Wigner's ``The Unreasonable Effectiveness of Mathematics in the Natural Sciences''
Gelfand
``Eugene Wigner wrote a famous essay on the unreasonable effectiveness of mathematics in natural sciences. He meant physics, of course. There is only one thing which is more unreasonable than the unreasonable effectiveness of mathematics in physics, and this is the unreasonable ineffectiveness of mathematics in biology.''
Physics has these nice patterns, using ``core'' mathematics.
\section{Conclusions}
It's not surprising that physics should have a math,
that chemistry should have a math;
what's surprising is that they share much of the same math.
We'd naively expect a *tree*:
you dig deeper and into subtleties.
What's *weird* is when there are connections,
and *inter*connections.
[and that's what's cool and beautiful,
and more present in math than other fields afaict]
it's not surprising that a field should have a few big ideas
of major value
...but it's when the subareas interconnect that's weird
It's not surprising that various objects have their own fields of study;
what's powerful and surprising is when some fields have overlap.
EG, chemistry is very powerful b/c it covers the study of all manner of
physical things
(there is a common theory underlying water, fire, air, wood, metal,
earth, etc., etc.).
Different sciences use math differently,
but there are big commonalities (esp. calc / lin alg / stats, hence
their centrality;
more subtly, PDEs):
there is a "math for chemists" and "math for physicists" and "math for
economists" and "math for engineers" (yes, exactly those classes) -
which is not surprising, as the fields are different
...but it's the same core math!]