Center for Lifetime Study
The Center for Lifetime Study provides opportunities for intellectual and cultural exploration and development for people of retirement age. It is connected to Marist College in Poughkeepsie, NY. This page represents the plans being made for an eight week course on the history of mathematics to be conducted beginning April 7 and concluding May 26. What follows is early planning for these lectures. Suggestions would be most welcome.
Title of the course: Marvels of Mathematics History
Time: 8 weeks
Abstract: Mathematics has a long and fascinating history. We will look at several individuals and events in mathematics that have positively influenced our modern world. We will consider Archimedes the Master, the contributions of the Arab world, Fermat's Theorem, the magnificent Euler, mathematics on the plain of West Point, Lewis Carroll's logic, women in mathematics, and Alan Turing's provocative question of whether computers can think. This course is designed for the inquisitive lay person who is willing to do a bit of advanced preparation and who wants to actively participate in an intellectual dialogue. Further information about the plans for this course is available at www.dean.usma.edu/math/people/rickey/talks/cls/ (which is this page).
Class Manager: Stan Schmidt
Presenter: V. Frederick Rickey, United States Military Academy, West Point, NY.
For high level biographical information about the individuals (and their work) who will be mentioned in these presentations, see the Dictionary of Scientific Biography, edited by Charles Coulson Gillispie. This is available in the Marist Library (Q141 D5 1981) and the Vassar Library (Q141 D5). If you would prefer to look on the web, the St Andrews site in Scotland usually has reliable information on individuals and their contributions.
Lecture 1: Archimedes, A Genius from Antiquity.
Archimedes was the greatest mathematician of antiquity, and one of the greatest of all time, but his writings were difficult and so survive in very few copies, some in unique copies. The most fascinating of these, which contains his wonderful work that we call "the Method," was sold at auction by Christie's in 1998. This manuscript was copied in the tenth century, palimpsested in the twelfth, rediscovered and published early in the twentieth, and sold at auction in 1998. It is presently under restoration and extensive scholarly study at the Walters Art Gallery in Baltimore. Scholars have great hope for what the manuscript will reveal. All of this makes for a fascinating story. To begin, we will discuss what little is known of the life of Archimedes, discuss a few of his contributions to mathematics and then describe his Method and debate whether it was a precursor of the calculus. Our main focus will be on the history of this manuscript, its restoration by the Walter's staff and its study by scholars.
Before the lecture:
Further reading:
Show and Tell:
Thoughts about things to include.
Lecture 2: The Arab World Preserves and Expands Mathematics.
The Arabic speaking world played a vital role in the development of mathematics. They valued learning and so preserved the Greek texts from the ancient world. They translated them into Arabic, developed those ideas, and created entirely new areas of mathematics such as algebra. We will discuss the work of a number of important mathematicians, including al-Khwarizmi (whose work gave us the word 'algebra'), Al-Haytham (who is pictured on the new Iraqi 10,000 dinar note), and Omar Khayyam (the poet who worked on cubic equations).
Before the lecture:
Further reading:
http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Arabic_mathematics.html
http://www.arabicnews.com/ansub/Daily/Day/980422/1998042208.html
www.math.tamu.edu/~dallen/masters/islamic/arab.pdf
Lecture X: Fermat and his Last Theorem.
In June of 1993, Andrew Wiles announced his proof of one of the most long standing problems in mathematics, Fermat's Last Theorem. It is a seemingly easy generalization of the Pythagorean Theorem, which says that a triangle is right if an only if the sum of the squares of the lengths of the sides of the triangle is equal to the square of the length of the hypotenuse. But unlike the Pythagorean Theorem, FLT was not a theorem of geometry, but of Number Theory. It states that the equation x^{n} + y^{n} = x^{n} has no solution in positive integers when n is bigger than 2. This conjecture has fascinated the mathematical community every since Fermat's son first published it in1670. We shall explain the background of the problem, describe some of the partial solutions of the problem, and then discuss some of the events surrounding the proof of Wiles and its reception by the mathematical community. The mathematics that Wiles did is too complicated even to give a summary of, but the story is very interesting.
Before the lecture:
Further Reading:
Video:
Lecture 4: Leonhard Euler.
Leonhard Euler (1705 - 1783) was the most prolific mathematician of all time. We will discuss his life, some of his works, and his influence on mathematics and society.
Before the lecture:
Further reading:
Lecture 5: How West Point Influenced American Mathematics.
Before the lecture:
Further Reading:
Something extra: Field Trip to West Point.
This field trip will have two aspects. We will go on a tour of Math on the Plain which will discuss the contributions of some of West Point's scientific graduates. Then we will Visit the Rare Book Room and look at some of the books which have come up in these lectures. Items for the visit to the Rare Book Room will be especially chosen for this group. The link given is just a sample. You will need to provide your own transportation.
Before the lecture:
Read the text of the Math on the Plain tour. Make suggestions about what you would like to see on the library tour. Here is my running list of things to show.
Lecture 6: Lewis Carroll and His Friend Alice.
Read some short portion, say the Jabberwocke. Discuss various points where mathematics come up in Alice. Give a general discussion of Oxford in his day and what sort of people were there and what they did.
Before the lecture:
Further reading:
Video:
Show and tell:
Lecture 7: Women in Mathematics.
Hypatia, du Chatelet, Agnesi (play some music by her sister), Kovalevskaya, Noether,
Julia Robinson. We will discuss the social issues and prejudices that prevented women from entering mathematics and argue that things have changed and that women are now welcomed into the mathematical ranks.
Before the lecture:
Further reading:
Lecture 8: Alan MathisonTuring: An Original Math Nut
His life is a very interesting one. His work on computers. See if his paper on distinguishing between a computer and a person could be read by the group.
Keith Devlin, Reflections on Deep Blue. This deals with the question of whether computers can think.
Further Reading:
Video:
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