Art: Problem of Perspective (02:57)
Piero della Francesca is one of the greatest Renaissance practitioners of linear perspective. The artist uses mathematics to create the proper perspectives.
Descartes: Certainty of Numbers (03:20)
By the 17th century, Europe is the powerhouse of mathematical ideas. Descartes has a dream in which he learns that philosophy must be built on a foundation of mathematics.
Descartes: Giant of Mathematics (03:08)
At the University of Leyden, Descartes proposes to link algebra and geometry. He unlocks the possibility of navigating geometry's higher dimensions.
Festival of Mathematics (05:45)
Each year in Toulouse, a mathematics festival honors Pierre Fermat, who virtually invented modern number theory. Technology that society relies on for today's coding all comes from the work of Pierre Fermat.
Isaac Newton (03:32)
A Newton scholar takes film viewers on a tour of the Newton's childhood home. At the age of 22, Newton develops a new theory of light, discovers gravitation, and wrote revolutionary approach to math: calculus.
Isaac Newton's Calculus (02:04)
Using Newton's calculus, one can work out the exact speed and precise distance traveled by an accelerating car. Newton's calculus helps us to understand the changing world such as motion and orbits.
Contributions of Gottfried Leibniz (04:00)
Gottfried Leibniz (1946-1716) invented infinitesimal calculus independently of Newton. The philosopher and mathematician worked for the royal family of Hanover. His work is a precursor to the development of computers.
Rivalry Between Newton and Leibniz (03:43)
Rivalry between Leibniz and Newton was so intense that the Royal Society intervened. Leibniz was not content with the Society's decisions. Leibniz's mathematics eventually triumphs.
Bernoulli Family and Mathematics (05:19)
The Bernoulli brothers used the techniques of Leibniz’s calculus as a means for handling a wide range of astronomical and physical problems. They spread Leibniz’s work throughout Europe.
Leonhard Euler: Mathematician (04:50)
Leonhard Euler: finds his intellectual home in St. Petersburg. Euler was the most prolific writer of mathematics of all time.
Contributions of Leonhard Euler (03:10)
Euler contributed to knowledge in many other areas. He did important work in astronomy, the theory of music, and cartography. We owe to Euler the notations f(x), e, i, the Greek letter pi, the summation symbol, and many more.
Carl Friedich Gauss: Mathematician (02:58)
Carl Friedrich Gauss kept diaries. His writings and proofs are at least one hundred years ahead of their time.
Mathematics: Imaginary Numbers (04:10)
Gauss's mathematics have touched many parts of the mathematical world. Imaginary numbers have essential concrete applications in a variety of sciences and related areas. Gauss questioned Euclid's geometry.
Janos Boylai and Hyperbolic Geometry (04:03)
A characteristic property of hyperbolic geometry is that the angles of a triangle add to less than a straight angle (half circle). Gauss had already worked out this theory ten years before.
Bernhard Riemann's Mathematics (04:56)
One exception is. One of Bernhard Riemann's most famous contributions to mathematics is a lecture on the foundations of geometry. Riemann's mathematics changed the way we see our world.
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