1. Men of Calculus Who should we thank?

2. Who am I?

3. Newton (1642-1727) Major Works Published: Principia(87) and Opticks(04) Cambridge closes due to Plague outbreak. 1665-67 he returned home. Genius burst of discoveries – Binomial series, differential and integral calculus, gravity, sunlight separated into visual spectrum Spent 27 years as a full professor at Cambridge. Math discoveries was a means for furthering his science discoveries, only discussed in correspondence. 1696 left Cambridge The Great Sulk. – 1695 Wallis (British colleague at Hague) told him his notions where known as Leibniz’s Calculus Differentials. Storm of correspondence to discredit Leibniz as plagerist. – Disastrous effect on British math and science. British loyalty to Newton’s clumsy notation caused the dismissal of great thinkers in Europe who continued to advance the ideas.

4. Leibniz (1646-1716) Extremely brilliant. Made contributions to math, logic, history, law, diplomacy, politics, philosophy, metaphysics, and theology. Never published a major work but left thousands pages of private notes. Officially a courtier and public official. Travelled to Paris, London, The Hague in Holland forming relationships with the greatest scholars. Greatest creation is differential and integral calculus published in papers 1684 and ’86. Studying Pascal’s work “a great light” burst upon him. 1673+ – Differences (Slope of Tangent line) and Sums (area) are linked by the differential triangle (sides of dx, dy, ds) Invented Math Symbols: =,,~, – Vocab: function, constant, variable, parameter, coordinates, abscissa, ordinate – Calculus notation: d(), dy/dx, integral sign

5. Bernoulli Brothers (John 1667- 1748 and James 1654- 1705) After reading Leibniz’s papers they taught themselves the new Calculus and regularly corresponded with him. They became his most important students and disciples. James was professor of Mathematics at Basel until he died and John filled the position. John applied calculus to differential equations and mechanics. – Became leader of European mathematicians against the English.

6. Leonhard Euler (1707-1783) Most prolific author of all time in any field. The Shakespeare of Math. Extended plane and analytical geometry, introduced trigonometry and modern treatment of e x and ln x functions. All Calculus textbooks are considered copies of Euler’s publications.

7. Bernherd Riemann (1826 – 1866) Studied at same German university where Gauss was professor. Earned his doctor’s degree and highly praised by the remote Gauss. 1851 -1859 endured extreme poverty yet produced the bulk of his mathematical work. Riemann sum notation and geometric series. Died of tuberculosis just after being appointed the head math professor at the university and making a decent salary for the first time.