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Early Mathematical Advances
A main condition necessary for the advancement of physics and astronomy that progressed during the Scientific Revolution was the advance of mathematics, which allowed the proof of abstract theories and provided a more logical method for disproving the Aristotelian system. During the late 16th century, a French lawyer, Francois Viete, was among the first to use letters to represent unknown quantities, or variables. By applying this algebraic method to geometry, he laid the foundation for the invention of trigonometry. Another useful advancement was the decimal system, introduced by the Fleming Simon Stevin. However, perhaps the most important mathematical advance of the early period of the Scientific Revolution was the invention of logarithms in 1594 by John Napier of Scotland.
Applications of Mathematics
Johannes Kepler also did a great deal of work in geometry, which proved significant to his subsequent work in astronomy. In 1637, René Descartes published Geometry, in which he described how geometry relates to motion and defined points in relation to their surrounding planes of reference. Further progress in mathematics was made by Oxford professor John Wallis. His first work, Arithmetica Infinitum, published in 1655, set the stage for the invention and development of differential calculus, and was a major influence on Sir Isaac Newton.
Many mathematicians applied their knowledge to the study of optics, a field that had garnered great interest since the Middle Ages. The advances made in this field, including the development of techniques for higher resolution with glass lenses, led to the better construction of optical instruments, such as the microscope and telescope, which played a large part in the later work of Galileo.
The Need for Mathematics in the Scientific Revolution
Mathematics developed as a response to the demands of the sciences. The thinkers of the early Scientific Revolution had provided their descendants with a broad framework of new philosophies, hypotheses, and qualitative observations, all of which pointed to a revolution in thought. However, the old order was at first easily preserved in the face of this onslaught, in part due to the lack of substance to back up the theories of thinkers such as Nicolas Copernicus. Though these scientists sensed that their hypotheses were correct, it was difficult to bring their theories to the position of respect they deserved without the benefit of clear and logical evidence.
The realm of mathematics potentially offered this clear and logical evidence. The scientists of the early Scientific Revolution knew that there were forces acting on the physical world that would explain the phenomena they observed, but they had no way to quantify these forces and apply them to the geometry of the physical world. Mathematicians strove to solve this problem with the development of trigonometry and the application of new mathematical theorems to the physics of motion. Armed with these tools, the scientists of the early Scientific Revolution began to back up their hypotheses with mathematical proofs were nearly beyond question.
Evaluating Descartes’s Contributions to Mathematics
Descartes took perhaps the greatest mathematical step in the realm of applied mathematics in the development of the graphical representation of motion by the use of Cartesian coordinates, which plot points in relation to each other. In this way, Descartes could represent the fundamental correspondence between number and form. This paved the way for the explanation of the motions of heavenly bodies, the effects of gravity on projectiles, and many more phenomena that had previously been described but never explained in the clear logic of mathematics. It is possible that the application of algebraic methods to the geometry of form and motion is the most important step taken in the progress of the exact sciences.
