I had a rather protracted FB “discussion” last night with an individual who claimed the “Star Spangled Banner” was racist. Not, mind you, because the words are (they’re not) or that the subject matter was (the original title of Francis Scott Key’s poem was “The Heroic Defense of Fort McHenry). Born into a slave holding Maryland family, Key had owned slaves, but became later in life strongly against slavery, freeing his own and hiring one former slave as his foreman. He also became a mover in the movement which resulted in the foundation of Liberia.
My point to the
individual was that considering something as racist simply because an
individual associated with it was, is illogical. I used the analogy of the
Bayer chemical company. In WWII they were part of I.G. Farben and Nazi
supporters. Bayer developed several elements of chemical warfare and mass
extermination of Jews (Chlorine Gas, Zyklon B and VX); using forced labor
during World War II. Obviously racist (anti-Semitic) Has anyone suggested we
should ban use of their invention which has become synonymous with the product for
many…..Aspirin? Didn’t think so. (This
back and forth was, in part, in the interest of full disclosure, based on the
fact that two of my maternal forebears were in Fort McHenry at the time, and I
have a bit more information on the events than most.)
I should also
mention that I have an opinion on playing the national anthem (Key’s words and
an English barroom ballad tune) before public sporting events and that is “Why?” Actually, No one did until 1918, when it was
played at a Boston Red Sox game during WWI.
Reflecting on
this “baby with the bath water” condemnation made me think of the Constitution,
written by slave owner James Madison. Pretty good document, really, and has
served us well. That led to my feeling that while there are serious issues of
racism in America and we should address all of these, there are also those who
transfer the label to things which, like Key’s poem, are not racist in either
intent or content.
This brought to mind an essay I wrote in 2018, after reading
an article (portrayed as scholarly, but not really “all that”) in which one of
the authors actually insisted that the ability to comprehend mathematics was “White
Privilege.” I doubt that Neil DeGrasse Tyson would keep a straight face reading
it. She further alleged that all math is derived from “the Greeks and Europeans.” It was at this point that the my inner Historian
screamed an internal “Bull Shit!!”
The Article
I wrote follows this intro, but for clarity sake, I am not minimizing the reality
of racism in America or my antipathy to it which has been a lifelong trait and
that of my parents. I am however wary of those who demean a noble cause by painting
with too broad a brush. If you like math, read on to find out how(mostly) brown people
invented it.
Hidden Figures or Hidden Agenda?
Sooo. Let me get this straight…one writer out of 40 who collaborated on a math education book has decided that math is “whiteness” (or, at least, chose that unfortunate way to describe a common issue in education) and the Far Rightists will claim that this is representative of the entire educational establishment’s “liberal bias?” Puhleeze! That is no more true than to say that Charles Manson’s racist rants were representative of all White people or that Tiny Tim reflected the epitome of American musical talent.
It’s hard to decide which is more egregious – Rochelle Gutierrez’ ignorance, or the willingness of the moronic right to paint half a nation with her brush. What is, unfortunately, lost in the shuffle is that among Ms. Gutierrez’ statements, many of which reflect her own ignorance, are some basic truths which are rather less racial than simply the variety of human talents and focus.
“School mathematics curricula emphasizing terms like Pythagorean Theorem and pi perpetuate a perception that mathematics was largely developed by Greeks and other Europeans." This is a quote from some of Gutierrez’ commentary. Is it true? As far as modern teaching, yes, in too many cases, it is. This reflects as much as anything that many westerners are ignorant of the history involved in the refining of mathematical constructs, as well as the fact that geographical separation, amplified by religious bias, under- emphasizes early efforts because of the origins of the theorists.
What this really reflects is that the lady is ignorant of much of the history related to her own subject. She apparently cannot process that the Pyramids, exhibiting the application of considerable math skills, were built by civilizations which would not be considered “white.” The Pyramids are an indication of the sophistication of Egyptian mathematics. In addition to claims that the pyramids are first known structures to observe the golden ratio of 1: 1.618 (which may have occurred for purely aesthetic, and not mathematical, reasons), clearly, they knew the formula for the volume of a pyramid (1⁄3 times the height times the length times the width) as well as of a truncated or clipped pyramid. They were also aware, long before Pythagoras, of the rule that a triangle with sides 3, 4 and 5 units yields a perfect right angle, and Egyptian builders used ropes knotted at intervals of 3, 4 and 5 units to ensure exact right angles for their stonework (in fact, the 3-4-5 right triangle is often called "Egyptian triangle”). The Berlin Papyrus, which dates from around 1300 BCE, shows that ancient Egyptians could solve second-order algebraic (quadratic) equations. (with which this writer struggles!)
In similar manner, she is apparently unaware that some of the math she maligns as “Greek” was developed elsewhere and previously. She is simply ignorant as are many westerners.
“ दीर्घचतुरश्रस्याक्ष्णया रज्जु: पार्श्र्वमानी तिर्यग् मानी च यत् पृथग् भूते कुरूतस्तदुभयं करोति ॥“
The above Sanskrit in Roman characters becomes:
“dīrghachatursrasyākṣaṇayā rajjuḥ pārśvamānī, tiryagmānī, cha yat pṛthagbhūte kurutastadubhayāṅ karoti.”
In English: “If a rope is stretched along the diagonal’s length, the resulting area will be equal to the sum total of the area of horizontal and vertical sides taken together.” This is, of course, a rewording of the concepts iterated by the Pythagorean theorem.
It is translated from Baudhayana Sulbasutra, one of the earliest Sulba Sutras written. The SulbaSutras are appendices to famous Hindu tradition Vedic scriptures and primarily dealt with rules of altar construction. In the Baudhayana Sulbasutra, there are several mathematical formulae that told how to precisely construct an altar. In essence, the Baudhayana Sulbasutra was more like a pocket dictionary, full of formulae and results for quick references. It was also written about 800 BCE, probably 350 to 400 years prior to Pythagoras’ discussion of the same construct. Oddly enough, the Greeks also made it (math) into a semi-religion, while it had had similar attachments to it for altar construction. As early as the 8th Century BCE, long before Pythagoras, the “Sulba Sutras” listed several simple Pythagorean triples, as well as a statement of the simplified Pythagorean theorem for the sides of a square and for a rectangle (indeed, it seems quite likely that Pythagoras learned his basic geometry from the "Sulba Sutras"). The Sutras also contain geometric solutions of linear and quadratic equations in a single unknown, and give a remarkably accurate figure for the square root of 2, obtained by adding 1 + 1⁄3 + 1⁄(3 x 4) - 1⁄(3 x 4 x 34), which yields a value of 1.4142156, correct to 5 decimal places. Mantras from the early Vedic period (before 1000 BCE) invoke powers of ten from a hundred all the way up to a trillion, and provide evidence of the use of arithmetic operations such as addition, subtraction, multiplication, fractions, squares, cubes and roots.
In the 14th century, The greatest of all Indian mathematicians, Madhava, went further and linked the idea of an infinite series with geometry and trigonometry. He realized that, by successively adding and subtracting different odd number fractions to infinity, he could home in on an exact formula for π (this was two centuries before Leibniz was to come to the same conclusion in Europe). Through his application of this series, Madhava obtained a value for π correct to an astonishing 13 decimal places. He applied the same mathematics to obtain infinite series expressions for the sine formula, which could then be used to calculate the sine of any angle to any degree of accuracy, as well as for other trigonometric functions like cosine, tangent and arctangent. Perhaps even more remarkable, though, is that he also gave estimates of the error term or correction term, implying that he quite understood the limit nature of the infinite series.
Madhava’s use of infinite series to approximate a range of trigonometric functions, which were further developed by his successors at the Kerala School, effectively laid the foundations for the later development of calculus and analysis, and either he or his disciples developed an early form of integration for simple functions. Some historians have suggested that Madhava's work, through the writings of the Kerala School, may have been transmitted to Europe via Jesuit missionaries and traders who were active around the ancient port of Cochin (Kochi) at the time, and may have had an influence on later European developments in calculus.
Among the greatest mathematicians of ancient China was Liu Hui, who in 263 CE, produced a detailed commentary on the “Nine Chapters,” an earlier Chinese text, containing concepts dating as far back as two millennia BCE. The ancient Chinese numbering system was a decimal place value system, very similar to the one we use today - indeed it was the first such number system, adopted by the Chinese over a thousand years before it was adopted in the West - and it made even quite complex calculations very quick and easy. Master Liu was one of the first mathematicians known to leave roots unevaluated, giving more exact results instead of approximations. By an approximation using a regular polygon with 192 sides, he also formulated an algorithm which calculated the value of π as 3.14159 (correct to five decimal places), as well as developing very early forms of both integral and differential calculus, more than 1800 years before Newton and Leibnitz began bitch slapping each other over who “invented” it.
The importance of astronomy and calendar calculations in Mayan society required mathematics, and the Maya constructed quite early a very sophisticated number system, possibly more advanced than any other in the world at the time. The Mayan and other Mesoamerican cultures used a vigesimal number system based on base 20. The pre-classic Maya and their neighbors had independently developed the concept of zero by at least as early as 36 BCE, and we have evidence of their working with sums up to the hundreds of millions, and with dates so large it took several lines just to represent them. The Mayans produced extremely accurate astronomical observations and measured the length of the solar year to a far higher degree of accuracy than that used in Europe (their calculations produced 365.242 days, compared to the modern value of 365.242198), as well as the length of the lunar month (their estimate was 29.5308 days, compared to the modern value of 29.53059).Of course white guys (Spanish priests) later attempted and largely succeeded in the destruction of all Mayan codexes in the name of Gawd-uh.
Perhaps the most rapid explosion of mathematical advance, however, happened while Europe and most of the “white” world was languishing in the Medieval period, when knowledge and its pursuit was a “Church” thing and clearly restricted and defined by that institution. Again, it was persons who today would be considered “non-white” who led the way.
The 10th Century Persian mathematician Muhammad Al-Karaji worked to extend algebra still further, freeing it from its geometrical heritage, and introduced the theory of algebraic calculus. Al-Karaji was the first to use the method of proof by mathematical induction to prove his results, by proving that the first statement in an infinite sequence of statements is true, and then proving that, if any one statement in the sequence is true, then so is the next one. He also used mathematical induction to prove the binomial theorem. The coefficients needed when a binomial is expanded from a symmetrical triangle, are, today, usually referred to as Pascal’s Triangle after French mathematician Blaise Pascal, although many other non-white, non-European mathematicians had studied it centuries before him in India, Persia, China and Italy, including Al-Karaji.
Even some hundred years after Al-Karaji, Omar Khayyam (perhaps better known as a poet and the writer of the “Rubaiyat”, but an important mathematician and astronomer in his own right) codified Indian methods for extracting square and cube roots to include fourth, fifth and higher roots in the early 12th Century. He carried out a systematic analysis of cubic problems, revealing there were actually several different sorts of cubic equations. He did, in fact, succeed in solving cubic equations, and is usually credited with identifying the foundations of algebraic geometry.
Among other Arab mathematical exploits: The 13th Century Persian astronomer, scientist and mathematician Nasir Al-Din Al-Tusi was perhaps the first to treat trigonometry as a separate mathematical discipline, distinct from astronomy. Building on earlier work by Greek mathematicians such as Menelaus of Alexandria and Indian work on the sine function, he gave the first extensive exposition of spherical trigonometry, including listing the six distinct cases of a right triangle in spherical trigonometry. One of his major mathematical contributions was the formulation of the famous law of sines for plane triangles, a⁄(sin A) = b⁄(sin B) = c⁄(sin C), although the sine law for spherical triangles had been discovered earlier by the 10th Century Persians Abul Wafa Buzjani and Abu Nasr Mansur.
Other medieval Muslim mathematicians worthy of note include:
Thabit ibn Qurra, who developed a general formula by which amicable numbers could be derived, re-discovered much later by both Fermat and Descartes(amicable numbers are pairs of numbers for which the sum of the divisors of one number equals the other number, e.g. the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110, of which the sum is 284; and the proper divisors of 284 are 1, 2, 4, 71, and 142, of which the sum is 220);
10th Century Arab mathematician Abul Hasan al-Uqlidisi, who wrote the earliest surviving text showing the positional use of Arabic numerals, and particularly the use of decimals instead of fractions (e.g. 7.375 instead of 73⁄8); the 10th Century Arab geometer Ibrahim ibn Sinan, who continued Archimedes' investigations of areas and volumes, as well as on tangents of a circle; the 11th Century Persian Ibn al-Haytham (also known as Alhazen), who, in addition to his groundbreaking work on optics and physics, established the beginnings of the link between algebra and geometry, and devised what is now known as "Alhazen's problem" (he was the first mathematician to derive the formula for the sum of the fourth powers, using a method that is readily generalizable); and
The 13th Century Persian Kamal al-Din al-Farisi, who applied the theory of conic sections to solve optical problems, as well as pursuing work in number theory such as on amicable numbers, factorization and combinatorial methods;
The 13th Century Moroccan Ibn al-Banna al-Marrakushi, whose works included topics such as computing square roots and the theory of continued fractions, as well as the discovery of the first new pair of amicable numbers since ancient times (17,296 and 18,416, later re-discovered by Fermat) and the first use of algebraic notation since Brahmagupta.
With the stifling influence of the Turkish Ottoman Empire from the 14th or 15th Century onwards, Islamic mathematics stagnated, and further developments moved to Europe. Curiously enough it was a case of bureaucracy throttling progress, previously the domain on the Roman catholic Church!
By the 13th century and from that point on, mathematicians like Fibonacci and other early theorists began shaking off the shackles of Church driven dogmatic focus on the pressing theosophical “issues” such as “How many angels can dance on the head of a pin?” and rediscovered the works of earlier persons of other colors and cultures in the fields of mathematics and science.
“dīrghachatursrasyākṣaṇayā rajjuḥ pārśvamānī, tiryagmānī, cha yat pṛthagbhūte kurutastadubhayāṅ karoti.”
In English: “If a rope is stretched along the diagonal’s length, the resulting area will be equal to the sum total of the area of horizontal and vertical sides taken together.” This is, of course, a rewording of the concepts iterated by the Pythagorean theorem.
It is translated from Baudhayana Sulbasutra, one of the earliest Sulba Sutras written. The SulbaSutras are appendices to famous Hindu tradition Vedic scriptures and primarily dealt with rules of altar construction. In the Baudhayana Sulbasutra, there are several mathematical formulae that told how to precisely construct an altar. In essence, the Baudhayana Sulbasutra was more like a pocket dictionary, full of formulae and results for quick references. It was also written about 800 BCE, probably 350 to 400 years prior to Pythagoras’ discussion of the same construct. Oddly enough, the Greeks also made it (math) into a semi-religion, while it had had similar attachments to it for altar construction. As early as the 8th Century BCE, long before Pythagoras, the “Sulba Sutras” listed several simple Pythagorean triples, as well as a statement of the simplified Pythagorean theorem for the sides of a square and for a rectangle (indeed, it seems quite likely that Pythagoras learned his basic geometry from the "Sulba Sutras"). The Sutras also contain geometric solutions of linear and quadratic equations in a single unknown, and give a remarkably accurate figure for the square root of 2, obtained by adding 1 + 1⁄3 + 1⁄(3 x 4) - 1⁄(3 x 4 x 34), which yields a value of 1.4142156, correct to 5 decimal places. Mantras from the early Vedic period (before 1000 BCE) invoke powers of ten from a hundred all the way up to a trillion, and provide evidence of the use of arithmetic operations such as addition, subtraction, multiplication, fractions, squares, cubes and roots.
In the 14th century, The greatest of all Indian mathematicians, Madhava, went further and linked the idea of an infinite series with geometry and trigonometry. He realized that, by successively adding and subtracting different odd number fractions to infinity, he could home in on an exact formula for π (this was two centuries before Leibniz was to come to the same conclusion in Europe). Through his application of this series, Madhava obtained a value for π correct to an astonishing 13 decimal places. He applied the same mathematics to obtain infinite series expressions for the sine formula, which could then be used to calculate the sine of any angle to any degree of accuracy, as well as for other trigonometric functions like cosine, tangent and arctangent. Perhaps even more remarkable, though, is that he also gave estimates of the error term or correction term, implying that he quite understood the limit nature of the infinite series.
Madhava’s use of infinite series to approximate a range of trigonometric functions, which were further developed by his successors at the Kerala School, effectively laid the foundations for the later development of calculus and analysis, and either he or his disciples developed an early form of integration for simple functions. Some historians have suggested that Madhava's work, through the writings of the Kerala School, may have been transmitted to Europe via Jesuit missionaries and traders who were active around the ancient port of Cochin (Kochi) at the time, and may have had an influence on later European developments in calculus.
Among the greatest mathematicians of ancient China was Liu Hui, who in 263 CE, produced a detailed commentary on the “Nine Chapters,” an earlier Chinese text, containing concepts dating as far back as two millennia BCE. The ancient Chinese numbering system was a decimal place value system, very similar to the one we use today - indeed it was the first such number system, adopted by the Chinese over a thousand years before it was adopted in the West - and it made even quite complex calculations very quick and easy. Master Liu was one of the first mathematicians known to leave roots unevaluated, giving more exact results instead of approximations. By an approximation using a regular polygon with 192 sides, he also formulated an algorithm which calculated the value of π as 3.14159 (correct to five decimal places), as well as developing very early forms of both integral and differential calculus, more than 1800 years before Newton and Leibnitz began bitch slapping each other over who “invented” it.
The importance of astronomy and calendar calculations in Mayan society required mathematics, and the Maya constructed quite early a very sophisticated number system, possibly more advanced than any other in the world at the time. The Mayan and other Mesoamerican cultures used a vigesimal number system based on base 20. The pre-classic Maya and their neighbors had independently developed the concept of zero by at least as early as 36 BCE, and we have evidence of their working with sums up to the hundreds of millions, and with dates so large it took several lines just to represent them. The Mayans produced extremely accurate astronomical observations and measured the length of the solar year to a far higher degree of accuracy than that used in Europe (their calculations produced 365.242 days, compared to the modern value of 365.242198), as well as the length of the lunar month (their estimate was 29.5308 days, compared to the modern value of 29.53059).Of course white guys (Spanish priests) later attempted and largely succeeded in the destruction of all Mayan codexes in the name of Gawd-uh.
Perhaps the most rapid explosion of mathematical advance, however, happened while Europe and most of the “white” world was languishing in the Medieval period, when knowledge and its pursuit was a “Church” thing and clearly restricted and defined by that institution. Again, it was persons who today would be considered “non-white” who led the way.
The 10th Century Persian mathematician Muhammad Al-Karaji worked to extend algebra still further, freeing it from its geometrical heritage, and introduced the theory of algebraic calculus. Al-Karaji was the first to use the method of proof by mathematical induction to prove his results, by proving that the first statement in an infinite sequence of statements is true, and then proving that, if any one statement in the sequence is true, then so is the next one. He also used mathematical induction to prove the binomial theorem. The coefficients needed when a binomial is expanded from a symmetrical triangle, are, today, usually referred to as Pascal’s Triangle after French mathematician Blaise Pascal, although many other non-white, non-European mathematicians had studied it centuries before him in India, Persia, China and Italy, including Al-Karaji.
Even some hundred years after Al-Karaji, Omar Khayyam (perhaps better known as a poet and the writer of the “Rubaiyat”, but an important mathematician and astronomer in his own right) codified Indian methods for extracting square and cube roots to include fourth, fifth and higher roots in the early 12th Century. He carried out a systematic analysis of cubic problems, revealing there were actually several different sorts of cubic equations. He did, in fact, succeed in solving cubic equations, and is usually credited with identifying the foundations of algebraic geometry.
Among other Arab mathematical exploits: The 13th Century Persian astronomer, scientist and mathematician Nasir Al-Din Al-Tusi was perhaps the first to treat trigonometry as a separate mathematical discipline, distinct from astronomy. Building on earlier work by Greek mathematicians such as Menelaus of Alexandria and Indian work on the sine function, he gave the first extensive exposition of spherical trigonometry, including listing the six distinct cases of a right triangle in spherical trigonometry. One of his major mathematical contributions was the formulation of the famous law of sines for plane triangles, a⁄(sin A) = b⁄(sin B) = c⁄(sin C), although the sine law for spherical triangles had been discovered earlier by the 10th Century Persians Abul Wafa Buzjani and Abu Nasr Mansur.
Other medieval Muslim mathematicians worthy of note include:
Thabit ibn Qurra, who developed a general formula by which amicable numbers could be derived, re-discovered much later by both Fermat and Descartes(amicable numbers are pairs of numbers for which the sum of the divisors of one number equals the other number, e.g. the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110, of which the sum is 284; and the proper divisors of 284 are 1, 2, 4, 71, and 142, of which the sum is 220);
10th Century Arab mathematician Abul Hasan al-Uqlidisi, who wrote the earliest surviving text showing the positional use of Arabic numerals, and particularly the use of decimals instead of fractions (e.g. 7.375 instead of 73⁄8); the 10th Century Arab geometer Ibrahim ibn Sinan, who continued Archimedes' investigations of areas and volumes, as well as on tangents of a circle; the 11th Century Persian Ibn al-Haytham (also known as Alhazen), who, in addition to his groundbreaking work on optics and physics, established the beginnings of the link between algebra and geometry, and devised what is now known as "Alhazen's problem" (he was the first mathematician to derive the formula for the sum of the fourth powers, using a method that is readily generalizable); and
The 13th Century Persian Kamal al-Din al-Farisi, who applied the theory of conic sections to solve optical problems, as well as pursuing work in number theory such as on amicable numbers, factorization and combinatorial methods;
The 13th Century Moroccan Ibn al-Banna al-Marrakushi, whose works included topics such as computing square roots and the theory of continued fractions, as well as the discovery of the first new pair of amicable numbers since ancient times (17,296 and 18,416, later re-discovered by Fermat) and the first use of algebraic notation since Brahmagupta.
With the stifling influence of the Turkish Ottoman Empire from the 14th or 15th Century onwards, Islamic mathematics stagnated, and further developments moved to Europe. Curiously enough it was a case of bureaucracy throttling progress, previously the domain on the Roman catholic Church!
By the 13th century and from that point on, mathematicians like Fibonacci and other early theorists began shaking off the shackles of Church driven dogmatic focus on the pressing theosophical “issues” such as “How many angels can dance on the head of a pin?” and rediscovered the works of earlier persons of other colors and cultures in the fields of mathematics and science.
Again, in a perhaps unintentional but nonetheless meaningful turn, this resulted in primarily Greek (white?) works being of interest in Europe, since the Bible had been written in Greek and Latin from earliest times (Paul wrote in Greek), and were considered appropriate subjects for study when considering the Trivium (pre-Renaissance university curricula in logic, rhetoric and grammar). It would have been incredibly difficult for a Northern European to access works in Sanskrit, Chinese or Arabic for obvious reasons, including the Church's consideration of them as heretical or pagan. How pervasive this attitude was and remained can be shown by Darwin's hesitation to publish, even in 1859, the work he had begun decades before.
A large part of the rate of such advances in the West was the commercial explosion in Europe where the quest for locally unavailable raw materials became the driving force behind colonial exploits, which were themselves held back at first by a Church dictated world view of an earth of which five sixths was land surrounded by the remaining one sixth of the surface – water. The Chinese and Islamic states knew, and had known, better for centuries.
Now, back to the issue which triggered all this (remember, history is what I do, not math!) If, in the teaching of mathematics, there is a focus on “White” mathematicians, that is wrong, and wrong-headed. It is also largely the result of ignorance of history, a subject frequently under attack from the Far Right, if it doesn’t agree with the party line, which for some seems to be condensed to “White guys did everything good in the world.” I know that when, as a world history teacher, I discussed the Gupta dynasty in India and innovation of the use of zero, or the Arab invention of algebra (the word itself “al-jabr” is Arabic) I was telling tenth graders something they’d never heard in math class. So perhaps Ms. Gutierrez makes a semi legitimate point hidden in her biased diatribe.
On the one hand, her implication that most students are fed a diet of “white developed” math is accurate. It was so in my own educational experience and, I suspect in most schools today in America. As a historian I regret that. If I were a math teacher knowing what I know as a historian, I’d do it differently. What is lost, of course, in the fog of ethnocentric sour grapes is the fact that mathematics is colorless, odorless and tasteless. It just is. Like any language, it is a tool, not an end in itself.
Additionally, Ms. Gutierrez alleges that mathematics expertise becomes synonymous with “intelligence” in some circumstances. Of course, it does! We live in a technological world, based on the application of mathematics to almost everything we touch, use, watch or listen to in everyday life. Those who provide, moderate, invent, and/or manipulate these technologies are regarded by many as “smart,” like the booger eating, dandruff ridden tech guy who plugs the computer in when the erudite and well dressed exec can't "make it work." Would she have us become Luddites, smash the looms (and TVs, cell phones, computers, airplanes, etc…?)
Finally, she states that math skill is seen as “whiteness” in society and here I lose the thread, if any, of her logic. Looking at the burgeoning Indian and East Asian participation in engineering and applied math areas, worldwide and in the USA, clearly, she isn’t really referring to “mathematics ability” as an exclusively Caucasian stronghold, or if she is, she’s as blind to current applications as to the history of her discipline. If she is referring to some White, Black and Hispanic American students preferring to avoid math or seeing it as something they’d rather not do, that is another and even more tragic current reality and perhaps what she's really lamenting.
Now, back to the issue which triggered all this (remember, history is what I do, not math!) If, in the teaching of mathematics, there is a focus on “White” mathematicians, that is wrong, and wrong-headed. It is also largely the result of ignorance of history, a subject frequently under attack from the Far Right, if it doesn’t agree with the party line, which for some seems to be condensed to “White guys did everything good in the world.” I know that when, as a world history teacher, I discussed the Gupta dynasty in India and innovation of the use of zero, or the Arab invention of algebra (the word itself “al-jabr” is Arabic) I was telling tenth graders something they’d never heard in math class. So perhaps Ms. Gutierrez makes a semi legitimate point hidden in her biased diatribe.
On the one hand, her implication that most students are fed a diet of “white developed” math is accurate. It was so in my own educational experience and, I suspect in most schools today in America. As a historian I regret that. If I were a math teacher knowing what I know as a historian, I’d do it differently. What is lost, of course, in the fog of ethnocentric sour grapes is the fact that mathematics is colorless, odorless and tasteless. It just is. Like any language, it is a tool, not an end in itself.
Additionally, Ms. Gutierrez alleges that mathematics expertise becomes synonymous with “intelligence” in some circumstances. Of course, it does! We live in a technological world, based on the application of mathematics to almost everything we touch, use, watch or listen to in everyday life. Those who provide, moderate, invent, and/or manipulate these technologies are regarded by many as “smart,” like the booger eating, dandruff ridden tech guy who plugs the computer in when the erudite and well dressed exec can't "make it work." Would she have us become Luddites, smash the looms (and TVs, cell phones, computers, airplanes, etc…?)
Finally, she states that math skill is seen as “whiteness” in society and here I lose the thread, if any, of her logic. Looking at the burgeoning Indian and East Asian participation in engineering and applied math areas, worldwide and in the USA, clearly, she isn’t really referring to “mathematics ability” as an exclusively Caucasian stronghold, or if she is, she’s as blind to current applications as to the history of her discipline. If she is referring to some White, Black and Hispanic American students preferring to avoid math or seeing it as something they’d rather not do, that is another and even more tragic current reality and perhaps what she's really lamenting.
Equating math ability with intelligence is a slippery slope, and Ms. Gutierrez should be aware of where that comparison is sometimes made and by whom, since perhaps it’s actually originating in the groups she purports to be “defending” from discrimination. Is “acting white” being conflated with academic effort and ability? Don’t tell that to the ladies of “Hidden Figures!”
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