I am here with another entry from my weekly write-up of topics talked about in my History of Mathematics class. This one is a bit longer:

We started this week with a reading of a few section from chapter two of our book, The History of Mathematics by Roger Cooke, specifically those dealing with the mathematical history of India and the Maya. The mathematical history of India is itself, removed from any external context such as the over-all study of the history of mathematics, incredibly interesting.

One of the oldest cultures in the world the history of Indian mathematics reaches, of course, well into BCE. As is common with mathematics of that time, the math seems to be mostly concerned with geometry and artimetics. In fact, according to Cooke, sometime between 800 to 500 BCE the Sulva Sutras, who’s root words come from measure and cord, a collection of mathematically based verses were inserted into the Vedas. These verses, and the idea that the content probably springing from the maintenance of altars, are intimately tied to a conversation that we had in class on Tuesday: The importance that culture and religion have on studies, and mathematics in particular.

Professor Bhatnagar brought up the semester he spent at the University of Nizwa in Oman, and the perspective the students there brought to their education, specifically that they came into classes expecting to be able to memorize their way through instead of learning basic concepts and then extrapolating from there to solve here to fore unseen problems. Professor Bhatnagar then posited that there was a good reason for this and someone else from the class spoke up that it could have something to do with the practice of memorizing large section of the Qur’an for recitation, a hypothesis that was quickly seconded by many in the class and was agreed with by our Professor. Of course it does simply end there because, as our Professor quite rightly pointed out, it is also a great honor to be one chosen to do the recitation and because of that the students were not only well practiced in memorization but have a large respect for the method.

There is no reason to stop the speculation on the effect that religion and culture have on mathematics there though, let me spend a second talking about mathematics in the United States. As we spoke about on Thursday after the USA declared its independence from the Untied Kingdom way back in 1774 it was not only in governing that we decided to break away from the British model. We also changed our education system quite a but as well, so much so in fact that there is very little in common with the two systems now only 236 years since independence. The United States university system tends to function on the idea of: If more than one person wants to study it, it is probably worth studying as opposed to a more track based system such as that in the United Kingdom. While I can not say I agree completely with this idea, I am proud to say that I am a product of a system that does, for some reason that eludes even my radically liberalized mind, offer underwater basket weaving as a for-credit course in more than one university.

The important part of offering all of these courses, and all the different ways to take them, is that having such an open system allows and encourages innovation. There are universities such as Evergreen in Washington state that do not seem to even have grades in classes, Redd where you get to design your own degree from the bottom up, and technical colleges where regimentation is the name of the game. This culture of openness has also nurtured special minds like Terrance Tao, a man more brilliant than even his Fields Medal gives him credit for as he managed to use Analytic techniques in Number Theoretic fields a marriage that many great mathematicians had thought impossible, to their greatest possible potential where it is possible a more discretely structured system could have stunted the creativity in Tao’s intellect which would have never the less produced a great mathematician but not one who could have generated the same results. It is not all greener grass in the United States though, we also have a very strong fundamentalist Christian population and I would be remiss if I did not mention the effect I feel that that religion has on mathematics.

One of the biggest philosophies of the fundamentalist Evangelical sects in the USA is that science is much more than simply wrong, it is the work of the devil. That science makes people question the truth of the world being 5000 years old, the truth that dinosaur bones are just a test of faith, and the truth that humans, and everything else, were created by the One True God. This has become a very large problem in the education system in the United States, from schools being forced to put stickers on their science books stating that evolution is just a THEORY to teaching creationism in biology class. There are much more insidious and non-obvious effects though and the one that I feel most dangerous is a distrust that all of these preachings cause in science and, by extension, mathematics. Students will go into a class room having been told that everything they will learn there are falsehoods and therefore they see no reason to pay any mind to what is being taught. Mathematics really challenges such dogmatic beliefs with the idea of proof and mathematical truths. If there can only be one truth, the truth of God, where does the Pythagorean Theorem fit?

This conversations quickly spun into a discussion of the conditions that are needed in order to have a flourishing mathematical culture. Going from the reading it seems that one possible way is to have a lot of questions that needed answered. Look at say the Mayans, who had a very strong culture of Mathematics; a huge amount of it centered around astronomy and the calender, such as the Dresden Codex that Cooke wrote about, questions very central to the Mayan culture and religion. I also feel that one of the sufficient conditions for mathematics is having a liberal and available education system, as most of the Western World have accompanied by a huge amount of new work being published in mathematics, because as long as people have access to a subject at least some of the people will work on it something. That is obviously not true if they can not receive the education necessary to understand said subject. One final thing on this subject we covered in class was: what happens to mathematics in a despotic system?

The two examples that were mentioned in class I believe are quite good illustrations, but I do not know if they are inclusive. The first was Napoleon. While Napoleon took control in France he was of the mind that pure mathematical research was not of that much import, he was much more worried about applied mathematics and of course how it could help him win his war with the rest of the world. This was at least part of the reason he sank so much money into the Ecole Polytechnique in France where mathematicians were trained in the applied side of the science. While this very well could mean that we lost out on some very good pure mathematicians but it did not completely backfire for mathematics as a whole as Poisson and Poinsot were proud products of the Ecole Polytechnique. Also left out of the Polytechnique though were the women. Sophie Germain chief among them. A correspondent of both Lagrange and Gauss, Germain was not allowed at attend the Ecole Polytechnique and was therefore forced to teach herself mathematics eventually winning an award from the French Academy of Sciences. Germain was due to finally receive the deserved doctorate the Ecole Polytechnique would not give her from Gottingen University when she perished to breast cancer before she was able to meet with Gauss, who was to award her the degree.

The other despot that was mentioned in class was the one that almost all conversation of despots and dictators end up, Adolph Hitler. Nazi Germany was of course well known for the suppression of any sort of creative art that did not coincide with the philosophies of the National Socialist Party, but the Nazis did invest a lot of money in the sciences. The reasons were not that different than the reasons that Napoleon had, they had a war they needed to win. Once again it was applied mathematics that was to benefit over the pure as the Nazis sank more and more money into the creation of more accurate guns, fighter jets, bombs, and, of course, missiles. One important thing that can be seen from this more modern example though is the effect that a despot can have on the mathematics and sciences of other countries. Without the shadow of the Nazis, and the Japanese, there is a good chance that the breakthroughs in cryptanalysis at Bletchly Park and the amazing work of the Manhattan Project, no matter your thoughts on the Atomic Bomb still an amazing feat, would have happened. In fact, while Turing had already written his seminal paper in Computational Theory when the war broke out, would we have seen a working digital computer as quickly as we had without World War Two? I personally do not think that we would have had the knowledge without the computational machines built to help defeat the Axis powers.

As I mentioned before this is not a sufficient example to make any causative claims about the effect that despots have on mathematics, and the sciences, but I would be willing to wager, and living in Las Vegas I now know the true strength of those words, that looking at a much larger samples the same results would continue to appear. The reasoning is quite trivial: despots crave power above all, in order to gain and maintain said power they need more and better weapons than all of their foes, to gain this advantage they have to leverage all of their options, and the best of those options are the mathematicians and scientists whose mind are singularly skilled to tackle such problems.

We finished off the week with a discussion of the projects that we will be tackling as our main research task during the semester. The projects are all tied to the task of giving the 50 year history UNLV Mathematics Department. The basics are good listings of faculty, graduates, and class histories. I personally decided to do something a bit different and volunteered to put together an oral history of the UNLV Mathematics Department. This is of course because of my experience working with audio in the podcast world, but also because in history I think the story is perhaps the most important, and definitely the most captivating, thing. Oral histories have also become incredibly popular, especially as a way to consume history. I can only conjecture that this is because most raw data, facts, figures, and the like, is now not only available, but easily searchable on the internet. As a matter of fact Google has really killed the old practice of sitting in libraries until all hours, coughing from the dust shot into the air by opening old tomes to skim and losing one’s eyesight scanning microfiche for some tiny piece of information. The one thing that can not be found on the internet a lot of times though is the story of what happened by someone that was there. As a mathematician I am quite aware that numbers rarely tell the whole story, and analyzing a topic from a fact only perspective will lose all the nuance and color that a real history should have.

Interesting… which math course is this? Professor Bhatnagar was in Oman? Nice I, myself lived there for 14 years, awesome country I say.

Have you tried looking into Vedic Mathematics? They are interesting.

I write these as a weekly assignment in my 714 History of Mathematics class. Professor Bhatnagar spent a semester at the newly formed University of Nizwa helping to build their mathematics program if I remember correctly.

Nice. What is the time line of history for the class? Babylonians until the modern age?

It is much more of a jump around sort of course. We do not have a set time line, or set material.

Interesting… a totally Random Class 😀

Pretty much