MATH 4400, History of Mathematics

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1 MATH 4400, History of Mathematics Lecture 5: The 17th Century Professor: Peter Gibson October 13, 2015

2 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 ). In particular, Peter the Great (r ) 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 ( ). 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 / 17

3 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 , 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 ) 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 / 17

4 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 ( ) Blaise Pascal ( ) Pierre de Fermat ( ) Evangelista Torricelli ( ) Christiaan Huygens ( ) John Wallace ( ) Isaac Barrow ( ) P. Gibson (YorkU) Math / 17

5 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 / 17

6 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 / 17

7 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 / 17

8 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... -Franois-Marie Arouet to Maupertuis P. Gibson (YorkU) Math / 17

9 1689 Newton in P. Gibson (YorkU) Math / 17

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

11 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 / 17

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

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16 Year Population of London , , , , , , , , , ,655,000 P. Gibson (YorkU) Math / 17

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

18 During the years 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 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 / 17

19 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 / 17

From Paleolithic Times. to the Present FIFTH EDITION. LARRY NEAL University of Illinois at Urbana-Champaign

From Paleolithic Times. to the Present FIFTH EDITION. LARRY NEAL University of Illinois at Urbana-Champaign A CONCISE ECONOMIC HISTORY OF THE WORLD From Paleolithic Times to the Present FIFTH EDITION LARRY NEAL University of Illinois at Urbana-Champaign RONDO CAMERON Emory University New York Oxford OXFORD UNIVERSITY