Great Thinkers, Great Theorems

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Theorems as Masterpieces
Episode overview
Certain theorems stand out as great masterpieces of mathematics that can be appreciated as great works of art. After hearing Professor Dunham explain this approach, discover the two ways .. show full overview
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Mathematics Before Euclid
Episode overview
Investigate three non-Greek civilizations that had robust traditions in mathematics. Then encounter a pair of Greek mathematicians who predated Euclid, but who left very deep footprints: .. show full overview
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The Greatest Mathematics Book of All
Episode overview
Begin your exploration of the work widely considered the greatest mathematical text of all time: Euclid's Elements. Discover why these 13 succinct books have been so influential for so .. show full overview
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Euclid's Elements - Triangle and Polygons
Episode overview
Continuing your journey through Euclid, work your way toward his most famous result: his proof of the Pythagorean theorem—a demonstration of remarkable visual and intellectual beauty. .. show full overview
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Number Theory in Euclid
Episode overview
In addition to being a geometer, Euclid was a pioneering number theorist, a subject he took up in books VII, VIII, and IX of the Elements. Focus on his proof that there are infinitely .. show full overview
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The Life and Works of Archimedes
Episode overview
Even more distinguished than Euclid was Archimedes, whose brilliant ideas took centuries to fully absorb. Probe the life and famous death of this absent-minded thinker, who once ran .. show full overview
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Archimedes' Determination of Circular Area
Episode overview
See Archimedes in action by following his solution to the problem of determining circular area—a question that seems trivial today but only because he solved it so simply and decisively. His unusual strategy relied on a pair of indirect proofs.
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Heron's Formula for Triangular Area
Episode overview
Heron of Alexandria (also called Hero) is known as the inventor of a proto-steam engine many centuries before the Industrial Revolution. Discover that he was also a great mathematician .. show full overview
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Al-Khwarizmi and Islamic Mathematics
Episode overview
With the decline of classical civilization in the West, the focus of mathematical activity shifted to the Islamic world. Investigate the proofs of the mathematician whose name gives us .. show full overview
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A Horatio Algebra Story
Episode overview
Visit the ruthless world of 16th-century Italian universities, where mathematicians kept their discoveries to themselves so they could win public competitions against their rivals. Meet .. show full overview
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To the Cubic and Beyond
Episode overview
Trace Cardano's path to his greatest triumph: the solution to the cubic equation, widely considered impossible at the time. His protégé, Ludovico Ferrari, then solved the quartic .. show full overview
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The Heroic Century
Episode overview
The 17th century saw the pace of mathematical innovations accelerate, not least in the introduction of more streamlined notation. Survey the revolutionary thinkers of this period, .. show full overview
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The Legacy of Newton
Episode overview
Explore the eventful life of Isaac Newton, one of the greatest geniuses of all time. Obsessive in his search for answers to questions from optics to alchemy to theology, he made his .. show full overview
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Newton's Infinite Series
Episode overview
Start with the binomial expansion, then turn to Newton's innovation of using fractional and negative exponents to calculate roots—an example of his creative use of infinite series. Also .. show full overview
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Newton's Proof of Heron's Formula
Episode overview
Return to Heron's ancient formula for determining the area of a triangle to consider Newton's proof using algebraic techniques—an approach he also applied to other geometry problems. The .. show full overview
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The Legacy of Leibniz
Episode overview
Probe the career of Newton's great rival, Gottfried Wilhelm Leibniz, who came relatively late to mathematics, plunging in during a diplomatic assignment to Paris. In short order, he .. show full overview
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The Bernoullis and the Calculus Wars
Episode overview
Follow the bitter dispute between Newton and Leibniz over priority in the development of calculus. Also encounter the Swiss brothers Jakob and Johann Bernoulli, enthusiastic supporters .. show full overview
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Euler, The Master
Episode overview
Meet history's most prolific mathematician, Leonhard Euler, who went blind in his sixties but kept turning out brilliant papers. A sampling of his achievements: the number e, crucial in .. show full overview
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Euler's Extraordinary Sum
Episode overview
Euler won his spurs as a great mathematician by finding the value of a converging infinite series that had stumped the Bernoulli brothers and everyone else who tried it. Pursue Euler's .. show full overview
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Euler and the Partitioning of Numbers
Episode overview
Investigate Euler's contribution to number theory by first warming up with the concept of amicable numbers—a truly rare breed of integers until Euler vastly increased the supply. Then .. show full overview
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Gauss - The Prince of Mathematicians
Episode overview
Dubbed the Prince of Mathematicians by the end of his career, Carl Friedrich Gauss was already making major contributions by his teen years. Survey his many achievements in mathematics .. show full overview
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The 19th Century - Rigor and Liberation
Episode overview
Delve into some of the important trends of 19th-century mathematics: a quest for rigor in securing the foundations of calculus; the liberation from the physical sciences, embodied by .. show full overview
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Cantor and the Infinite
Episode overview
Another turning point of 19th-century mathematics was an increasing level of abstraction, notably in the approach to the infinite taken by Georg Cantor. Explore the paradoxes of the .. show full overview
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Beyond the Infinite
Episode overview
See how it's possible to build an infinite set that's bigger than the set of all whole numbers, which is itself infinite. Conclude the course with Cantor's theorem that the .. show full overview
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Professor Biography
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