MATH 4400, History of Mathematics

MATH 4400, History of Mathematics Lecture 5: The 17th Century Professor: Peter Gibson pcgibson@yorku.ca http://people.math.yorku.ca/pcgibson/math4400 October 13, 2015

Overview and historical context The 17th century was marked by imperial expansion and rivalry. The Russian empire expanded to encompass vast territories, governed by the Romanov imperial family (which ruled from 1584-1917). In particular, Peter the Great (r. 1682-1725) consolidated both territory and political power. In western Europe there was rivalry between the French Bourbon kings and the Hapsburg rulers of Spain and Austria. The Dutch Republic broke away from Spanish control at the end of the Thirty Years War (1618-1648). There was an expansion of naval power among European states, accompanying increased overseas trade and colonisation of the Americas. The slave trade flourshed during this time. P. Gibson (YorkU) Math 4400 13.10.2015 2 / 17

Overall, mercantalism was the dominant economic model, involving extraction of wealth from colonial territory in the Americas and elsewhere, and transportation of goods to Europe. An estimate 12M tons of sugar was transported to Europe in the century 1690-1790, during which time an estimated 12M African slaves were forced into labour in European colonies. Politically, the prevailing model was one of absolutist, dynastic monarchy, as typified by Louis XIV (r. 1643-1715) in France or Peter the Great in Russia. (The situation in England was an exception, with the civil war having resulted in power sharing between the monarchy and the nobility.) The balance of power shifted away from Spain and Portugal, toward Britain and France. P. Gibson (YorkU) Math 4400 13.10.2015 3 / 17

Mathematics in 17th century Just as political power gradually shifted toward Britain and France, so too did intellectual achievement. Some mathematicians active in this period: Girard Desargues (1591-1661) Blaise Pascal (1623-1662) Pierre de Fermat (1601-1665) Evangelista Torricelli (1608-1647) Christiaan Huygens (1629-1695) John Wallace (1616-1703) Isaac Barrow (1630-1677) P. Gibson (YorkU) Math 4400 13.10.2015 4 / 17

There were new developments in (synthetic) geometry, in probability, and in the calculation of areas of regions and lengths of curves. A considerable amount of work centred on infinitesimals, about which there was much dispute. Laplace credits Fermat with the discovery of differential calculus,what is clear, is that mathematics and physics were profoundly impacted by one person (who is traditionally credited with co-development of differential and integral calculus). P. Gibson (YorkU) Math 4400 13.10.2015 5 / 17

Newton est notre Cristophe Colomb. Il nous a mene dans un nouveau monde, et je voudrais bien y voyager... Newton is our Cristopher Colombus. He has led us to a new world, and I would very much like to go there... P. Gibson (YorkU) Math 4400 13.10.2015 6 / 17

1689 Newton in P. Gibson (YorkU) Math 4400 13.10.2015 7 / 17

Newton lived from 1642-1727. His self-proclaimed annus mirabilis was 1666. Some of his works: Philosophiæ Naturalis Principia Mathematica (1687) Opticks (1704) Method of Fluxions (1736) P. Gibson (YorkU) Math 4400 13.10.2015 8 / 17

Newton s mathematical and scientific contributions are well known. Less known is his career as Warden and Master of the Royal Mint. Also, Newton worked extensively on alchemy and theology. P. Gibson (YorkU) Math 4400 13.10.2015 9 / 17

Two important events took place in London during Newton s most productive years: the Great Plague (1664-1666) the Great Fire of London (1666) P. Gibson (YorkU) Math 4400 13.10.2015 10 / 17

P. Gibson (YorkU) Math 4400 13.10.2015 11 / 17

P. Gibson (YorkU) Math 4400 13.10.2015 12 / 17

P. Gibson (YorkU) Math 4400 13.10.2015 13 / 17

Year Population of London 1100 10-20,000 1300 20-50,000 1350 25-50,000 1500 50-100,000 1600 200,000 1650 350,000 1700 550,000 1750 700,000 1801 959,300 1831 1,655,000 P. Gibson (YorkU) Math 4400 13.10.2015 14 / 17

Newton entered Trinity College at Cambridge University in 1661. P. Gibson (YorkU) Math 4400 13.10.2015 15 / 17

During the years 1664-1666 Newton (having recently received his first degree) was forced to the family farm in Woolsthorpe because of the bubonic plague, which is estimated to have killed 100 000 people. In 1669 he bacame Lucasian Professor of Mathematics, taking the place of Isaac Barrow. In the late 1680s he became famous, with the publication of his Principia. In 1695 he left Cambridge to become Warden of His Majesty s Mint. P. Gibson (YorkU) Math 4400 13.10.2015 16 / 17

There are many, many secondary sources on Newton. Among these are: Never at Rest, a biography by Richard Westfalls Huygens & Barrow, Newton & Hooke, by Vladimir Arnol d Newton and the Counterfeiter, Thomas Levenson P. Gibson (YorkU) Math 4400 13.10.2015 17 / 17