(This is an extended text of the address at the discussion on teaching of
mathematics in Palais de Découverte in Paris on 7 March 1997.)
Mathematics is a part of physics. Physics is an experimental science, a
part of natural science. Mathematics is the part of physics where
experiments are cheap.
The Jacobi identity (which forces the heights of a triangle to cross at one
point) is an experimental fact in the same way as that the Earth is round
(that is, homeomorphic to a ball). But it can be discovered with less
expense.
In the middle of the twentieth century it was attempted to divide physics
and mathematics. The consequences turned out to be catastrophic. Whole
generations of mathematicians grew up without knowing half of their science
and, of course, in total ignorance of any other sciences. They first began
teaching their ugly scholastic pseudo-mathematics to their students, then
to schoolchildren (forgetting Hardy's warning that ugly mathematics has no
permanent place under the Sun).
Since scholastic mathematics that is cut off from physics is fit neither
for teaching nor for application in any other science, the result was the
universal hate towards mathematicians - both on the part of the poor
schoolchildren (some of whom in the meantime became ministers) and of the
users. ...
Jane Jackson, Co-Director, Modeling Instruction Program
Box 871504, Dept.of Physics & Astronomy,ASU,Tempe,AZ 85287
480-965-8438/fax:965-7331 <http://modeling.asu.edu>