Algebra and geometry were useful for describing size...
but an understanding of motion in time required the development of calculus



Theoretical
physicists use mathematics to describe certain aspects of Nature. Sir
Isaac Newton was the first theoretical physicist, although in his own
time his profession was called "natural philosophy".
By
Newton's era people had already used algebra and geometry
to build marvelous works of architecture, including the great cathedrals
of Europe, but algebra and geometry only describe things that are sitting
still. In order to describe things that are moving or changing in some
way, Newton invented calculus.
The
most puzzling and intriguing moving things visible to humans have always
been been the sun, the moon, the planets and the stars we can see in the
night sky. Newton's new calculus, combined with his "Laws of Motion",
made a mathematical model for the force of gravity that not only described
the observed motions of planets and stars in the night sky, but also of
swinging weights and flying cannonballs in England.
Today's
theoretical physicists are often working on the boundaries of known mathematics,
sometimes inventing new mathematics as they need it, like Newton did with
calculus.
Newton
was both a theorist and an experimentalist. He spent many many long hours,
to the point of neglecting his health, observing the way Nature behaved
so that he might describe it better. The socalled "Newton's Laws of Motion"
are not abstract laws that Nature is somehow forced to obey, but the observed
behavior of Nature that is described in the language of mathematics. In
Newton's time, theory and experiment went together.
Today
the functions of theory and observation are divided into two distinct
communities in physics. Both experiments and theories are much more complex
than back in Newton's time. Theorists are exploring areas of Nature in
mathematics that technology so far does not allow us to observe in experiments.
Many of the theoretical physicists who are alive today may not live to
see how the real Nature compares with her mathematical description in
their work. Today's theorists have to learn to live with ambiguity and
uncertainty in their mission to describe Nature using math. 


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