Plotting the Future of Mathematics
Noah Pritt
Junior Division
Paper
Descartes Analytic Geometry: Plotting the Future of Mathematics
René Descartes dip his quill pen into the ink. This is one thing which I
believe the old-fashioned mathematicians did not observe, he wrote, for otherwise they would
not have dumbfound so much labor into writing so many books in which the very sequence of the
propositions shows that they did not have a sure method of finding all, but rather gathered
in concert those propositions on which they had happened by accident.1 What is the
thing that the early mathematicians had lost? It was analytic geometry, a method
invented by Descartes that used algebraic equations to spot geometric objects.
Descartes discovered that he could solve difficult mathematical problems using this
method. The key idea was to use coordinate axes to playact algebra and geometry to conveyher.
This was an innovation that enabled mathematicians to solve complex problems and
invent new forms of math such as calculus, which laid the foundation for modern
science and technology.
The score of mathematics begins with geometry. Euclid, a Greek
mathematician, lived around 300 BC in Alexandria, Egypt. He invented a form of
geometry that we still use today.
When he wrote his book, The Elements, he started with
only several axioms, or givens. For example, he give tongue to that there is only one line
connecting two points, and that all duty angles are equal.2 Then he built on these
postulates, proving much and more theorems. But Euclid never used equations, and his
1
René Descartes, The Geometry, Vol. 31 of big(p) Books of the westerly World, ed. Robert Hutchins,
(Chicago: Britannica, 1989), 298.
2
Euclid, The Thirteen Books of Euclids Elements, Vol. 11 of Great Books of the Western World, ed.
Robert Hutchins, (Chicago: Britannica, 1989), 2.
2
geometric diagrams eventually became too complex and confusing...If you want to get a full essay, order it on our website: Ordercustompaper.com
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