One of the foundational works of Western (or, for that matter, human) civilization is Euclid’s Elements which lays out the foundations of geometry and parts of algebra. In the West, the Elements was lost, along with many other texts, in the wake of the final disintegration of the Roman Empire in the fifth century. In the East, the Elements was preserved by the Byzantines and passed on by them to scholars in the Islamic Empire who translated it and other mathematical and scientific works into Arabic. When the Muslims conquered and held most of Spain, they brought these books along with them, and cultural interchange between medieval Islamic Spain and medieval Christian Europe led to the retranslation into Latin of these priceless works, long lost to the West. Quoting wikipedia:

Though known in Byzantium, the Elements was lost to Western Europe until c. 1120, when the English monk Adelard of Bath translated it into Latin from an Arabic translation.

In fact, much of what Western Europe knows about the “the glory that was Greece and the grandeur that was Rome” came to us through cultural links between the West and the Islamic Empire and its successor states.

In talking about his discipline, Occupy Math has always taken the position that understanding math, that solving problems, works much better if we include everyone we can. The lack of inclusiveness is a very real problem, as the linked post about a man suspected of terrorism for working differential equations on an airplane, shows.

**In this context, if Donald Trump’s Islamophobia had arisen at another time, it could have crippled western civilization.**

It is not that hard to imagine an alternate history in which a pope with really bad hair decided to declare that intercourse with a competing religion was sinful and cut off much of the contact with Muslim scholars. In that alternate history, what becomes of the West? I will leave answering that question to people like Harry Turtledove, a Byzantine historian turned science fiction writer. The good outcomes seem improbable.

The service done to human civilization in the Islamic Empire goes far beyond preserving the knowledge of Greek and Roman authors which medieval Europe had lost. The mainspring of mathematics is algebra from the Arabic “al-jabr” meaning “reunion of broken parts”. Like much of mathematics, algebra does not create new knowledge, but it often can tell you things you didn’t know you knew. An example of this is the quadratic equation which can be very annoying to solve – unless someone who knows algebra has done all the work ahead of time and provided a formula. In medieval Europe, quadratic equations were part of accurately aiming cannon. A civilization with algebra has a scientific, logistic, economic, and military advantage over one that lacks it.

**Humanity owes Islamic scholars for the discovery and formalizing of algebra.**

One feature of Islam is a ban on pictures of sentient beings, called Aniconism. Not able to use statues and pictures of major human figures in their religion, Islam applied mathematics to the problem of the beautification of their mosques. They managed to discover versions of Penrose tilings about five centuries before Roger Penrose proved they were infinite aperiodic tilings. These tilings are remarkable and beautiful. Gihri tiles demonstrate that these tilings were not one-off creations of brilliant artists but part of a systematic discovery of mathematical structures that support the creation of art. Occupy Math thinks these tiles would make a wonderful children’s toy. The mathematics discovered by Islamic civilization is complex and diverse. In addition to inventing algebra, they recognized trigonometry as being its own discipline, they adopted Hindu notation for numbers – including zero – which notation we not only use but call *Arabic numerals*. Another gift to the West from Islam. There is not room here to explain just how incredibly cool *zero* is, but Occupy Math will take this up in a future post.

**Hatred, fear, and division are the enemies of reason and civilization.**

Many of the incredible discoveries of the Greeks and Romans were lost to the West after the fall of classical civilization. It was really lucky that someone else took extensive notes – but a lot of things from that period are just *gone*. We know civilizations, large and small, can fall for reasons ranging from natural disasters to social dynamics. Occupy Math has published more than thirty peer-reviewed papers on the prisoner’s dilemma, a simple mathematical model of cooperation and conflict. Almost all of this work consisted of spotting flaws in existing methods and improving them. This research, his and others, makes Occupy Math sure that there is excellent mathematical evidence for the proposition that *cooperation is usually the better policy*. Cooperation is impossible, of course, when one side of a potential conflict absolutely refuses to engage, but this usually happens when important factors are hidden.

Scientific and mathematical research absolutely depends on transparency. Occupy Math referees many scientific papers and will reject a paper when he thinks the authors did not explain what they did well enough for another researcher to check their results. A wonderful discussion about how we badly need to check our results far more than we currently do is available at Veritasium. Occupy Math found watching this video rewarding.

**In mathematics and science transparency is the currency of cooperation.**

The term “dog whistle” (a supersonic whistle that dogs can hear but people can’t) has been used in reference to the current U. S. election for phrases used to imply things or evoke positions without saying them out loud. This permits a certain amount of plausible deniability, but it gets in the way of understanding what the problems really are and solving them. Mathematics is often very hard to explain and so mathematicians have turned saying what they actually mean into a high art – the mathematical proof. You define your terms as clearly as possible and explain each logical deduction with the utmost care until your conclusion is inevitable.

This love of and need for clarity is the primary reason Occupy Math chose to use a current candidate for the Presidency of the United States in his discussion of the debt we owe to our fellow humans who are Muslim. In the interest of transparency, the secondary reason is that it is pretty good click-bait, but Occupy Math hopes his regular readers will forgive this device for building the brand. This post raises many issues – reproducibility of results, the coolness of zero, and even prisoner’s dilemma as a tool for modeling cooperation and conflict. Please comment or tweet to let Occupy Math know what topics you might like to see in future posts!

I hope to see you here again,

Daniel Ashlock,

University of Guelph,

Department of Mathematics and Statistics

Beautifully explained. I appreciate your efforts.

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Very well-written and the message is well-received. Thank you!

Robert

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