. The education destroys these potential
geniuses—we do not have them! This means that
education does not serve this particular function.
The crucial point is that you have to treat every-
body in a different way. That is not happening
today. We don’t have more great people now than
we had one hundred, two hundred, or five hundred
years ago, starting from the Renaissance, in spite
of a much larger population. This is probably due
to education. This is maybe not the most serious
problem with education. Many people believe in
very strange things and accordingly make very
strange decisions. As you know, in the UK, in some
of the universities, there are faculties of homeopa-
thy that are supported by the government. They
are tremendously successful in terms of numbers
of students. And anybody can learn that nonsense.
It is very unfortunate.

You point out that we don’t
have anybody of Abel’s stature today, or at least
very few of them. Is that because we, in our educa-
tional system, are not clever enough to take care
of those who are exceptionally gifted because they
may have strange ideas, remote from mainstream?
Gromov: The question of education is not
obvious. There are some experiments on animals
that indicate that the way you teach an animal is
not the way you think it happens. The learning
mechanism of the brain is very different from how
wmechanisms. We superimpose our view from
everyday experience, which may be completely
distorted. Because of that, we can distort the
potentially exceptional abilities of some children.
There are two opposite goals education is
supposed to achieve: firstly, to teach people to
conform to the society they live in; on the other
hand, to give them freedom to develop in the best
possible way. These are opposite purposes, and
they are always in collision with each other. This
creates the result that some people get suppressed
in the process of adapting them to society. You
cannot avoid this kind of collision of goals, but we
have to find a balance between the two, and that
is not easy, on all levels of education.
There are very interesting experiments per-
formed with chimpanzee and bonobo apes and
under which conditions they learn, or even how
you teach a parrot to talk. How do you do that? The
major factor is that it should not see the teacher.
You put a mirror between you and the parrot and
then you speak behind the mirror. The parrot then
sees a bird—it talks to a bird. But if it sees you, it
will learn very badly.
e think it works: like in physics, there are hidden


That is not an obvious thing. The very pres-
ence of a teacher, an authority, moves students in
a particular direction and not at all the direction
the teacher wants them to move. With all this ac-
cumulated evidence, you cannot make any simple
decision. If you say “do this and this,” you are
wrong for sure. Solutions are not obvious; they can
only come after analyzing deeply what is actually
known and by studying the possibilities. I think
the answers will be unexpected. What children
can learn and what they cannot learn, we don’t
know because we don’t know how to conduct ex-
periments to be ethical and instructive at the same
time. It is a very nontrivial issue, which has not
been studied much. With animals we have results
but not very much with people.
t is a very difficult question because
we have to project mathematical ideas to people
who work very far from mathematics—to people
who make decisions in society. The way we think
is very different from the way they operate.
I don’t know but I think that within our math-
ematical society we can make some steps to-
wards education, like creating good mathematical
sources for children. Today we have the Internet
so we should try to make Internet presentations.
Actually, in France there are some people trying
to organize extracurricular activities for younger
children on a small scale. We should try to do
something like that on a big scale: big centers of
stimulating creativity in all directions. I would not
only focus on mathematics but on science and
art and whatever can promote creative activity in
young people. When this develops, we may have
some influence but not before that. Being inside
our ivory tower, what can we say? We are inside
this ivory tower, and we are very comfortable there.
But we cannot really say much because we don’t
see the world well enough either. We have to go
out, but that is not so easy.


From: http://www.ihes.fr/~gromov/PDF/rtx100300391p.pdf
and http://www.ihes.fr/~gromov/PDF/16[102].pdf

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Сопоставление прикладной математики с чистой совершенно в точку. Меня лично, как механика, особенно радует упоминание Курантовского института, где делалось (и делается) очень много нетривиальной и, в хорошем смысле, по-настоящему прикладной науки.
Вопрос об образовании очень сложный. Математики много говорят о том, что нужно учить "учёных" более правильной математике. А надо бы ещё поговорить о том, что самим математикам очень часто недостаёт понимания специфики других "наук". Ну и конечно, как всегда, снобизма и элементарной необразованности хватает с обоих сторон, что редко помогает диалогу.

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ага, он так и говорит, что про образование вопрос сложный...
вообще мне кажется, что хорошо бы---и проще!--*математиков* учить прикладным наукам, в студчестве---типа, обязать каждого студента-математика сдать курс-другой в техническом вузе (по выбору студента с согласия зав.чего-нибудь).

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По личному опыту, мне кажется, это не сработает. Мне повезло/не повезло (смотря кого спрашивать) сделать инженерный постдок; у меня ушёл год чтобы перестроиться. Если пичкать студента одним образом мысли вперемежку с другим, ничего кроме недоверия к одному из них не выйдет. Даже не нужно ходить за примером в инженерное дело; когда нам читали спецкурс по асимптотическим методам, как часть мех-мат. курса, мы все, как я вспоминаю, относились к идее считать "плохие" решения задач с большим недоверием.

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