I have a confession I need to get off my chest. I think Geometry is racist. Well, not geometry (the discipline of mathematics), but specifically Geometry (the course commonly taught in American High Schools). I realize that in presenting this argument I’m going to have to make some rather sweeping generalizations about human history, but I that it’s important for me to put this hypothesis into words because I don’t think there’s enough evidence to disprove it.

Fair warning: this may be a lengthy read.

I believe that the reason the curriculum of Geometry specifically references Pythagoras, Euclid, and Descartes is because this emphasis provided Whites another means by which to rationalize slavery. Greek society was a prototype for White society because it used mathematics and philosophy to moralize slavery, and Descartes provided Whites a method of reconciling this position with Christianity.

To understand this, we first need to acknowledge that the entire human history of mathematics is intertwined with human slavery. Both mathematics and slavery emerged in early civilizations after the transition from hunter/gatherer to agricultural society lead to social stratification and the development of written language. In fact, I think mathematics is a necessary precondition for slavery. The very concept of slavery depends on a life being assigned a quantifiable value. Slave labor provided the ruling class with the time and resources to work on furthering mathematical knowledge, and then advances in mathematics were used to increase the efficiency of the slave trade. This vicious cycle quickly elevated the slavers to a god-king status which they then exploited to moralize their slavery.

Our oldest mathematical texts are from Egypt and Babylon, approximately 4000 years ago. Surviving records such as Plimpton 322, the Moscow Mathematical Papyrus, and the Rhind Mathematical Papyrus show that teachers have been giving math worksheets of roughly high school level difficulty since at least 1900 BC. What’s interesting about these three texts is that all three of them show evidence of the Pythagorean Theorem — over a thousand years before Pythagoras was even born! There’s also a strange lack of evidence attributing the theorem to Pythagoras, along with indications that proofs of it may have been circulating in Mesopotamia and India several hundred years prior. The very fact that this theorem bears the name of Pythagoras despite this questionable lack of evidence should alone be sufficient evidence of Geometry’s racism, but Pythagoras is only the first of three dominoes.

When Pythagoras supposedly lived around 500 BC, the Greeks (and Romans) had lively slave trades. However, unlike the god-king theocracies of Babylons and Egypt, the Greeks fashioned themselves as a “Democracy”. The Greeks needed an alternative means of moralizing slavery and whether he intended it or not, Pythagoras’ merger of mathematics and philosophy provided them with all the justification they needed. The Greeks used philosophy and mathematics to separate themselves from the people they enslaved, which served as a prototype for White society. Those that didn’t measure up to Greece’s intellectual standards were labeled as “barbarians” and treated as less than human. To paraphrase Plato, these barbarians were in the dark and needed to be shown the light. Incidentally, the “barbarian tribes” of Northern Europe enslaved by Greeks and Romans were likely a source of genetic markers for light skin, light hair and light eyes that would later be associated with “Whiteness”.

Meanwhile, mathematics probably continued to develop in the Middle East with influence from early civilizations in India and China. However, we don’t know by exactly how much. There’s another strange lack of mathematical records from Babylonian society under the Persian Empire. What we do know is that when Alexander the Great conquered the region in 331 BC, the Greeks assimilated a wealth of astronomical data. It’s quite likely that the Greeks stole whatever mathematical data they could through military conquests and these materials ended up in the Library of Alexandria where Euclid would have had access to them. Euclid’s work is based on a set of stolen mathematical literature that Euclid was privileged to have access to. While it’s impossible to discount the probability that Euclid might have added some original ideas, I do think this fact merits taking a closer look at his work and evaluating whether or not it belongs in our school’s curriculum.

My problem with the presentation of Euclid in Geometry (the course) is the parallel postulate. To be fair, presenting Euclid’s axioms as fundamental truths about the universe made sense in mathematics education up until as recently as 1905. We now know that space is not “flat” as Euclid assumed, but that gravitational forces can bend space around a mass. My understanding is that we teach Euclidean geometry because (a) it’s a useful approximation of reality and (b) it provides an introduction to axiomatic systems. The main issue with Euclid as presented in Geometry is that its axioms are presented without proof and we have solid scientific evidence that one is not always true. How can we ever expect students to think critically about information when we don’t question the assumptions made in mathematics?

Euclid’s mathematics is not irreplaceable within the mathematics curriculum. We could just as easily teach students about axiomatic systems using first-order logic. Instead of teaching compass and straightedge constructions, we could teach origami. In fact, teaching these alternatives could not only increase the diversity of the mathematics but simultaneously increase the rigor. There is some really great math showing that we can solve problems with paper folding that are impossible to do with a compass and straightedge only. Learning origami would help prepare students for high level physics and computer science. We owe it to our students to do better than Euclid.

Approximately 300 years after Euclid, the Roman Empire was nearing its peak and Christ was born. The death of Christ coincides with the start of two centuries of peace. It’s no wonder that early people considered this a miracle. Early Christians were originally persecuted in the Roman Empire, but by 380 AD it would become the state religion. If you think about it, Christianity offered the Romans a pretty sweet deal considering their involvement in the religion’s origin. The Romans killed Jesus, and through Jesus’ death were forgiven all their sins. And that meant all their sins: slavery included. To suggest that otherwise would be heresy. Before long, Christianity had accumulated so much Power that they rewrote the entire calendar around their own beliefs.

The spread of Christianity throughout Europe is relevant to our discussion because the next major event in mathematical history happens to coincide closely with the birth of Islam. Around 800 AD, Muhammad ibn Musa al-Khwarizmi developed the branch of mathematics we now call “Algebra” and started a new mathematical revolution in the Middle East. This presented Christianity with a threat because geometry was always considered sacred and the followers of Islam were creating new mathematics for another god. The bible says “Thou shalt have no other gods before me“. By 1100 AD, Christianity had come to the conclusion that since they couldn’t disprove the Muslims mathematically, the only other option was through force. The Christians took to war against the Muslims and with each mosque they burned they destroyed part of that mathematical progress. Remnants of this “Holy War” persist through the present day.

It’s because of this religious tension between Muslims and Christians that our story leads to Rene Descartes. Another essential component of the Geometry curriculum is the idea of Cartesian geometry which is an merger of algebraic principles with Euclidean geometry. The very name would have you believe that Descartes invented it, but that honor should probably be attributed to Fermat. No, I think there’s another reason we attribute it to Descartes, and that is because of his work in ontology. Most people are familiar with “I think, therefore I am“, but that statement is really the first axiom in a system that Descartes constructed in order to develop a mathematical argument proving the existence of God. Descartes is one of a few mathematicians that attracts cross-curricular study because of this. We don’t even provide his argument a fair critique. Like his Greek counterparts, we treat Descartes’ work as gospel when in reality he was just repackaging the ideas of others. In this case, Descartes had taken the Muslim-sounding “algebra” and re-packaged it in form that would be more acceptable for Christians.

The philosophical assertion “I think, therefore I am” takes on another meaning when we put it in context of mid-1600s White society. By associating “thinking” with “existing”, Whites were able deny Blacks basic human rights by labeling them as “unthinking savages”. It’s the very same strategy employed by the Greeks to justify slavery, only the vocabulary had shifted. The same idea would later manifest itself through literacy tests, and persists today through standardized testing practices. Whites retain Power by defining a culturally biased set of standards.

A few weeks ago I listened to a podcast from Freakonomics that described America’s Math Curriculum as a “Geometry Sandwich”. Ever since I taught it I’ve been asking myself the same kinds of questions:

• Why “sandwich” Geometry in the middle of two years of Algebra?
• Why are Euclid, Pythagoras and Descartes the only three names that students explicitly learn in Geometry?
• Why is the name al-Khwarizmi not given the same level of treatment in Algebra?

The most probable explanation I can come up with to answer all three of these questions is that the American Math Curriculum is racist. It is probably not the intent of the Curriculum developers to be racist, but racism is not about the intent — it’s about the consequences of the behavior. There is a non-zero probability that cultural biases exist within our Math Curriculum and they produce racist consequences. Mathematics is a just tool, but people decide how that tool is used. We can either continue to use that tool to enable racism, or we can use that tool identify and dismantle it.

For me, I’ve decided that the probability of the Math Curriculum being racist is too high for me to ignore. I’ve decided on the following course of action:

• I plan to start substituting “Right Triangle Theorem” in place of “Pythagorean Theorem”.
• I plan to start substituting “Rectangular Coordinate System” in place of “Cartesian Coordinate System”.
• I plan to pay closer attention to situations where Euclidean geometry is implicitly assumed and question whether or not this assumption is warranted.
• I plan to make a consistent effort to present a diverse range of mathematicians in my classrooms.
• I plan to actively look for other artifacts of racism in the curriculum and address them accordingly.

I realize that my argument here needs work and that I’m personally having difficulty disentangling race and religion. Even if I haven’t yet convinced you that “Geometry is racist”, I think there’s sufficient evidence here to conclude that it’s definitely not anti-racist. That fact alone is reason enough for me to act. If you’re also a teacher of mathematics, I hope I’ve convinced you enough to join me in these actions.