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Rated 5 out of 5 by Jmcd from Excellent This course is amazing. I have a bachelor's degree in mathematics and I had briefly read and discussed these great mathematics when their theorems would appear. To go through history with professor Dunham and see the mathematics evolve from Geometry and the Greeks to Calculus in European 17th century is eye opening. He allows you to consider how absurd the genius of these great men were that laid the these theorems with only their predecessors to build on. It is enough to make one want to live in another time with the ridiculous idea that one could contribute.

Date published: 2023-04-16

Rated 5 out of 5 by Jeff82 from A truly enjoyable learning experience! It's been more than 40 years since I took my last college math class during my studies in electrical engineering. Through a dozen or so courses I was exposed to many of the names discussed by Prof. Dunham and even a few of the background stories, but beyond that I simply learned to use the tools first discovered by these great thinkers. It's been a true pleasure to see how some of the proofs were constructed while gaining an appreciation for how far above my skills these geniuses lived. Thanks!

Date published: 2023-03-14

Rated 5 out of 5 by Bill34239 from Great course, great profesor I agree with most of the five star reviews. His knowledge is broad, and is his enthusiasm is infectious, and his presentation is humorous and engaging at the same time. My only complaint is it's about 50 years too late for me. Where were you when I needed you? Kudos.

Date published: 2023-03-08

Rated 5 out of 5 by Margot70 from Entirely worth watching! I haven’t done Math for 50 yrs and was an unremarkable student when I did. Although I have not always followed the actual Math, I have really enjoyed Prof. Dunham’s presentation and the background he provides. This was a really delightful series for me. Thank you!

Date published: 2023-03-07

Rated 5 out of 5 by Avinash from loved it Reading his book + listening to his course is a joy which could not be expressed in words , I Wish such professors existed in my school/college

Date published: 2023-02-24

Rated 5 out of 5 by WatchingU from A lovely sampler of the history of mathematics My point of view is that of a senior physical scientist, retired after many years. I have used a lot of math, mainly calculus based, to solve problems, and I am also accustomed to the didactic teaching style of typical advanced math courses. This course was a delicious treat after a long labor. I enjoyed the instructor's low key approach and the emphasis on history, with carefuly selected proofs presented as artistic masterpieces. The flow of the subject matter from geometry to calculus and beyond is presented in a very natural way, and the selected proofs are indeed beautiful. It was wonderful to be reacquainted with Archimedes' area of the circle -- so simple and yet so clever! The discussion of infinities at the end of the course reminded me that I am too earthbound to be a mathematician, but that was also useful. Well worthwhile in my opinion.

Date published: 2023-02-21

Rated 5 out of 5 by rjDel from Enjoyed this journey! As one with a graduate degree in mathematics, I was a bit skeptical as to whether or not I would enjoy this course. I was pleasantly surprised that I did and also learned a number of new things. Professor Dunham provides insight into the lives and works of some of the greatest mathematicians and does so with sincere enthusiasm. So relax, have a cup of coffee, tea or whatever, and enjoy the journey!

Date published: 2023-02-12

Rated 4 out of 5 by Sparweb from Please, sir, can I have a little more? I enjoyed all of these lectures and my only regret is that it feels incomplete - he skipped the 20th Century! I would love additional lectures featuring Turing, von Neumann, and Kurt Godel, but alas this series is too short. For example, we could see how Einstein searched for a way to describe the distortions of space-time, and discovered the solution in Gauss's work. Or the challenging conclusions of Godel which turned the concept of proof on its head when self-references entered the realm.

Date published: 2023-02-05

Overview

Explore the most awe-inspiring theorems in the 3,000-year history of mathematics with the 24 lectures of Great Thinkers, Great Theorems. Professor William Dunham, an award-winning teacher with a talent for conveying the essence of mathematical ideas, reveals how great minds like Pythagoras, Newton, and Euler crafted theorems that would revolutionize our understanding of the world. Approaching great theorems the way an art course approaches great art, Professor Dunham will open your mind to new levels of mathematics appreciation.

About

William Dunham

Mathematics is perhaps the most useful of subjects, but my interests are not utilitarian. Rather, I look to the great landmarks from the history of mathematics and present them as creative achievements that are a joy to behold.

ALMA MATER

The Ohio State University

INSTITUTION

Muhlenberg College

Dr. William Dunham is the Truman Koehler Professor of Mathematics at Muhlenberg College in Allentown, Pennsylvania. He earned his undergraduate degree from the University of Pittsburgh and his M.S. and Ph.D. in Mathematics from The Ohio State University. Before his current appointment at Muhlenberg, Dr. Dunham taught at Hanover College in Indiana, receiving teaching awards from both institutions as well as the Award for Distinguished College or University Teaching from the Eastern Pennsylvania and Delaware Section of the Mathematical Association of America. He was a Visiting Professor at Ohio State and at Harvard University, where he was invited to teach an undergraduate course on the work of Leonhard Euler and to deliver the Clay Public Lecture in 2008. Dr. Dunham's great theorems approach to teaching mathematics was fostered by a 1983 summer grant from the Lilly Endowment, which also led to his first book, Journey Through Genius: The Great Theorems of Mathematics—a Book-of-the-Month Club selection that has been translated into five languages. Other books followed in addition to articles on mathematics and its history, earning him numerous awards from the Mathematical Association of America and other organizations. He has presented popular talks on mathematics throughout the United States and has appeared on the BBC and NPR's Talk of the Nation: Science Friday.

By This Professor

01: Theorems as Masterpieces

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 of proving a theorem: direct proof and indirect proof. Also, meet some of the great thinkers whose ideas you will be studying.

32 min

02: Mathematics before Euclid

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: Thales and Pythagoras—the latter renowned for the theorem that bears his name.

31 min

03: The Greatest Mathematics Book of All

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 long as you delve into the ground-laying definitions, postulates, common notions, and theorems from book I.

29 min

04: Euclid's Elements-Triangles and Polygons

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. Also, cover some of the techniques from book IV for constructing regular polygons.

32 min

05: Number Theory in Euclid

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 many prime numbers, which Professor Dunham considers one of the greatest proofs in all of mathematics.

29 min

06: The Life and Works of Archimedes

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 unclothed through the streets, shouting "Eureka!" ("I have found it!") on solving a problem in his bath.

29 min

07: Archimedes' Determination of Circular Area

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.

32 min

08: Heron's Formula for Triangular Area

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 who devised a curious method for determining the area of a triangle from the lengths of its three sides.

31 min

09: Al-Khwarizmi and Islamic Mathematics

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 our term "algorithm": al-Khwarizmi. His great book on equation solving also led to the term "algebra."

30 min

10: A Horatio Algebra Story

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 one of the most colorful of these figures: Gerolamo Cardano, who solved several key problems. In secret, of course.

29 min

11: To the Cubic and Beyond

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 equation. Norwegian mathematician Niels Abel later showed that no general solutions are possible for fifth- or higher-degree equations.

32 min

12: The Heroic Century

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, including John Napier, Henry Briggs, René Descartes, Blaise Pascal, and Pierre de Fermat, whose famous "last theorem" would not be proved until 1995.

31 min

13: The Legacy of Newton

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 biggest mark in mathematics and science, inventing calculus and discovering the law of universal gravitation.

30 min

14: Newton's Infinite Series

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 see how infinite series allowed Newton to approximate sine values with extraordinary accuracy.

31 min

15: Newton's Proof of Heron's Formula

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 steps are circuitous, but the result bears Newton's stamp of genius.

32 min

16: The Legacy of Leibniz

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 discovered the "Leibniz series" to represent π, and within a few years he invented calculus independently of Newton.

31 min

17: The Bernoullis and the Calculus Wars

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 of Leibniz. Their fierce sibling rivalry extended to their competition to outdo each other in mathematical discoveries.

31 min

18: Euler, the Master

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 calculus; Euler's identity, responsible for the most beautiful theorem ever; Euler's polyhedral formula; and Euler's path.

30 min

19: Euler's Extraordinary Sum

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 analysis through the twists and turns that led to a brilliantly simple answer.

31 min

20: Euler and the Partitioning of Numbers

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 move on to Euler's daring proof of a partitioning property of whole numbers.

31 min

21: Gauss-the Prince of Mathematicians

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 and other fields, focusing on his proof that a regular 17-sided polygon can be constructed with compass and straightedge alone.

30 min

22: The 19th Century-Rigor and Liberation

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 non-Euclidean geometry; and the first significant steps toward opening the field to women.

31 min

23: Cantor and the Infinite

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 "completed" infinite, and how Cantor resolved this mystery with transfinite numbers, exemplified by the transfinite cardinal aleph-naught.

29 min

24: Beyond the Infinite

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 transcendental numbers greatly outnumber the seemingly more abundant algebraic numbers—a final example of the elegance, economy, and surprise of a mathematical masterpiece.

31 min