Today was the day I finished listening to the recordings of Dr. Eves’ History of Mathematics course (for the most part. More will be explained later). Before I sat down to listen to the recordings, I asked the Head of the Department, David Benjamin, about the time sheets I am supposed to fill in. Apparently, either Mr. Ogreten or Ms. Rubin is supposed to help me out with that. So, that will be among Friday’s tasks. As for today, this marks the end of a portion in the processing of the Howard Eves Audio Collection that I actually enjoyed.
Resuming where I left off from yesterday, the recording continued with Dr. Eves as he presented the previous edition of his An Introduction to the History of Mathematics written in Chinese. He mentioned some of his other books that were also translated in Chinese (though he could not read them). The professor mentioned some of the translators he was aware of and have corresponded with since. The topic were soon shifted back to that of Chinese Mathematics.
After giving a brief description of the Chinese Dynasties, Dr. Eves noted Jesuit missionaries began arriving in China during the Ming Dynasty and were exposed to Chinese knowledge of science and mathematics. He also mentioned Marco Polo’s arrival in China and how Kublai Khan consolidated China during the Yuan Dynasty. This set the background for a discussion on the key developments of Chinese mathematics.
Dr. Eves mentioned mathematical accomplishments in China such as how the Chinese devised the rod numerals, which presented one of the first decimal positional systems. The oldest known source was the I Ching (also known as the Book of Changes, though Dr. Eves called it the Book of Permutations). The work contained the Pa Kua and the dashes involved in its construction shadows a binary system. Next was the Lo Shu Square, which consisted of nine knots and is the reason why it is also known as the Nine Halls Diagram. Dr. Eves demonstrated it properties and said the square is allegedly older than the I Ching.
The professor shared the mythic origins of the Lo Shu Square involving Emperor Yu and jewels on the back of a divine turtle. He then mentioned the square was an inspiration for the Loubère method (named after Simon de la Loubère). Dr. Eves then demonstrated how the method worked.
A student asked question about the sequence of magic square and the professor answered it. He then resumed lecturing on magic squares. Dr. Eves used a chess board as an example for magic squares, citing Leonhard Euler’s movement known as a knight’s tour.
Dr. Eves asked the question if a knight’s tour is at the same time a magic square. This led to a discussion of mathematical motivated art and quilted blankets. The professor remembered he spoke at in a high school in San Francisco with a lecture on the magic square. He had made a comment that the design would “make a nice gate.”
Dr. Eves returned to the topic of major Chinese mathematical accomplishments with the Zhoubi Suanjing, which contained a special Pythagorean Theorem known as the Gougu Theorem. After a brief mention of more rod numerals, he spoke about the suanpan (the Chinese abacus) that was developed during Han Dynasty. But, Dr. Eves felt the most important of ancient Chinese texts on mathematics was The Nine Chapters on the Mathematical Art (Dr. Eves called it the Arithmetic in Nine Sections).
The nine chapters consisted of the following: first chapter involved areas and π, the second chapter involved percentage and proportions, the third chapter involved the Rule of Three for solving proportions, chapter four involved the size of figures and square and cubed roots, chapter five involved volumes, chapter six involved motion problems and allegation (a business term), chapter seven involved false position, chapter eight involved simultaneous linear equations solved by matrix method, and chapter nine had Pythagorean right triangles and how to compute them.
Then, Dr. Eves had the class return to the practice problems at the beginning of the book as a demonstration of how the properties mentioned in The Nine Chapters on the Mathematical Art. As he finished talking about empirical procedures in The Nine Chapters on the Mathematical Art, the professor mentioned how Liu Hui’s Haidao Suanjing (The Sea Island Mathematical Manual) began as a commentary on The Nine Chapters on the Mathematical Art. Dr. Eves then offered more practice studies on The Nine Chapters in the textbook.
After discussing the Chinese approximations of π, Dr. Eves noted the Mathematical Inventions during the Tang through the Ming Dynasties, when The Nine Chapters on the Mathematical Art was first printed. However, he explained the Song and Yuan Dynasties were known as the greatest period of Chinese mathematics. Among the accomplishments were solving indeterminate equations (Diophantine equations). Dr. Eves explained a few equations related to help the students understand this point.
Dr. Eves diverted the conversation and talked about how College Algebra and Algebraic Structure are essential for high school teachers to know the content before teaching their classes. He believed the same for Geometry. However, the professor commented on the University of Central Florida’s Mathematical Department as “lopsided” in that there was “nothing for geometers” to advance their studies and similar circumstances for those studying abstract algebra.
Returning to the topic, Dr. Eves noted the method developed British mathematician William George Horner had origins in Chinese mathematics as did Pascal’s triangle. He also mentioned the Chinese Remainder Theorem (also known as the Formosa Theorem) had similar circumstances. To end the lecture on the topic, the professor reiterated the two Chinese correspondents he had been in contact with had sent him scholarly materials and he hoped that 1987 book would get translated.
Dr. Eves briefly spoke about the Mathematics in India and contributions in computing and calculating numbers, solving algorithms, long division, and multiplication. He then took some time to explain why Indians were customarily referred to as Hindus (to avoid confusion with Native Americans) and noted it was an inaccurate term. Dr. Eves commented that despite the Indians’ contributions to mathematics, they were not “good geometers.” He stated though there is some great work in quadrilaterals, a contrast can be made between Greek and Indian mathematical systems in content. Unfortunately, the recording ended as Dr. Eves was beginning to speak the spread of Islam in the Middle East and the impact on mathematics.
The final disc has the problem of having its class subject divided strangely with having its beginning at the of Track Two. Regardless, the content was rather touching. After reviewing some equations on the faces of triangular prisms and decahedrons, Dr. Eves wanted to share a personal story regarding ethics and philosophy of scholars. The story was about how he adopted his attitudes of a scholar.
Dr. Eves started his tale with while attending high school in New Jersey, he and his friends were “crazy about mathematics.” He bought an edition of Euclid’s Elements and studied the book thoroughly. In his sophomore year, he bought a copy of Florian Cajori’s A History of Mathematics. The young Howard Eves was inspired by that book.
He and his friends were interested calculus but they did not know what it was. When Dr. Eves was a primary student, the course was only taught as a sophomore in college. His teachers did not help, so they bought copies of William Anthony Granville’s Elements of the Differential and Integral Calculus to teach themselves. Dr. Eves commented that he would not say anything negative about the book and still had his copy. He said this because of his own experiences with how math teachers complained on lack of material in text books, while he still sees value in those books (if anything, it was for the equations).
Returning to his story, Dr. Eves reminisced how he and his friends would use a room in one of their houses to conduct their studies. Dr. Eves told his friends about three mathematical fanatics in Cambridge in the early nineteenth century: George Peacock, John Frederick William Herschel, and Charles Babbage. Dr. Eves explained these three scholars wanted to improve the state of the calculus in England.
Dr. Eves gave a short biography of George Peacock, who made sure all the calculus problems on the tripod was given misnotations to force mathematicians to change their thinking. The professor mentioned that three translated Sylvestre François Lacroix’s Traité du Calcul Différentiel et du Calcul Intégral as Differential and Integral Calculus and published it in 1816. George Peacock himself would publish Treatise on Algebra in 1830.
Among his other contributions, Peacock began annual reports in the British Association for the Advancement of Science on the progress of mathematical science. Peacock was also instrumental in helping Cambridge University gain an astronomical observatory. He then gave a short biography of John Herschel.
John Frederick William Herschel, also known The Wrangler, was the son of British astronomer William Herschel. Like his father, John Herschel catalogued the stars in the southern hemisphere while in Cape Town, South Africa. Herschel submitted first paper on mathematics on complex number systems to geometrical problem. He wrote other papers on mathematical analysis and the mathematical theory of light. He also discovered sodium hyposulphite. Next, Dr. Eves gave a short biography on Charles Babbage.
Charles Babbage founded the British Association for the Advancement of Science and spent his fortune on the development of differentiation engine and the analytical engine (forerunners of the calculator). Dr. Eves noted Babbage was interested in clubs and societies: founded the Statistical Society and was part of a chess club along with a rowing club. Babbage apparently hated hated organ grinders.
Dr. Eves commented the three scholars made a vow to leave the world wiser than they found it. Eves and his two friends thought of doing the same and vowed to “do our best to leave the world better than we found it.” This lead to another story.
Dr. Eves reminisced about a non-mathematical friend who loved to ramble (an activity to hiking) and made comparisons to camping with a heavy backpack. This friend’s father decided they were going to move to Ohio. After the move, the young Howard Eves was invited to visit his friend at their grandfather’s farm.
Dr. Eves told how he met his friend and his grandfather at the train station at Wooster, Ohio. He reminisced about the visit at the farm that was eight miles from Wooster. While discussing with the locals about schoolwork, he was introduced to the Scholar’s Creed.
The Scholar’s Creed: “I believe the knowledge I received or may receive from teacher and book does not belong to me. That is committed only [I think that is what Dr. Eves quoted] in trust that still belongs and always will belong to the humanity that produced it through all the generations. I believe I have no right to administer distrust in any manner whatsoever that may result in injury to mankind, its beneficiary. On the contrary, I believe it is my duty to administer simply for the good of this beneficiary to the ends that the world may become a kindlier, a happier, and a better place in which to live.”
The Creed was similar to what Dr. Eves and friends wanted, so he wanted to share with it his friends. Dr. Eves made comparisons to how Native American’s felt about land before sharing a story about Rachel Carson, author of The Sea Around Us, living in Maine. Dr. Eves returned to his story with friends with how all of the adopted the Creed.
Dr. Eves spoke about the fate of his friends and how the vow was broken (one of them became a chemist). Unfortunately, the chemist became bigoted and handed in his resignation. His other friend accepted to work on the super bomber project Dr. Eves had previously mentioned in another class. This friend left after a year of unhappiness.
After he spoke of words of wisdom regarding high ideals and such vows, Dr. Eves brought copies of the Scholar’s Creed for the class to have. The professor began handed back graded papers and thanked his students. After an applause, he dismissed the class for the final time. This would have been a good place to end the recording, but unfortunately a previous recording of finding a centroid of a semi-circular arc and other equations came afterwards (I am sure this is actually the beginning of the lecture).
While I am going to double check the final disc to make sure I did not miss anything tomorrow, the class is dismissed. All that that remain to do with the collection is to perhaps label the discs, attach new labels on the box, and certainly create a finding aid. For the record, the textbook that Dr. Eves used for the class was his An Introduction to the History of Mathematics (though, it may have been the fifth edition as the sixth edition was not published until 1990). So, if anyone wants to follow along with the class, that is the book to get (I recommend Dr. Eves’ personal memoirs, Mathematical Reminiscences, as well).
This has been an interesting collection. It was as if you was sitting in class with each recording. The George L. Stuart Collection, however, will not offer such an experience and there will be a return to to standard operating procedures. Nonetheless, my experience will be recorded here. Enjoy the rest of the evening and stay safe! Bye!