SLICING HISTORY OF MATHEMATICS
“If two mathematicians disagree on the solution of a mathematics problem, then at least one of them is wrong. However, if two historians agree completely on an historic issue, then one of them is taking a free ride on the shoulders of the other,” thus said I today during my lecture in a Linear Algebra (Math 330) class. That is the bottom line nature of these two disciplines. Mathematics is absolutely binary in the resolution of its problems; whereas, history is ‘polynary’ (my coinage).
This remark was made in the context of finding the eigenvalues of a matrix, which is reduced to solving a polynomial equation. Students knew the quadratic formula, but most did not know that the formulas exist for cubic and biquadratic equations too. They were surprised to hear that all proofs for solving equations of order greater than four had been wrong – for over two centuries. After nearly 300 years comes Evariste Galois (1811-1832) who proved, at the age of 21, that such a formula does not even exist! Period.
Interjecting such snippets from History of Mathematics (HoM) does not take me more than two-three minutes, but their impact on students’ learning is long and deep. At this point, I made a brief pitch for the History of Mathematics (Math 314) course that I am scheduled to teach next semester (Spring-2019), which is offered every two years. This course is required for students majoring in Secondary Education, and who want to go on to teach mathematics in high schools. Other students can take it as one of the elective courses included in every degree program. The elective courses expand students’ horizons in their twilight disciplines – a strength of the US college education.
This lecture being just a day before the Thanksgiving recess, I stressed upon the general importance of knowing the history of one’s discipline, one’s family, society and country. However, when it comes to teaching a course on HoM, no department of history would offer such a course, as most history faculty have not gone beyond pre-calculus. On the other hand, faculty in mathematics departments, in pursuits of their doctorates and research publications, get too far away from humanities and social studies. In order to teach any history course effectively, one must have a developed sense of history, which is evidenced by being able to connect the dots of an event in a manner that gives a unique interpretation. History is far beyond the memorization of dates of events and names of key people, just as mathematics is far beyond arithmetic calculations. History requires holistic thinking and mathematics is all about deductive thinking.
At one time, I considered myself a history buff, but now I also claim (by Gladwell’s 10,000-hour dissertation in the Outliers: The Story of Success; 2008) to be an historian of contemporary events connected with the past. My book, Vectors in History, Volume I (2012) deals with history in general. Its ‘historical’ corollary, Darts on History of Mathematics, Volume I (2014) has 72 reflective and independent essays on varied aspects of HoM. The students have liked this book as a supplement to any traditional textbook on HoM.
I always look forward to teaching HoM courses, which are offered at UNLV both at the undergraduate and graduate levels. This is one of my intellectual passions as I am nearing the age of 80.
Satish C. Bhatnagar, PhD
Professor, Department of Mathematical Sciences,
University of Nevada, Las Vegas,
Author of the following books (Available at Amazon):
2. Vectors in History: Main Foci; India and USA, Volume I
3. Epsilons and Deltas of Life: Everyday Stories, Volume I
4. My Hindu Faith & Periscope, Volume I
6. Swami Deekshanand Saraswati: My Swami Mama Ji
7. Darts on History of Mathematics,Volume I
8. Converging Matherticles: Mathematical Reflections, Volume II
9. Plums, Peaches and Pears of Education, Volume I
10. Via Bhatinda: A Braid of Reflected Memoirs, Volume II