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History of Mathematics 17Th Century Developments

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History of Mathematics 17Th Century Developments History of Mathematics 17th century developments Peter Gibson November 5, 2019 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 Math 4400 2 / 19 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. 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. P. Gibson Math 4400 3 / 19 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 Math 4400 3 / 19 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, in addition to Kepler, Galileo and Descartes: Girard Desargues (1591-1661) Blaise Pascal (1623-1662) Pierre de Fermat (1601-1665) Evangelista Torricelli (1608-1647) Christiaan Huygens (1629-1695) John Wallis (1616-1703) Isaac Barrow (1630-1677) P. Gibson Math 4400 4 / 19 Fermat was a lawyer and member of the parlement of Toulouse. He communicated with Blaise Pascal, Marin Mersenne, Ren´eDescartes, John Wallis, Gilles de Roberval, as part of a long distance community of scholars that would come to be known as the Republic of Letters. P. Gibson Math 4400 5 / 19 while Arnol'd asserts that Barrow understood the fundamental theorem of 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). 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, P. Gibson Math 4400 6 / 19 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). 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, while Arnol'd asserts that Barrow understood the fundamental theorem of calculus. P. Gibson Math 4400 6 / 19 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, while Arnol'd asserts that Barrow understood the fundamental theorem of 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 Math 4400 6 / 19 -Fran¸cois-Marie Arouet to Maupertuis 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 Math 4400 7 / 19 -Fran¸cois-Marie Arouet to Maupertuis 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 Math 4400 7 / 19 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... -Fran¸cois-Marie Arouet to Maupertuis P. Gibson Math 4400 7 / 19 Newton in 1689 P. Gibson Math 4400 8 / 19 Some of his works: Philosophiæ Naturalis Principia Mathematica (1687) Opticks (1704) Method of Fluxions (1736) Newton lived from 1642-1727. His self-proclaimed annus mirabilis was 1666. P. Gibson Math 4400 9 / 19 Philosophiæ Naturalis Principia Mathematica (1687) Opticks (1704) Method of Fluxions (1736) Newton lived from 1642-1727. His self-proclaimed annus mirabilis was 1666. Some of his works: P. Gibson Math 4400 9 / 19 Opticks (1704) Method of Fluxions (1736) Newton lived from 1642-1727. His self-proclaimed annus mirabilis was 1666. Some of his works: Philosophiæ Naturalis Principia Mathematica (1687) P. Gibson Math 4400 9 / 19 Method of Fluxions (1736) Newton lived from 1642-1727. His self-proclaimed annus mirabilis was 1666. Some of his works: Philosophiæ Naturalis Principia Mathematica (1687) Opticks (1704) P. Gibson Math 4400 9 / 19 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 Math 4400 9 / 19 Less known is his career as Warden and Master of the Royal Mint. Also, Newton worked extensively on alchemy and theology. How can this be reconciled with his scientific achievement? Newton's mathematical and scientific contributions are well known. P. Gibson Math 4400 10 / 19 Also, Newton worked extensively on alchemy and theology. How can this be reconciled with his scientific achievement? Newton's mathematical and scientific contributions are well known. Less known is his career as Warden and Master of the Royal Mint. P. Gibson Math 4400 10 / 19 How can this be reconciled with his scientific achievement? 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 Math 4400 10 / 19 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. How can this be reconciled with his scientific achievement? P. Gibson Math 4400 10 / 19 the Great Plague (1664-1666) the Great Fire of London (1666) Two important events took place in London during Newton's most productive years: P. Gibson Math 4400 11 / 19 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 Math 4400 11 / 19 P. Gibson Math 4400 12 / 19 P. Gibson Math 4400 13 / 19 P. Gibson Math 4400 14 / 19 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 Math 4400 15 / 19 Newton entered Trinity College at Cambridge University in 1661. P. Gibson Math 4400 16 / 19 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. 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. P. Gibson Math 4400 17 / 19 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. 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. P. Gibson Math 4400 17 / 19 In 1695 he left Cambridge to become Warden of His Majesty's Mint. 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.
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