Great Thinkers, Great Theorems

Course No. 1471
Professor William Dunham, Ph.D.
Muhlenberg College
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Course No. 1471
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Course Overview

Mathematics is filled with beautiful theorems that are as breathtaking as the most celebrated works of art, literature, or music. They are the Mona Lisas, Hamlets, and Fifth Symphonys of the field—landmark achievements that repay endless study and that are the work of geniuses as fascinating as Leonardo, Shakespeare, and Beethoven. Here is a sample:

  • Pythagorean theorem: Although he didn't discover the Pythagorean theorem about a remarkable property of right triangles, the Greek mathematician Euclid devised an ingenious proof that is a mathematical masterpiece. Plus, it's beautiful to look at!
  • Area of a circle: The formula for the area of a circle, A = π r2, was deduced in a marvelous chain of reasoning by the Greek thinker Archimedes. His argument relied on the clever tactic of proof by contradiction not once, but twice.
  • Basel problem: The Swiss mathematician Leonhard Euler won his reputation in the early 1700s by evaluating an infinite series that had stumped the best mathematical minds for a generation. The solution was delightfully simple; the path to it, bewilderingly complex.
  • Larger infinities: In the late 1800s, the German mathematician Georg Cantor blazed the trail into the "transfinite" by proving that some infinite sets are bigger than others, thereby opening a strange new realm of mathematics.

You can savor these results and many more in Great Thinkers, Great Theorems, 24 half-hour lectures that conduct you through more than 3,000 years of beautiful mathematics, telling the story of the growth of the field through a carefully chosen selection of its most awe-inspiring theorems.

Approaching great theorems the way an art course approaches great works of art, the course opens your mind to new levels of math appreciation. And it requires no more than a grasp of high school mathematics, although it will delight mathematicians of all abilities.

Your guide on this lavishly illustrated tour, which features detailed graphics walking you through every step of every proof, is Professor William Dunham of Muhlenberg College, an award-winning teacher who has developed an artist's eye for conveying the essence of a mathematical idea. Through his enthusiasm for brilliant strategies, novel tactics, and other hallmarks of great theorems, you learn how mathematicians think and what they mean by "beauty" in their work. As added enrichment, the course guidebook has supplementary questions and problems that allow you to go deeper into the ideas behind the theorems.

An Innovative Approach to Mathematics

Professor Dunham has been taking this innovative approach to mathematics for over a quarter-century—in the classroom and in his popular books. With Great Thinkers, Great Theorems you get to watch him bring this subject to life in stimulating lectures that combine history, biography, and, above all, theorems, presented as a series of intellectual adventures that have built mathematics into the powerful tool of analysis and understanding that it is today.

In the arts, a great masterpiece can transform a genre; think of Claude Monet's 1872 canvas Impression, Sunrise, which gave the name to the Impressionist movement and revolutionized painting. The same is true in mathematics, with the difference that the revolution is permanent. Once a theorem has been established, it is true forever; it never goes out of style. Therefore the great theorems of the past are as fresh and impressive today as on the day they were first proved.

What Makes a Theorem Great?

A theorem is a mathematical proposition backed by a rigorous chain of reasoning, called a proof, that shows it is indisputably true. As for greatness, Professor Dunham believes the defining qualities of a great theorem are elegance and surprise, exemplified by these cases:

  • Elegance: Euclid has a beautifully simple way of showing that any finite collection of prime numbers can't be complete—that there is always at least one prime number left out, proving that the prime numbers are infinite. Dr. Dunham calls this one of the greatest proofs in all of mathematics.
  • Surprise: Another Greek, Heron, devised a formula for triangular area that is so odd that it looks like it must be wrong. "It's my favorite result from geometry just because it's so implausible," says Dr. Dunham, who shows how, 16 centuries later, Isaac Newton used algebra in an equally surprising route to the same result.

Great Thinkers, Great Theorems includes many lectures that are devoted to a single theorem. In these, Professor Dunham breaks the proof into manageable pieces so that you can follow it in detail. When you get to the Q.E.D.—the initials traditionally ending a proof, signaling quod erat demonstrandum (Latin for "that which was to be demonstrated")—you can step back and take in the masterpiece as a whole, just as you would with a painting in a museum.

In other lectures, you focus on the biographies of the mathematicians behind these masterpieces—geniuses who led eventful, eccentric, and sometimes tragic lives. For example:

  • Cardano: Perhaps the most bizarre mathematician who ever lived, the 16th-century Italian Gerolamo Cardano was a gambler, astrologer, papal physician, convicted heretic, and the first to publish the solution of cubic and quartic algebraic equations, which he did after a no-holds-barred competition with rival mathematicians.
  • Newton and Leibniz: The battle over who invented calculus, the most important mathematical discovery since ancient times, pitted Isaac Newton—mathematician, astronomer, alchemist—against Gottfried Wilhelm Leibniz— mathematician, philosopher, diplomat. Each believed the other was trying to steal the credit.
  • Euler: The most inspirational story in the history of mathematics belongs to Leonhard Euler, whose astonishing output barely slowed down after he went blind in 1771. Like Beethoven, who composed some of his greatest music after going deaf, Euler was able to practice his art entirely in his head.
  • Cantor: While Vincent van Gogh was painting pioneering works of modern art in France in the late 1800s, Georg Cantor was laying the foundations for modern mathematics next door in Germany. Unappreciated at first, the two rebels even looked alike, and both suffered debilitating bouts of depression.

Describing a common reaction to the theorems produced by these great thinkers, Professor Dunham says his students often want to know where the breakthrough ideas came from: How did the mathematicians do it? The question defies analysis, he says. "It's like asking: ‘Why did Shakespeare put the balcony scene in Romeo and Juliet? What made him think of it?' Well, he was Shakespeare. This is what genius looks like!" And by watching the lectures in Great Thinkers, Great Theorems, you will see what equivalent genius looks like in mathematics.

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24 lectures
 |  Average 30 minutes each
  • 1
    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. x
  • 2
    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. x
  • 3
    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. x
  • 4
    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. x
  • 5
    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. x
  • 6
    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. x
  • 7
    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. x
  • 8
    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. x
  • 9
    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." x
  • 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. x
  • 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. x
  • 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. x
  • 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. x
  • 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. x
  • 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. x
  • 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. x
  • 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. x
  • 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. x
  • 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. x
  • 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. x
  • 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. x
  • 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. x
  • 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. x
  • 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. x

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Your professor

William Dunham

About Your Professor

William Dunham, Ph.D.
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...
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Great Thinkers, Great Theorems is rated 4.8 out of 5 by 100.
Rated 5 out of 5 by from Great Thinkers, Great Theorems Good course on the history of math without getting to deep into proofs. Could use a few more worked out examples.
Date published: 2020-01-19
Rated 5 out of 5 by from Fantastic Course!!! I loved this course from beginning to end. I am an engineer and have a basic applied math education. Math is a tool I use but I am not necessarily an advanced math enthusiast. But this course was fascinating to me! Professor Dunham is entertaining and a great presenter. If The Great Courses had other course offerings by Professor Dunham, I would purchase them immediately. Highly, highly recommended!
Date published: 2020-01-11
Rated 5 out of 5 by from Fabulous Course on Math History I have loved this course and learned a lot! Professor Dunham is very clear and tells a great story. You do not need much math to really enjoy each lecture. Very great and significant math concepts are explained in an understandable fashion. It's told in a narrative stream that shows the people involved and the progression of mathematical thought. I highly recommend this course, it's one of the best!
Date published: 2019-12-26
Rated 5 out of 5 by from Professor Dunham gives an in depth description of the Great Thinkers thought processes, and the Great Theorems that they discovered. This remarkable historical insight gives life to "how tos" of mathematical thought, providing roadmaps for the viewers to discover their own mathematical landscapes. Great Course!!
Date published: 2019-12-12
Rated 5 out of 5 by from Fun for everyone I have been familiar with the work of Prof. Dunham for years after reading his books Journey through Genius and The Mathematical Universe. When I discovered he had a Great Courses series, I had to watch it. I was not disappointed. He is a very entertaining man as well as an excellent speaker. His presentations were easy enough for me to understand even after 40 years since my last college calculus class. I hope he will do more.
Date published: 2019-08-15
Rated 5 out of 5 by from Great course! Even though I majored in Applied Mathematics, I learned quite a bit from this course. The instructor was amazing in his explanations and sense of humor.
Date published: 2019-03-21
Rated 5 out of 5 by from Essential If you enjoy the history of Mathematics, this collection of lectures is a must-have for your library.
Date published: 2019-03-07
Rated 5 out of 5 by from Amazing accomplishments Took me a few lectures to get into the rhythm of the subject again (age 58... been a few years since my last math class) but then I was hooked. Professor does a fine job of both presenting the thinker AND the thinking. I found it very engaging, understandable and well-paced. The video would seem a “must”, in order to fully benefit from the careful step-by-step proofs presented. Math proofs really can be fun, and sharpens your own thinking, too.
Date published: 2019-02-13
Rated 5 out of 5 by from What A Trip! If you like to read the 'Foreward' and 'Introduction' parts of a book to get the setting of what you are about to experience, then you will really enjoy taking this ride through the timeline of mathematical history, progress, and other exciting math discoveries. The professor stops at appropriate points and lets one get a view of who's doing what and why it is important. We get acquainted with personalities behind the names and even some of their little quirks. We become aware of how geographically vast was the interest in mathematical thinking. And the professor shares some of the unexpected delight in elegant results to profound problems - 'the mathematical stuff'. To top it all, Professor Dunham knows how to relate well with his students. As to intended audience, it helps to have something more than basic knowledge of mathematics but the professor sometimes goes to great depth to make sure he doesn't lose anyone regardless of background. This is a great course. I wish there had been more stops, its that good.
Date published: 2019-01-21
Rated 5 out of 5 by from good coverage of great men & great discovereys 3 December 2018 Great Courses Great Thinkers, Great Theorems #1471 Great coverage of major math people & ideas. Well presented, limited graphics, but OK Review the Tale of contents to see the scope of coverage. The guide book is limited in scope & value. It should have more detailed info. Presenter is OK, nothing exceptional, but OK.
Date published: 2018-12-04
Rated 5 out of 5 by from A WONDERFUL COURSE I have purchased many of your courses. I am an engineer and know math at a very high level. This course introduced me to many things I had not studied. It gave me an appreciation of Euclid and euclidian thinking I had not had. The selection and presentation of these great ideas and great thinkers was truly extraordinary. I recommend this most highly
Date published: 2018-11-29
Rated 5 out of 5 by from Wonderful topics with great presentation I enjoyed this Great Course immensely. Excellent topic and great presentations.
Date published: 2018-11-03
Rated 5 out of 5 by from GREAT IDEAS, GREAT LECTURES I have an earned Ph.D. in Mech. Engr. and am very educated in applied Mathematics. I have purchased a number of your math courses and have enjoyed them. In all of my studies and research I have never encountered some of the things Dr Dunham shared and I have a hobby of reading Math. history. I very much enjoyed the sessions on Euclid and Euler. I heartily congratulate Dr Dunham for this beautiful and clear presentation. If I have any criticism it would be that he sometimes goes into too much detail while discussing certain simple expressions. Dr. Richard Pendleton
Date published: 2018-10-06
Rated 5 out of 5 by from Great Thinkers, Great Theorems Easy to follow and enjoyable to watch. Excellent presentation!
Date published: 2018-09-29
Rated 5 out of 5 by from Simply Delightful I have listened/viewed well over 100 Teaching Company courses over the past 20 years and rarely take the time to comment. I do find them generally outstanding, almost never disappointing. This one is at the top of my heap. Prof Dunham's style, organization, the twinkle in his eye, his command of the material-- were so enjoyable, I was truly sorry when I came to the end. The course was not advertised as a math course per se but rightly as a math appreciation course. I have over 50 semester hours of undergraduate and graduate math and am familiar with much of the content and personalities but this was a unique perspective on the great theorems and great men. So very enjoyable.
Date published: 2018-09-02
Rated 5 out of 5 by from A wonderful course. I was sad to see it end This course touches on the history of math, the great men (and woman) behind the history, and some of the theorems and proofs they established. I am a math major, had encountered most of the names mentioned, but this course gave me a greater appreciation for the mathematicians, the times they lived in, and even some of their personal "oddities". Really enjoyed it, especially the historical sense conveyed to what could have been a disjoint collection of names. (e.g. as presented in an academic setting)
Date published: 2018-08-17
Rated 5 out of 5 by from Great features and well presented I learned a lot about the subject of mathematics and I'm very happy that I bought this course.
Date published: 2018-08-06
Rated 5 out of 5 by from A fun look at a few mathematical ideas and people I just finished viewing the 24 lectures in this course. The selection of people began with Euclid and ended with Cantor at the turn of the 20th century. The professor told the stories of some of the mathematicians (thinkers) and their lives. He also described one or more of their results in detail. His style of presentation was an appropriate mix of relaxed and excitement when a topic warranted it. He included some basic algebra calculations that was necessary, and on these he was going very slow. For some people this may be too slow but they can fast forward. And of course, if something goes by fast there is always the review. The video format is essential for this course because there are a lot of diagrams and some calculations. The only complaint is about what is missing from the course. If an expanded edition of this course is planned in the future, maybe to 36 lectures then here is what I would recommend as a list of new names to choose from: Liouville, Hamilton, Lagrange, Galois, Noether, Cauchy, Poincare, Hilbert. Including a mathematician from India like Madhava who knew a great deal about infinite series of functions, including sine, well before Newton and Euler, and also Liu from China would round things up nicely! Anyway, the current 24 lectures are very informative and the delivery is well done. Time (and money) is well spent on them.
Date published: 2018-07-22
Rated 5 out of 5 by from Math major's opinion I really enjoyed this course. It made me feel small to realize that some people have more talent and genius in their little finger than I have in my whole body. Even though I studied math (many years ago), there are ideas that I had never heard. In a short course like this of course, there are several concepts not covered, such as Fourier transforms. I would like to see a second edition.
Date published: 2018-07-04
Rated 5 out of 5 by from Clumsy Title Being a bit of a history buff and trained technologist, I acquired this course in spite of its blah-blah title partly because of its description and also to check out the author who teaches at a local college. To my surprise, of around a dozen Great Courses that I acquired over the years, this is by far the best in clarity, presentation and sheer entertainment. Very nice job !
Date published: 2018-07-03
Rated 5 out of 5 by from Visualize Yourself as a Great Thinker This material is not difficult, yet challenges my reasoning capability. Couched in biographical and historical anecdotes, the reasoning of humanity's great mathematicians is presented clearly. I'm learning to think greatly, and have added a few useful formulas to my own mathematics toolkit.
Date published: 2018-07-01
Rated 4 out of 5 by from Very interesting Professor Dunham is very enthusiastic and presents the mathematics slowly and carefully so that anyone can follow easily. I understand Euclid's contributions as seminal in the field, but lectures 2 and 3 of this course is mostly a rehash of high school geometry and could have been eliminated, or at least, other material from Euclid could have been substituted. Dr. Dunham could have saved about an hour of lecture time if he wouldn't have started almost every sentence with "let me show you..." or "let me explain...". Just say it, man.
Date published: 2018-06-28
Rated 5 out of 5 by from Nice presentation. William Dunham makes the subject(s) interesting and fun. I looked forward to each new chapter
Date published: 2018-06-19
Rated 5 out of 5 by from Exciting Math People in History! I enjoyed each topic on a different Math Theorist. Some of the lectures devoted and extra lecture for some of the Math Theorists.
Date published: 2018-05-03
Rated 5 out of 5 by from Great Course I thoroughly enjoyed this course. Professor Dunham is a wonderful teacher. His enthusiasm and passion is captivating.
Date published: 2018-04-05
Rated 5 out of 5 by from Wonderful Lecture Series I currently own almost 20 lecture series from Great Courses, but this is the first that I've enjoyed so much that I feel compelled to praise it with a review. The presenter, William Dunham, is my personal favorite lecturer so far. He's animated, engaging, concise, thoroughly informative, very well spoken, and never repetitive. He's simply one of the best teachers I've ever seen. Note that this is a math HISTORY series, and is not necessarily intended to teach mathematics. While some mathematics is demonstrated, that simply isn't the main focus of the course. For what it is though, I think it's excellent and very, very enjoyable. I love it.
Date published: 2018-04-01
Rated 5 out of 5 by from Love the course I loved this course! I majored in math in university but I switched my major to accounting half way thru. I always regretted not getting my math degree, so I pick up this course just out of interest. This course reignited my love of pure math, and I was so excited to get home every day to listen to the lectures.
Date published: 2018-03-20
Rated 5 out of 5 by from Terrific Course I purchased this course to further assist my desire to learn about how and why certain mathematical tools came about. For example, "who first realized that they needed The Calculus to solve a particular problem"? This course exceeded my expectations. Professor Dunham is a gifted speaker and at times seemed to be lecturing without aids. He just knows his subject. This is a chronological journey from Euclid to the present and he touches all the advancements. Professor Dunham is very patient with his proof calculations, so a non math person should not be afraid. His book "Journey Through Genius" is a nice companion piece to this course.
Date published: 2018-01-30
Rated 5 out of 5 by from Great Thinkers, Great Theorems Great review of history and mathematics. Professor William Dunham was one of the best of the many Great Courses teachers I have watched or listened to. He makes the subject interesting and informative.
Date published: 2018-01-21
Rated 5 out of 5 by from Great Teacher, Great Course My wife who is not a math/science person (other than marrying me) listened (in the background) to a bits and pieces of some of these lectures while I was watching. To my surprise, she piped up during lecture 23, “Cantor and the Infinite” and said, “This is how math should be taught”. And then expanded for several minutes. As an English major, I’m sure that she could spell “set theory” but that would be about it. Other than a statistics course in grad school, she had never liked any math class she had ever taken. Yet while listening to Dr. Dunham’s presentation of “the completed infinite” as opposed to “the potential infinite”, she loved the concept. A long way of saying that Professor Dunham knows how to present abstract mathematical concepts in a fashion and manner that can be understood and appreciated, even by those who do not love, or even like, math. To be sure, those with a sound math background may occasionally be put off when some concepts are presented in a deliberate fashion. Dr. Dunham clearly expects that his audience has basic algebra, geometry and trig. He does include a few gentle reminders should we have forgotten the definition of sin or cos along the way, so clearly he considers than many of us have forgotten some of what we once knew. I think that familiarity with differential and integral calculus while not necessary, would make the course even richer that it is. In short, while this is a course about mathematics and mathematicians, a deep knowledge of math in not at all necessary. There is even more for those who have a sound math background. The beauty of some of the theorems presented goes without saying and I found even more in the brief bios of many of the major players. For example while I knew about the development of algebra in the Islamic world, I had no idea at all that negative numbers at that time were not allowed, nor what this meant in the difficulty in solving quadratic equations. This lecture also treats us to a geometric representation of completing the square eventually leading to the algebraic quadratic formula. Nice and well done Al-Khwarizmi. I am ashamed to admit that I knew next to nothing about Cardano and his very colorful personality in Italy during the renaissance and the math competitions and challenges during that time. That people kept their discoveries to themselves in order to gain advantage in a challenge was completely unknown to me. Simaliry while everyone knows about Newton and Leibniz, the Bernoullis involvement was not something I knew much about, much less the brothers’ rivalry and caustic personalities. Just as I learned much about Euler the person, as opposed to master mathematician. There is of course much more. For me the last two chapters were the highlights. The concepts formulated by Georg Cantor are truly mind numbing and often counter-intuitive. Get the course and have as much fun with them as I did. History, biography and math, with comparisons to art and music. What else could one want?
Date published: 2018-01-03
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