The Transition to Calculus

In this chapter, you will see the blossoming of mathematics and an freedom of functional expression that would prove essential for the works of Newton and Leibnitz to follow in the seventeenth century.

Goals

Among the many features you should regard are:

Philosophy and Mathematics.

• Calculus. Note how many of the ideas of calculus are anticipated.
• The players. Mathematics is no longer an appendage of commerce, of religon, or any other interest - except physics. As in ancient times, we see a new class of professional mathematicians.
• Note how algebraic symbolism and methods trivialized many of the ancient problems solved using geometric methods. These successes inspired this new generation to a level of confidence which was to lead them to new areas of mathematics and results.
• What essential differences can you identify between this period and the period of the Renaissance?
• Physics is a driver for the new analysis. How and why?
• Note the subjects taught in the schools. Not the training of many of the mathematicians. Note the stature of the intellectual in the European community.

References

• J.M. Dunoyer de Segonzac, "Deux hommes de sciences dans les pays de la Loire aux XVIe et XVIIe siècles: Francois Viète et René Descartes," in 97e congres national des sociétés savantes, (Nantes, 1972) 1, 123-33.
• J. Grisard, "Francois Viète, mathematicien de la fin du seizième siecle," These de 3e cycle Ecole pratique des hautes etudes, (Paris, 1968).
• L. Geymonat, Galileo Galilei, 4th ed. (Torino, 1965).
• D M Clarke, Descartes' Philosophy of Science (1982).
• E S Haldane, Descartes: His Life and Times (1966).
• J F Scott, The Scientific Work of René Descartes (1987).
• W R Shea, The Magic of Numbers and Motion: The Scientific Career of René Descartes (1991).
• M S Mahoney, The Mathematical Career of Pierre de Fermat (1601-1665) (Princeton, 1994).