Greenspun's tenth law of programming: Any sufficiently complicated C or Fortran program contains an ad-hoc, informally-specified, bug-ridden, slow implementation of half of CommonLisp.
Trying to do science without mathematics is analogous. When Hartry Field tries to formulate science in terms of nominalistic theories (he wanted to demonstrate that one can do science without referring to abstract entities), those theories can't avoid using abstractions (e.g. you could encode PA in terms of his space-points).
Number theory, like Lisp, is a sort of universal structure, just waiting to be discovered. See Minsky - "Alien Intelligence" (search for "A REAL LIFE EPISODE")
It's possible to do science without mathematics, but you might as well develop mathematics on the way.