Queen of the Sciences: A History of Mathematics

Course No. 1434
Professor David M. Bressoud, Ph.D.
Macalester College
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Course No. 1434
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Course Overview

In the 17th century, the great scientist and mathematician Galileo Galilei noted that the book of nature "cannot be understood unless one first learns to comprehend the language and read the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures, without which it is not humanly possible to understand a single word of it."

For at least 4,000 years of recorded history, humans have engaged in the study of mathematics. Our progress in this field is a gripping narrative, a never-ending search for hidden patterns in numbers, a philosopher's quest for the ultimate meaning of mathematical relationships, a chronicle of amazing progress in practical fields like engineering and economics, a tale of astonishing scientific discoveries, a fantastic voyage into realms of abstract beauty, and a series of fascinating personal profiles of individuals such as:

  • Archimedes, the greatest of all Greek mathematicians, who met his death in 212 B.C. at the hands of a Roman soldier while he was engrossed in a problem
  • Evariste Galois, whose stormy life in 19th-century radical French politics was cut short by a duel at age 20—but not before he laid the foundations for a new branch of modern algebra called Galois theory
  • Srinivasa Ramanujan, an impoverished college dropout in India who sent his extraordinary equations to the famous English mathematician G. H. Hardy in 1913 and was subsequently recognized as a genius

An inquiring mind is all you need to embark on this supreme intellectual adventure in The Queen of the Sciences: A History of Mathematics, which contains 24 illuminating lectures taught by award-winning Professor of Mathematics David M. Bressoud.

The "Queen of the Sciences"

The history of mathematics concerns one of the most magnificent, surprising, and powerful of all human achievements. In the early 19th century, the noted German mathematician Carl Friedrich Gauss called mathematics the "queen of the sciences" because it was so successful at uncovering the nature of physical reality. Gauss's observation is even more accurate in today's age of quantum physics, string theory, chaos theory, information technology, and other mathematics-intensive disciplines that have transformed the way we understand and deal with the world.

The Queen of the Sciences takes you from ancient Mesopotamia—where the Pythagorean theorem was already in use more than 1,000 years before the Greek thinker Pythagoras traditionally proved it—to the Human Genome Project, which uses sophisticated mathematical techniques to decipher the 3 billion letters of the human genetic code.

Along the way, you meet a remarkable range of individuals whose love of numbers, patterns, and shapes created the grand edifice that is mathematics. These include astrologers, lawyers, a poet, a cult leader, a tax assessor, the author of the most popular textbook ever written, a high school teacher, a blind grandfather, an artist, and several prodigies who died too young.

You find the problems and ideas that preoccupied them can be stated with the utmost simplicity:

  • Is there a method for finding all the prime numbers below a given number? (Eratosthenes, c. 200 B.C.)
  • The equation xn + yn = zn has no whole-number solutions where n is greater than 2. (Pierre de Fermat, 1637)
  • What would it mean if space is non-Euclidean; that is, if it is not flat as described by Euclid? (János Bolyai, 1832)

The second of these propositions, called Fermat's last theorem, is one of the most famous in mathematics. It was followed by this postscript in the book where Fermat jotted it down: "I have a truly marvelous demonstration, which this margin is too narrow to contain." Since Fermat never wrote out his proof, his statement served as a tantalizing challenge to succeeding generations of mathematicians.

The difficult road to a proof of Fermat's last theorem is a theme that surfaces throughout the last half of this course. Among other intriguing facts, you learn that Circle Limit III, a mathematically inspired woodcut by the Dutch artist M. C. Escher, relates directly to the technique that eventually showed the way to a solution by mathematician Andrew Wiles in 1994.

See Mathematics in Context

Professor Bressoud begins the course by defining mathematics as the study of the abstraction of patterns. Mathematics arises from patterns observed in the world, usually patterns expressed in terms of number and spatial relationships. Furthermore, it is a human endeavor found in every culture extending back as far as records go.

The Queen of the Sciences focuses on the European tradition that grew out of early mathematics in Mesopotamia, Egypt, and Greece. The first eight lectures examine these foundations and the contributions of India, China, and the Islamic world, which played important roles in the development of European mathematical achievements. For example:

  • The earliest recorded use of zero as a placeholder was found in a Hindu temple in Cambodia constructed in A.D. 683. Zero had been used a few decades earlier by the Indian astronomer Brahmagupta not as a placeholder but as a number that could be manipulated.
  • An approximation for pi of 355/113 was developed in the 5th century by the Chinese astronomer Zu Chongzhi. Correct to seven decimal places, this approximation would remain the most accurate estimate for more than 1,000 years.
  • The first treatise on al-jabr (restoring) and al-muqabala (comparing)—the process of solving an algebraic equation—was written in A.D. 825 by the Islamic mathematician Abu Jafar al-Kwarizmi. Al-jabr eventually would become the word "algebra" and al-Kwarizmi would become the word "algorithm."

The next eight lectures show how Western Europe, beginning in the late Middle Ages, gathered existing mathematical ideas and refined them into new and powerful tools. The heart of this section is five lectures on the 17th century, when the separate threads of geometry, algebra, and trigonometry began to meld into a cohesive whole, one whose fruits included the creation of calculus by Isaac Newton and Gottfried Wilhelm Leibniz.

Calculus is another recurring theme throughout this course, making its first appearance in the method of exhaustion developed by the ancient Greeks. In the early 17th century, John Napier initiated the idea of logarithms, which added to the examples from which the general rules of calculus emerged. You discover how, in his ceaseless toying with his new invention, Napier chanced on a base that is the equivalent to the modern base of the natural logarithm used in calculus: the famous number now known as e (2.71828 ... ).

After studying the 18th-century contributions of Leonhard Euler—possibly the greatest mathematician who ever lived—you look at how art has influenced geometry and all of mathematics. You investigate mosaics from the Alhambra, prints by M. C. Escher and Albrecht Dürer, and other intriguing shapes and forms.

In the final eight lectures, you explore selected mathematical developments of the past 200 years, including:

  • Joseph Fourier's solution in the early 1800s to the problem of modeling heat flow, which led to a powerful technique called Fourier analysis for making sense of a wide range of complex physical phenomena
  • Bernhard Riemann's new system of geometry in the mid-1800s, which provided a framework for the revolutionary conception of space developed by Albert Einstein in his general theory of relativity
  • Grigori Perelman's recent, startling solution to the Poincaré conjecture proposed by Henri Poincaré in 1904, which earned Perelman the prestigious Fields Medal (which the reclusive Russian mathematician declined)

Learn with an Experienced Teacher

Experienced in teaching mathematics to students of all levels, Professor Bressoud was a Peace Corps volunteer in the West Indies before earning his Ph.D., where he taught mathematics and science to intermediate students. In addition, he has written numerous articles on mathematics education and related issues, including four textbooks that draw heavily on the history of mathematics.

His depth of knowledge and passion for teaching mathematics—which earned him the Mathematical Association of America's Allegheny Mountain Section Distinguished Teaching Award—make your journey through the story of mathematics all the more riveting and exciting.

Mathematics has exhibited an inexhaustible power to illuminate aspects of the universe that have been cloaked in mystery. In charting the storied history of its evolution, The Queen of the Sciences not only illustrates how these mysteries were revealed but exposes, with a wealth of insight, the enormous efforts that went into deciphering our natural world.

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24 lectures
 |  Average 30 minutes each
  • 1
    What Is Mathematics?
    You explore the peculiar nature of mathematics. Why is it that abstractions that arose in one context can lead to unexpected insights in another? This lecture closes with a look at the major conceptual advances that are the focus of this course. x
  • 2
    Babylonian and Egyptian Mathematics
    Egyptian and Mesopotamian mathematics were well developed by the time of the earliest records from the 2nd millennium B.C. Both knew how to find areas and volumes. The Babylonians solved quadratic equations using geometric methods and knew the Pythagorean theorem. x
  • 3
    Greek Mathematics—Thales to Euclid
    This lecture surveys more than 300 years of Greek mathematics, from Thales and Pythagoras to Euclid. Euclid's Elements covers much of the mathematical knowledge of the time and is considered the most important book of mathematics ever written. x
  • 4
    Greek Mathematics—Archimedes to Hypatia
    Foremost among Greek mathematicians was Archimedes, who developed methods equivalent to the modern technique of integration. Hypatia was the first woman known to have made important contributions to mathematics and was one of the last scholars of the famous Museion at Alexandria. x
  • 5
    Astronomy and the Origins of Trigonometry
    The origins of trigonometry lie in astronomy, especially in finding the length of the chord that connects the endpoints of an arc of a circle. Hipparchus discovered a solution to this problem, that was later refined by Ptolemy who authored the great astronomical work the Almagest. x
  • 6
    Indian Mathematics—Trigonometry Blossoms
    You journey through the Gupta Empire and the great period of Indian mathematics that lasted from A.D. 320 to 1200. Along the way, you explore the significant advances that occurred in trigonometry and other mathematical fields. x
  • 7
    Chinese Mathematics—Advances in Computation
    At least as early as the 3rd century B.C., Chinese civil servants had to solve problems in surveying and collecting taxes. x
  • 8
    Islamic Mathematics—The Creation of Algebra
    Algebra was perfected here in the 9th century by the great mathematician Abu Jafar al-Kwarizmi, whose name would become the word "algorithm." x
  • 9
    Italian Algebraists Solve the Cubic
    Mathematics from the Islamic world gradually spread into Europe in the 13th century, starting with Leonardo of Pisa, also known as Fibonacci. Italian mathematicians began to make original contributions in the 16th century when they discovered how to solve the general cubic and quartic equations. x
  • 10
    Napier and the Natural Logarithm
    Working at the turn of the 17th century, John Napier found a way to facilitate calculation for astronomers by inventing logarithms. He also discovered the number now designated by the letter e. x
  • 11
    Galileo and the Mathematics of Motion
    In the early 17th century, Galileo Galilei made important innovations in the study of motion, establishing the pattern of relying on mathematical models to explore physical phenomena. René Descartes and Christiaan Huygens would build directly on his insights. x
  • 12
    Fermat, Descartes, and Analytic Geometry
    A lawyer for whom mathematics was an avocation, Pierre de Fermat was instrumental in the origins of calculus. In 1637, both Fermat and René Descartes published explanations of analytic geometry. x
  • 13
    Newton—Modeling the Universe
    Isaac Newton famously said, "If I have seen further, it is by standing on the shoulders of giants." You learn who those giants were and explore Newton's invention of calculus to explain the motions of the heavens in Principia Mathematica, published in 1687. x
  • 14
    Leibniz and the Emergence of Calculus
    Independently of Newton, Gottfried Wilhelm Leibniz discovered the techniques of calculus in the 1670s, developing the notational system still used today. x
  • 15
    Euler—Calculus Proves Its Promise
    Leonard Euler dominated 18th-century mathematics so thoroughly that his contemporaries believed he had solved all important problems. x
  • 16
    Geometry—From Alhambra to Escher
    You look at the influence of geometry on art, exploring the intriguing types of symmetry in Moorish tiling patterns. You also examine the geometrical experiments of M. C. Escher and August Möbius. x
  • 17
    Gauss—Invention of Differential Geometry
    You explore Carl Friedrich Gauss and his interest in geometry on various kinds of surfaces, including his work on the parallel postulate, which laid the foundations for non-Euclidean geometry. x
  • 18
    Algebra Becomes the Science of Symmetry
    Algebra underwent a fundamental change in the 19th century, becoming a tool for studying transformations. One of the most tragic stories in mathematics involves Evariste Galois, who invented a set of transformations before dying at age 20 in a duel. x
  • 19
    Modern Analysis—Fourier to Carleson
    By 1800, calculus was well established as a powerful tool for solving practical problems, but its logical underpinnings were shaky. You explore the creative mathematics that addressed this problem in work from Joseph Fourier in the 19th century to Lennart Carleson in the 20th. x
  • 20
    Riemann Sets New Directions for Analysis
    Bernhard Riemann left two famous legacies: the Riemann hypothesis, which deals with the distribution of prime numbers and is the most important open problem in mathematics today, and Riemann's new system of geometry, which Einstein used to develop his general theory of relativity. x
  • 21
    Sylvester and Ramanujan—Different Worlds
    This lecture explores the contrasting careers of James Joseph Sylvester, who was instrumental in developing an American mathematical tradition, and Srinivasa Ramanujan, a poor college dropout from India who produced a rich range of new mathematics during his short life. x
  • 22
    Fermat's Last Theorem—The Final Triumph
    Pierre de Fermat's enigmatic note regarding a proof that he didn't have space to write down sparked the most celebrated search in mathematics, lasting more than 350 years. This lecture follows the route to a proof, finally achieved in the 1990s. x
  • 23
    Mathematics—The Ultimate Physical Reality
    Mathematics is the key to realms outside our intuition. You begin with Maxwell's equations and continue through general relativity, quantum mechanics, and string theory to see how mathematics enables us to work with physical realities for which our experience fails us. x
  • 24
    Problems and Prospects for the 21st Century
    This last lecture introduces some of the most promising and important questions in the field and examines mathematical challenges from other disciplines, especially genetics. x

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Your professor

David M. Bressoud

About Your Professor

David M. Bressoud, Ph.D.
Macalester College
Dr. David M. Bressoud is the DeWitt Wallace Professor of Mathematics in the Department of Mathematics and Computer Science at Macalester College. He earned his bachelor's degree in Mathematics from Swarthmore College and his master's degree and Ph.D. in Mathematics from Temple University. Professor Bressoud is experienced in teaching mathematics to students of all levels. As a Peace Corps volunteer before earning his Ph.D.,...
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Queen of the Sciences: A History of Mathematics is rated 4.6 out of 5 by 58.
Rated 4 out of 5 by from Good History I am up to lesson 10 but so far it has been a very interesting history. I would like to see/hear more of his stories to go along with the historical facts. Maybe make it a little more rigorous.
Date published: 2019-02-05
Rated 5 out of 5 by from Long Live the Queen! Professor David M. Bressoud’s lectures are a remarkable blend of fascinating history, close reasoning, and infectious passion for his subject matter. I wish I had had a teacher as engaging and clear as he is to present mathematics to me five and six decades ago. Though I did study mathematics back then, up through my second year of university, it has turned out that I did not have much practical need for algebra, trigonometry, calculus, so-called “imaginary” numbers, etc., during my subsequent working life. It feels great to be reminded of how aesthetically and philosophically pleasing those subjects can be. Do not expect “Queen of the Sciences: A History of Mathematics” to be either a how-to or a refresher course. As its title implies, the focus is on history. While sharing biographical information and cultural context about key thinkers and their discoveries, in roughly chronological order through the past 4000 years, it is true that Dr. Bressoud does also demonstrate some illustrative problems and solutions, mostly by way of explaining what kinds of things those thinkers were motivated to study, either because of their individual curiosity or because of societal spurs during particular eras. Be advised, however, that unless you have already got a familiarity with higher math, or you have a prodigy’s intuitive grasp of things mathematical, then you will need to consult texts or take other courses in order to understand more than just the gist of those illustrative examples. Of course, the biographies and general history discussed do have a certain stand-alone worth. The approach here reminds me of several presentations I’ve enjoyed on the history of music, wherein a presenter might share biographical and anecdotal information about someone like Beethoven, say, and then go on to give a revealing analysis of some sampling of Beethoven’s accomplishments, perhaps the form and themes of the First Movement of the Fifth Symphony—not a thorough review of everything Beethoven achieved and not a digression from the history of music to thorough training in music. Dr. Bressoud’s hand movements to illustrate such things as how the curve of a particular function might appear on a graph are quite good, better than those of most math professors I have known, but I must cite in reviewing this course that hand movements are too often all that is shown. I do not blame the professor for this shortcoming. It seems to me to be more a weakness in the overall staging and/or the videography for the course. Sometimes, Dr. Bressoud does appear in an inset while a graph or other display is simultaneously shown—too infrequently, in my opinion. It is said of Srinivasa Ramanujan, the Indian mathematical genius (1887–1920), that he regarded numbers as his personal friends. I have the same impression of Dr. Bressoud, am grateful for his Great Course, and highly recommend it.
Date published: 2018-09-20
Rated 4 out of 5 by from More graphics The courses need more graphics in the form of documentaries. A professor talking with no graphics is very difficult to follow.
Date published: 2018-07-29
Rated 5 out of 5 by from This course besides the excellent presentation and explanation provided background on the names I saw when studying Mathematics in undergraduate and graduate school. I also especially liked the Mobius transformation with ants crawling on it. (Picture in background.) I have not seen this since 1971. Yes I am really old, as my grand daughter informs me.
Date published: 2018-03-19
Rated 5 out of 5 by from History of Math; Not Math As someone who has a sound background in math, but is not a mathematician, I was really interested in this course. And was not disappointed. Professor Bressoud presents a fine history of math, without delving deeply into much of the math behind the mathematical concepts presented. Now this is a fine needle to thread and I think that Dr. Bressoud does so admirably. It is a hard task to not exclude those who are interested in the history (but not math itself) and keep those interested, who wish for rigorous proofs to be presented. I count my self as one of those who would have liked a bit more math, but I also acknowledge that the course would need another 12 lectures or so in order to accommodate more math, as I would not want any of the history, background or biographical material of the named mathematicians to be eliminated. And as I found this background material fascinating, clearly the course meets (for me) its goal. (Not to mention that rigor in some areas would have left me behind) There were a few times that I wished for more graphics, but the presentation of Escher’s Circle Limit III was outstanding. Other highpoints were the lecture on Euler, the all too human battle between Newton and Leibniz, the first half-dozen lectures setting the background, the individual mathematicians challenging each other during the Italian Renaissance and the weaving of Fermat’s Last Theorem into quite a bit of the last half of the course. I thought that Professor Bressoud came across as one who really knew and loved his material, but who was not particularly dynamic in his presentation. And he could have done a better job in lecture 10, describing natural logarithms and their importance. Otherwise, first rate.
Date published: 2018-03-09
Rated 5 out of 5 by from Interesting History This course was exactly what I wanted. I have often wondered, "Who was the first person that had a problem that required The Calculus to solve it"? This is a chronological journey of mathematical discoveries and the genius' behind them. I found Professor Bressoud to engaging, articulate and well prepared. At times I did wish that he would delve a little more into the math behind the topic, but that was not his intention. To supplement this course, I purchased "Great Thinkers, Great Theorems" by Professor Dunham. These two sets together answered all my questions admirably.
Date published: 2018-01-30
Rated 5 out of 5 by from Uniquely informative and engaging Professor Bressoud understands mathematics at a deep level that is unusual even for most professional mathematicians; he is particularly well versed in the relationships of mathematics to the empirical sciences. His account of the origins and history of trigonometry was a revelation! His presentations require more than passive listening; the learner must actively participate to follow the ideas and explanations. But this is an asset, not a liability!
Date published: 2017-12-04
Rated 4 out of 5 by from Good history and somes gems Prof. Bressoud promises right at the start to fill in what I always felt was missing from traditional math teaching : to examine the motivation leading to mathematical ideas and the difficulties encountered as the ideas were developed. A tall order which about half filled most of my expectations. The value of this course is that it provides the big picture, which is missing from the traditional teaching of mathematics – always segmented in unconnected blocks without any attempt to make the connection. This is not a maths course. You will hear about power series but just enough to understand why maths in antiquity went beyond calculating areas and volumes and why anyone would have bothered to work on extra dimensions to address astronomy observations. Prof. Bressoud reviews some of the big ideas from 4 millennia of mathematics history, back to Babylonia. The course is more about the history of maths and the significant milestones. Useful for someone who is already familiar with the concepts, the difference a nerd who just does the equation and absolutely no curiosity and someone who wants to learn more. You will learn how the heritage was preserved by successive transmission to other civilizations as the precious works were abandoned in their birthplace and were translated and amplified elsewhere. Why only a 4-star rating ? Mostly because of incomplete expositions and also because of the monumental works offered by The Great Courses, namely: - Grossman’s Thermodynamics - Wolfson’s Physics in Our Universe - Devaney’s Differential Equations – Visual Method These courses set the bar really high and the highest rating is limited to 5 stars. So, right off the starting line Prof. Bressoud’s work is not of the same scale as my three gold standards. Tough to be a star in a roomful of aces. Just do not let my less-than-perfect rating of this course discourage you. This course is beyond “good”, there are gems in there despite some less than lively delivery of the lectures. Lecture 16 is one such gem. A graphic illustration of the concept of transformation which I never saw anywhere even though I had to use them. Another gem is Lecture 18 which establishes transformations as the key to finding exact roots of higher-degree polynomials and provided my first exposure to the importance of symmetry in mathematics. Lecture 23 adds some context information to Maxwell’s equations of electromagnetism even though I did use them extensively to study propagation of microwave frequencies in rectangular waveguides. The graphical explanation of the retrograde path of Mars is very good. These gems and the frequent references to Escher Circle 3 Limit graph make me forgive the shortcoming of Lecture 10 which deals with logarithms. The explanation of how Napier calculated logarithms to simplify calculations on astronomic data. This is done without any graphics and is particularly dry. Sahara high noon dry. The arguments make sense but the whole demonstration remains obscure. Not cool. Words without pictures can only carry so far – not far enough in this case. I had been wondering how logarithms were calculated way before HP’s extraordinary HP 35 pocket calculator (1974) – I would have really appreciated a more detailed demonstration on how Napier only needed to perform about 200 calculations which were the basis for the extended table. Similarly, Lecture 19 covers the Fourier series but in a superficial way. Being myself familiar with this concept, I could almost hear newcomers wondering in the back of the classroom “so what ?” as this lecture begs for the explanation of how in infinite series actually makes calculations simpler. This lecture screams for a bit less math theory and at least a basic practical use of this powerful tool. Another flaw is in Lecture 23 – I cannot understand why the 4 beautiful equations were not shown. And for all the talk about symmetry, the absence of Emmy Noether and her deeply profound linking symmetries and conservation laws of physics is inexplicable. Lecture 20 on the zeta function and Riemann’s hypothesis was especially dry, catering more to a mathematician than to an engineer. Differential geometry is mentioned but also as a dry concept without any illustration. I would have gladly traded the whole lecture for a more concrete illustration of differential geometry. Overall, I did get my money’s worth with this course. I recognize that some people will find it rough sailing at times.
Date published: 2017-12-03
Rated 5 out of 5 by from very good presentation Instructor does a good job of presenting the history of mathematics. He gives a clear and organized presentation cover a fast amount of information.
Date published: 2017-05-10
Rated 5 out of 5 by from QUEEN OF SCIENCES: MATHEMATICSI I've just finished watching this coarse for the second time and I hope to watch it again. I'm 79 years old barely graduated college in 1960, but I've always had a fascination with mathematics and mathematicians. The lecturer was outstanding, he brought the subject to life for me.
Date published: 2017-04-23
Rated 4 out of 5 by from An adventure through Time ... I completed 'Queen of the Sciences: A History of Mathematics' a few months ago and decided to come back and share some thoughts on this lecture series. I work in the biological sciences and have not performed Math since college. However, this is NOT a mathematics course, it is a HISTORY course. A few of the previous reviewers were critical of the professor for not "teaching" a mathematics concept very well, which seems a bit unfair given that this course is about the 'history of math' and not a course on how to perform mathematical functions. Fortunately for me, I am a lover of history. I also love the sciences, so this course seemed a natural fit for me and I was not disappointed. I was mesmerized by this course and must confess that I really enjoyed it. Anyone who shares a love of history and of the sciences should find that they too, would enjoy this lectures series. The structure of this course is essentially chronological, starting with the earliest math (even speculation of pre-history math) up to the present day. The material covered near the end of the course was mostly over my head but I was still able to grasp the general concepts that the professor was focusing on. As to the professor ... Professor Bressoud has a clear and distinct manner of speaking. His pronunciation and enunciation represent a level of articulation that is second to none. You will have no trouble understanding the good professor. However, his style of speaking is also adynamic. While it is evident from his speech that he is passionate about the subject, that passion doesn't translate into the camera as well as some of his colleagues at The Great Courses. He does not exude his enthusiasm quite as visibly as those other TGC professors do. This is not a criticism, just an observation. The lectures are all organized well and build on one another, as might be expected. For me, these lectures were an Adventure through Time. I continued to marvel at the genius of mankind and what we have achieved with our brains. Professor Bressoud explains the driving concepts that motivated great thinkers to expand our understanding and use of mathematics, dividing these concepts into several broad areas: civil administration (need for counting and maintaining inventory and taxes), Astronomy (need to understand trigonometric functions), etc. In addition to explaining the driving forces that advanced the devleopment of mathematics, he also enlightens us with historical examples of how pre-existing math furthered our understanding of the sciences (physics, economics, etc). The course will start with simple arithmetic and follow the development of geometry, algebra, trigonometry and the calculus. You will learn about number systems and number theory and how math traveled from one part of the globe to another. It really is an adventure. You do not need to be a mathematician to appreciate or to follow these lectures. You will learn about many of the great Mathematicians of the past along with some interesting and entertaining anecdotal stories. Just sit back and enjoy the adventure. This will be one of those courses that I revisit, at some point in the future. It is worth a second viewing. Cheers.
Date published: 2017-04-18
Rated 3 out of 5 by from Good, but could be much better I regret that I can only marginally recommend this course. Positive aspects. The course is well thought out and each lecture makes perfect sense. The prof obviously spent lots of time preparing the syllabus. He is well spoken and and his presentation style for purely descriptive material keeps one’s interest. Negative aspects. The prof really doesn’t know how to teach anything other than descriptive type historic material. When it comes to teaching conceptual topics such as Napier’s development of logarithms all he does his waves his hands around forming imaginary lines that only he can see. His explanation of Galileo’s work is even worse. When he’s done with all that waving he puts up simple graphic of what he’s allegedly just explained. That is NOT teaching. It’s just blabbing away. He doesn’t seem to have heard of actual demonstrations, computer graphics or even a blackboard! Even with negative comments I still (barely) recommend this course. I did learn about the history of math, but it could have been so much better.
Date published: 2017-03-12
Rated 5 out of 5 by from Great Excellent review with many little known antic dotes of math history. It is obvious the professor loves his work and knows how to share his enthusiasm.Loved the course.
Date published: 2017-03-03
Rated 5 out of 5 by from No Proof Required Having taken Maths, Physics, and Chemistry in the UK equivalent of Years 11/12, I went to university to do the same three at Degree level. In the first year I realised that maths at that level was of no practical use to anybody except mathematicians ! Yet, I had always been fascinated by the development (history) of the science. Hence I purchased this course. Prof Bressoud speaks clearly and with the measured delivery one would expect of a Mathematician. The historical parts were excellent, but, I have to say, I skipped over the laborious proofs. Not, to me, in the least bit interesting...
Date published: 2016-08-22
Rated 4 out of 5 by from Excellent except for "X" Overall, the depth and breadth of coverage was excellent! As a non-mathematician, getting an idea of the kinds of things which are widely unknown by the general public, that mathematicians have discovered and continue to puzzle over, is fascinating. And as someone who was introduced to mathematics through the “new” math of the 1960’s in which history was totally ignored, I am now convinced that historic background is essential. That said, and understanding that there is a limit to how much can be covered in one course, I would like to have had a little more depth in two areas. First, a more thorough explanation of “e” and the exponential function would have been welcome. In particular, a brief discussion pointing out that a relationship exists between “e”, compound interest (and Babylonian mathematics), growth and decay in the natural world, the Fibonacci series, and the golden mean, as well as the related fact, which was covered, that the exponential function is its own derivative/integral, would provide a better understanding of why “e” is so important. I would also like to have heard a concise intuitive statement explaining why the derivative is the inverse of the integral and vice/versa. Not much to ask! A major highlight which was worth the entire cost of the course, was the Arnold/Rogness video in Lecture No. 16 showing an animation of the Mobius transformations. I came away thinking (at least) that I actually understood what it was Mobius was doing. Similar animations showing the geometry of other functions, though no doubt difficult to produce, would certainly make mathematics a lot more exciting, never mind much more comprehensible. In general, additional visual aids, perhaps three times as many, would have made these lectures more enjoyable and understandable to watch. The ones that were used were exceptionally well done, particularly those in which the lecturer was visible in cameo in one corner. A picture is certainly worth a thousand words (or hand gestures) bringing me to my only major disappointment. As a retiree, while I count myself fortunate to have access to world class “experts in field” made available by the Great Courses, life being short, I also expect the "presentation" to be of highest professional quality. In fact, I expect to be entertained! Generally, Professor Goldman’s presentation was exceptionally well done except for one distracting habit, namely, moving his hands in cadence with every syllable of every word. This takes away from the instances in which he does effectively uses hand gestures for clarifying the verbal explanation, or for emphasis. That particular mannerism is certainly not restricted to this professor, but is also present in too many of the other Great Course DVDs. I sometimes wonder if it would be better to enlist the services of a professional actor to actually perform the script since the professor, after all, doesn’t have to answer any questions.
Date published: 2016-07-18
Rated 5 out of 5 by from Superb, detailed overview Though I've taken a number of higher-level mathematics courses over the decades, this Professor awes and informs me in each lesson as he reveals the intricate, and complex development of mathematics over the centuries and across the world. In each lesson, I have at least one "Wow! I didn't know that." moment which makes me want to go back and delve deeper into one area of mathematics or another. His presentation is clear, detailed, and quite easy to follow as he weaves through the simplest and most complex areas of Mathematics. I find it almost impossible to believe this one person can so well understand and understand virtually all areas of Mathematical theory.
Date published: 2015-10-24
Rated 5 out of 5 by from Excellent course: Destroying the monster Professor Bressoud really can transform a difficult subject in a agreeable and interesting hours of pure admiration by Mathematics. My formation is Law and History but I have a passion by Mathematics. All the lectures are very very interesting and our attention is focused in Professor´s capacity to explore each topic with deep knowledge. He begins with a short biographical introduction of each great Mathematician and finishes presenting us the construction of formulas and practical examples. Highly recommended. I guarantee you that your vision of Maths will change.
Date published: 2015-04-26
Rated 5 out of 5 by from Superb history A passionate lecturer ,an interesting subject and great visuals make this an absorbing series of lectures .
Date published: 2015-03-02
Rated 4 out of 5 by from Nice Overview of the History of Mathematics Professor Bressoud does a commendable job of leading us through the labrynthine history of mathematics, from its earliest beginnings through its flowering in the modern age. He has a very clear, compact, style of teaching, which is very conducive to the subject matter. For anyone who is fairly conversant in mathematical concepts and ideas, I would highly recommend the course. However, I gave it less than a five-star rating because for those who are only marginally fluent in mathematical concepts and ideas, I think that much of the train of development that Professor Bressoud outlines will be beyond the student's ability to comprehend and appreciate it. This is almost inevitable in a course on the history of mathematics, though I have seen some other presentations which have been able to keep more of it accessible to a general audience. Professor Bressoud is clearly trying to highlight - particularly in the later history of mathematics - the trains of thinking that he feels are most significant in the recent evolution of this broadening field, but in doing so, it only makes it painfully apparent that the general scope of mathematics today has become too broad to comprehend it in a holistic fashion. Still, there is much to love in this overview, even for those who have only had a cursory expoure to mathematical ideas, and so I am sure that everybody will come away with something of lasting value as a result of applying themselves to this course.
Date published: 2014-12-02
Rated 5 out of 5 by from Superb history of math Very interesting facts about the lives of great mathematicians. Clear explanations of important mathematical ideas. The professor's articulation is perfect. The best presentation of math to a general audience I have seen in any lecture or book.
Date published: 2014-11-16
Rated 5 out of 5 by from REPEAT VIEWING = EXPONENTIAL INSIGHTS Perhaps one of the best ways to gauge the true usefulness of any course over time is to count the number of repeat viewings you give it even when you already know the material. This course has a subtle accumulative affect that isn't apparent if you just watch once and stay on its' surface. The organization brilliantly elucidates literally hundreds of clear approaches to solving challenging intractable problems and it has reliably helped me break through blocks in my own approaches. Whenever I need elucidation of some subtle point in an obscure mathematical area, whenever I can't seem to get a start on solving some stubborn problem, viewing this course will reveal the block and it always offers me fresh and entirely different directions for thinking perspectives. I find myself returning to the presentations, watching them in sequence over and over again, in spite of knowing the material, and always with breakthrough results. This course is far more than an historical compendium and frankly, I've found it worth its' weight in gold. Thank you, and Bravo, Professor Bressoud.
Date published: 2013-10-09
Rated 4 out of 5 by from Excellent Presentation Dr. Bressoud does a great job presenting the material. Graphics are used effectively, and although they aren't always necessary I found them really helpful in a number of cases. I appreciate the way he combines a little bit of background about the math (where simple enough# with the history to enable people--particularly those familiar with math--to understand the material on a deeper level even though it's still not as deep as a math course itself. He's very passionate about the topic, and that makes the lectures fun to listen to. He also presents his subjective views in a couple very delimited places #e.g. his perspective on who are the best mathematicians, and an appreciation for the rare women in math history#, adding a bit of color to the lecture without presenting everything from a highly biased perspective. I can't give it 5 stars because I wish to reserve that for a very small set of courses I really loved, but this isn't too far away from that. It would be hard for a lecture on this topic to earn 5 stars for me, so it's impressive that it came close. It might have been better if he just omitted recent history rather than making what he admits to being a relatively arbitrary selection, and I found his presentation of the Newton/Leibniz dispute to be slanted a bit toward Leibniz #although not to a terrible degree). I really appreciate his passion for the topic and hope to see more of his lectures in the future.
Date published: 2013-07-12
Rated 4 out of 5 by from Nice overview, no graphs The course is a nice overview and the choice of topics is interesting and full of memorable historical sidelines. A couple of things could have greatly improve the course. First, graphs. At places, it is just ridiculous to try to explain complex graphical concepts just verbally without using actual graphs. What's the point of that? Also, a few topics definitely required background knowledge of the concepts to make sense. So, a couple of easy fixes would make it a great course, as otherwise the material and presentation are very high standard.
Date published: 2013-07-10
Rated 4 out of 5 by from Good history, not mathematics As other reviewers have noted, this is a history of mathematics, not a course in all of mathematics—which would have to be far longer, with mandatory problem sets with strict deadlines and grading, and carefully tailored to the students’ level of preparation. Professor Bressoud does a good job given the necessary limitations, though I agree that more visual aids would be helpful—I listened to it in the gym, usually with my iPhone screen blanked (which required converting the media type to iTunesU), and didn’t seem to miss much. I can’t speak to whether the course would be comprehensible to someone without solid grounding in most of the math covered. One nit, about his explanation of the Uncertainty Principle. It’s admittedly difficult to explain in terms comprehensible to the layman, without contradicting one of the philosophical interpretations of quantuum mechanics, and without suggesting that it’s merely a difficulty of measurement; I’m afraid Professor Bressoud didn’t quite manage it.
Date published: 2013-06-21
Rated 5 out of 5 by from Great Thematic Presentation This course is a 5 star 24 lecture presentation.The professor covers alot of mathematics with a lucid presentation because he develops the historical material within several unifing themes. The first theme is that mathematices is the abstraction of patterns of the world around us. This theme gets us through the first eight lectures that cover mathematics in early and late antiquity. The beginning of mathematics seems to lie with the Egyptians and Babylonians whose knowledge of integer operations, fractions and the "Pythagorean" theorem probably predate the pyramids. The Greeks didn't invent mathematics. As pirates they seem to have stolen it, but Euclid did prove the results in a revolutionary way and the Greeks did have a concept of the integral calculus in their approximation of the area and volume of conics (the method of exhaustion). With the Greeks the lectures bring astronomy in a another unifying theme that leads us through the Indians and Chinese civilizations. He covers Indian mathematics well beyond their contributions to base 10 integers and zero to show in detail their advances in trigonometry (for astromical/astrological calculations). In particular they were probably the first to invent the differential calculus to interpolate the values of sine and cosine functions. Then there is a lecture on Chinese mathematics where he gives extensive coverage to the Chinese development of advanced calculations of the roots of polynomials using what westen mathematics calls Pascal's triangle. He also evaluates the controversy over the transfer of mathematic advances from India to China for vise versa. The history transitions to "modern mathematics" with two lectures on Islamic and Italian Renaissance mathematices that focus on the development of algebra and the discovery of the general method for the solution of the cubic polynomial. The real impact of which is the incorporation of imaginary numbers in algebra in a systematic way. The theme of astronomy is picked up again as 17th century mathematics provides the tools for the Galilean-Newtonian revolution of physics as the science of motion. Here we cover logarithm, the vector, analytical geometry, and the synthesis of the differential and integral calculus. We learn here of the interaction of many forgotten contributors to these advances in physics and mathematics. Significant time is given to Fermet whose last theorem becomes a unifying theme of the coverage of 19th and 20th century mathematics. Eighteenth century mathematics becomes the triumphal advance of the calculus, but the lecturer also gives extensive time to the use of complex numbers in the calculus to lay a foundation for development of four and higher dimensional geometries in the 19th Century. Indeed the transition to the nineteenth century coverage begins with a lecture on geometry, rotational symmetries, translations and projective geometry and another lecture on Gauss's developments in differential and non-euclidean geometries. The themes for the 19th century now split. In the first theme pure mathematics is covered in the development through the work of Galois of algebra as a logic of symmetries that leads to group theory and algeraic-geometry. Significant time is given to the mathematics of the torus (donut shape) upon which doubly periodic (elliptic) functions live. These ideas all lead to later concluding lecture on the explanation of the logic of the 20th century proof of Fermet's last theorem. The second theme renews the idea of mathematics as a study of the patterns of nature. The developement of the calculus is renewed with the work of Fourier, Fourier series and his early study of heat flow in the 19th century, These ideas will later lead to another lecture that covers Maxwell's equations of electrodynamics. A lecture on the work of Bernard Riemann covers a number of topics including prime numbers but the theme of patterns in nature is picked up directily in his work on non euclidian geometry that was used in the later development of Einstein's theories of special and general relativity. This lecture includes some elegant graphic aninmations. These themes all allow an excellent frame work to understand the development of mathematics over a period of approximately 5,000 years. My criticisms of the course involve the material left out of the lectures because of time limitations. My first objection is that the professor did not develop Galois work as leading specifcly group theory. If he had he could have tied the theme of symmetries in nature to the 20th century development of the theory of quarks, quantum chromodynamics. This was a specific case where the math came first and the experimental discovery came later. Ultimately this shortcoming is curable by reading Roger Penrose's "The Road to Reality." The book is listed in the bibliography and recommended by the professor. This book develops the math theory and the physics with considrable riigor but assumes only a good high school background in mathematics. I have read it and the book is excellant. It does requires an attentive reading, but technical sections can be skipped when necessary and the narrative carries the meaning and message along. The second item is that discrete mathematics gets little attention especially combinatorics and graph theory. Limits to time are the obvious reason. This problem too is curable by picking up the 24 lecture course on discrete mathematices by Professor Arthur Benjamin. I highly recommend it to fill in these gaps. Lastly, there is little or no coverage given to set theory, Cantor Infinities, and the Godol incompleteness theorem. Nor is there a good specific reference to these areas in the Bibiliography to fill the gap. A reference should be added there. I would recommend a 1992 puzzle book by Raymond Smullyan, "Satan, Cantor & Infinity" as an accessable introduction to the subjects. These limitations aside I throughly recommend this course for its thematic development of a grand overview of the history and development of mathematics.
Date published: 2013-04-28
Rated 5 out of 5 by from Enjoyable Prof. Bressoud does a nice job doing a survey of the history of mathematics. He is very well organized. I enjoyed his selection of topics. His course guide and bibliography were complete. I liked his dry sense of humor. I particularly enjoyed how he discussed the lives of the mathematicians involved as well as their mathematics. I particularly enjoyed the stories of the older mathematicians such as Archimedes and Galileo -- especially Galileo's encounters with the pope. Overall, I would recommend this course to anyone interested in history or in mathmatics.
Date published: 2012-11-18
Rated 5 out of 5 by from I Only Wish I found this lecture series to be outstanding. The progression of the series is based on history which provides excellent insight into how mathematics all came together. If I had been exposed to this material before starting college calculus, my GPA would have been significantly different!! But even now, the history detailed by Professor Bressoud provided great insight - easily understood by all. If you hate math, you'll enjoy this lecture series even more.
Date published: 2012-08-24
Rated 4 out of 5 by from Almost five stars Well presented and interesting, this course is a wonderful historical perspective on mathematics. The only reason that this isn't five stars is that I would have liked additional graphics to correspond to the mathematic principals discussed.
Date published: 2011-09-07
Rated 4 out of 5 by from Comprehensive Survey Course This course provides a comprehensive history of mathematics. It started from the earliest known & recorded mathematics done by humans, which were the Babylonian, Egyptian and Greek mathematics. It continued all the way to the advances in mathematics in the 18th, 19th, 20th and even 21st century, including the solving of Fermat's Last Theorem, which I think is the climax of this course. A few aspects and stories of this course which I like include: - The fact that mathematics often produces 'excess content' and through this excess content the universe can be better understood (e.g., Maxwell's four equations, Einstein's specific & general theory of relativity). - Phytagoras, who said, "At its deepest level, reality is mathematical in nature." - The fact that trigonometry might have been invented in India. - The fact that Pascal's Triangle was first discovered by a Chinese mathematician (mid 11th century). - The great multitalented mathematician Euler (18th century). - The fascinating story of the young & brilliant Indian mathematician Srinivasa Ramanujan (1887-1920), and - The solving of the Fermat's Last Theorem. The only recommendation I have about this course is (hence the four stars): Some mathematical concepts should have been explained better. So when the professor talked about concepts such as theta functions, modular functions, elliptical function, Poincare conjecture, I felt a bit lost as these concepts were covered too quickly. But overall, it's a good, comprehensive survey course.
Date published: 2011-04-26
Rated 5 out of 5 by from Very well balanced presentation, excellent course! This course is a survey of the history of mathematics from ancient Babylon to the present. The course does not go into great depth on any specific topic, which was fine for me. I found the course very well presented, the instructor is enthusiastic, and I learned a lot about a subject which I formerly knew very little. It hit the sweet spot giving enough information to allow me to dig deeper, and not focusing on any one aspect over any other, which created a very nice balance in the subject material. The course builds up to several high points, one of which is a presentation of the proof of Fermat's Last Theorem, another is a discussion of the seven open questions of the Clay Institute, and a discussion of the solution of one of those problems. The material is presented at a level that is very accessible to an educated audience, and shows a lot of the interesting and engaging aspects of mathematics. It was really great to see the connection from the ancient Greeks to the modern era, to see several women mathematicians presented, to learn some of the modern aspects of the field of mathematics, and also to learn a bit about the instructor's area of interest and expertise. I also found it very interesting to see the mathematics of China, India, Japan, and many other countries. It was also very fun to learn some of the higher mathematics that is being done today. The instructor ties the line of information together very well, I found the course to be very good, and can heartily recommend it to anyone with an interest in mathematics or science.
Date published: 2010-09-12
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