1.I agree with Manin that physicists more inquisitive to mathematics than mahematicians to physics.
2. I agree with Wittgenstein:
6.21 Mathematical propositions express no thoughts.
6.211 In life it is never a mathematical proposition which we need,
but we use mathematical propositions only in order to infer
from propositions which do not belong to mathematics to others
which equally do not belong to mathematics.
(In philosophy the question "Why do we really use that word,
that proposition?" constantly leads to valuable results.)
6.22 The logic of the world which the propositions of logic show in
tautologies, mathematics shows in equations.
6.23 If two expressions are connected by the sign of equality, this
means that they can be substituted for one another. But
whether this is the case must show itself in the two expressions
themselves.
It characterizes the logical form of two expressions, that they
can be substituted for one another.
6.234 Mathematics is a method of logic.
6.2341 The essential of mathematical method is working with equations.
On this method depends the fact that every proposition
of mathematics must be self-intelligible.
6.24 The method by which mathematics arrives at its equations is
the method of substitution.
For equations express the substitutability of two expressions,
and we proceed from a number of equations to new equations,
replacing expressions by others in accordance with the equations
3.Roger, i am agree with you naturally.
Please don't forget please impartially evaluate my essay
Sincerely
Yuri