“Re-imagining Undergraduate Mathematics…with Structural Disruptions”: Vanderbilt Professor Denounces the Math Field as Racist

We recently discussed a professor who declared that astrophysics is racist due to its focus on “individualism” and exceptionalism.” These critiques are part of a larger movement alleging that everything from math to meritocracy is racist. The latest controversy centers around a lecture by Luis Leyva, associate professor of mathematics education at Vanderbilt University entitled “Undergraduate Mathematics Education as a White, Cisheteropatriarchal Space and Opportunities for Structural Disruption to Advance Queer of Color Justice.” In other words, math is a racist field of study advancing white male, straight “conforming-to-assigned sex” individuals.

Leyva advocates the “re-imagining undergraduate mathematics education with structural disruptions that advance justice for learners marginalized across intersections of race, gender, and sexuality.”

This is part of a growing movement across the country. We previously discussed the view of University of Rhode Island and Director of Graduate Studies of History Erik Loomis that “Science, statistics, and technology are all inherently racist.” Others have agreed with that view, including denouncing math as racist or a “tool of whiteness.” There are also calls for the “decolonization” of math as a field.

Leyva does not address meritocracy, which has been denounced by others. The controversy over meritocracy recently enveloped Virginia high schools after various schools admitted to withholding National Merit awards. Some parents allege that they were told the withholding of the awards was to support efforts toward greater equity in schools.

Various teachers and professors have objected that meritocracy is a tool of white supremacy. For example, Alison Collins, the Vice President of the San Francisco Board of Education, declared meritocracy to be racist even in the selection of students at advanced or gifted programs. As we have previously discussed, this has been a building campaign in academia as educators and others denounce selection based on academic performance through testing.  Most cities have such gifted programs or institutions, though we have discussed calls for the elimination of all gifted and talented programs in cities like New York.

I can appreciate the calls for greater efforts to develop math skills and teachers in underrepresented populations. I hope that we are all committed to that goal. That does not require “structural disruptions” as opposed to outreach and supportive programs.

It is the repeated calls to “decolonize” math that are most concerning. Math has always been one of the greatest equalizers, no pun intended.  As I discussed earlier, it is a shame to see math treated as a field of privilege when many of us view it as a field of pure intellectual pursuit and bias neutrality.  Either the math is there or it is not.  The race of the mathematician will not change the outcome.

218 thoughts on ““Re-imagining Undergraduate Mathematics…with Structural Disruptions”: Vanderbilt Professor Denounces the Math Field as Racist”

    1. Sex is identified at birth. If there are genital defects then a test can tell if there is a Y chromosome which makes the baby a male.

  1. Jonathan: I don’t understand why you find Luis Leyva’s lecture objectionable. I read it and another study by him. Leyva’s basic thesis is that race and gender “give rise to variations in math achievements and participation among marginalized groups”. Leyva’s focus is on race and gender discrimination as the reason for the underrepresentation of Blacks, Latina’s and the LGBTQ+ communities in math careers. I don’t see why math would be any different than other disciplines when it comes to racism and sexism. So I did a little research.

    If you look at the Field medals, the equivalent of the Nobel Prize, for awards in mathematics what do we find? Overwhelmingly, the majority of Field medals have been given to White males. There have been 64 medal recipients since 1951. All have been White males except for 2 women in 2014 and last year. Other prestigious math awards show the same disparity. No Black mathematician has ever been given a Field medal. Saunders McLane, one of the most influential Black algebraists of the last century and president of the Mathematical Association of America (MAA), was never awarded the Field medal. In fact, in 1951 Vanderbilt University hosted a MAA conference. Three Black attendees were barred from the conference banquet because of segregation in Tennessee at the time. A number of other Black mathematicians have been refused appointments to university math departments because of persistent racism.

    But some still cling to the racist notion that White males (and even some Asian males) have a “natural” affinity for math. In 2012 John Derbyshire, a columnist for the Nation Enquirer, wrote an essay in which he said: “Only one out of six blacks is smarter than the average white”. Derbyshire didn’t cite any statistics and he was later fired because of his racism. You say math is a “field of pure intellectual pursuit and bias neutrality”. Leyva and others who have studied the field find just the opposite. Math is no different than linguistics, history or other disciplines. “Meritocracy” has been based only in part on merit but predominantly on race and gender. I know how “meritocracy” works from personal experience. At the end of my first year of middle school I was recommended for an advanced placement class. What was meritorious about my work I don’t recall. The class had about 40 students. All were White males, like me, and only a few White girls. There were no Blacks in my AP class although about 1/4 of the total student population was Black. Mere coincidence? I don’t think so. I was pushed along through middle and high school because I was White and “expected” to excel. Black students were less fortunate because mostly White teachers didn’t have the same expectations for them. So they were pushed into sports and the trades. That’s how racism and gender discrimination played out in much of my academic career. And I suspect you had similar experiences. You just don’t want to admit it.

    1. You are repeating a common fallacy which is why statistics can not be used to determine discrimination.

      I will provide one example, but the pattern is true of every single measurable attribute.

      Men and women are more similar than they are different – by far.
      Agression is found in both men and women, and the overall difference between mean and women is not large.
      The median male is more aggressive than 60% of women – but 40% of women are more agreessive than the median male.

      But males comitt crimes of violence an order of magnitude more frequently than women.

      Why ? Because statistical differences that are small near the center of the distribution curve are gargantuan at the tails.

      The differences in aggression between men and women within 1 std dev of their median is small.

      The differences at 3 std dev are orders of magnatude.

      The immage below should make this clear.

      https://imgs.search.brave.com/cGctaVSuUZLRiJUzW5reJEzKs51NRJQJ0zB-HamLT90/rs:fit:820:233:1/g:ce/aHR0cHM6Ly93d3cu/c2Vla3BuZy5jb20v/cG5nL2RldGFpbC84/MzktODM5MzQzN19z/bWFsbC1kaWZmZXJl/bmNlcy1iZXR3ZWVu/LW1lYW5zLW9mLXR3/by1ub3JtYWwtYmVs/bC5wbmc

      20% of blacks, 30% of hispanics, 50% of whites and over 80% of asians meet the SAT’s media score for Math for college students.

      If you do not understand that means that the percent of blacks who are going to be in the top 0.001% of everyone in math is going to be ZERO,
      While the percent of asians in the top 0.001% is likely to be abotu 50% or greater – then you are unable to understand statistics.

      These issues are true of pretty much EVERYTHING.
      This is why 80% of NBA players are black, and why there has been no White superstar in decades.

      1. But the differences between genders – even though small – make huge differences. Boys and girls may test at the same aptitude for math but girls naturally head towards fields that are nurturing. Most Boys like things, most girls like feelings. This proves that gender differences are innate – and gender expression is tied to sexuality – and not socialized.

        1. Your points are all relevant.

          My point was that even if the differences at the mean are small the differences at the margins are enormous.
          And this is not specific to gender.

          Any attribute such as IQ. Physical Ability, musical ability that distributes on a bell curve, where there is even a small differences with respect to an immutable attibute such as race or sex, will have LARGE differences at the margins.

          The original poster claimed that it was racism that no black had one some prestigious math award.
          The FACT is that there are small difference in mathematical apilities of the average black and the average white (or asian).
          These means next to nothing for a randomly selected person on the street.
          But it means the frequency of the rarest of the rare mathematicians will not be 4 times as comon for whites and 8 times for asians,
          but actually 1000’s of times. Because small differences at the mean are enormous differences at the margines.

    2. Using tests for school placement was the solution for helping all students to advance regardless of the variations in the quality of the lower schools they attended. The tests test for altitude and or knowledge. IQ tests are the most rigorously tested tests in existence and are used because they are highly accurate in predicting future success. The failure of Blacks and any other category other than white male to achieve awards or placement in higher learning has to do with the low quality of teachers, low quality of parenting and cultural expectations of the students sub-culture. It is not due to racism or sexism. In the most equal societies of all the gender roles are the most divergent. The Scandinavian societies are the best examples. They are the most equal yet when given the choice women choose fields associated with feminine traits and males choose fields associated with masculine traits.
      There were high performing Black schools in the US until liberals and leftists decided to remake them into social promotion experiments which have failed miserably. Get rid of all leftists from schools and go back to what used to be considered a rigorous, demanding, merit based old style liberal education where kids actually learn and drop the emphasis on self esteem and feelings. Kids will feel good about themselves naturally if they can make a contribution to society and support themselves and their families. High self esteem with out merit or accountability just breeds narcism and failure.

  2. Remember, a professor of “math education” is not a math professor. “Math Education” is basically a cargo cult of mathematics, trying to imitate the trappings and cachet of mathematical knowledge, while having none of the substance, being the creation of a culture completely alien to it.

  3. On average, students who perform well in math—or any other subject, for that matter—study more hours per week than students who don’t. How about using that widely known bit of information as a gateway to equitable performance?

    1. That is certainly true of Asian kids. I don’t know how many times I’ve seen the whole staff – including the chefs – at an Asian restaurant tutoring one of the owners kids. The staff might not know English but many of them know math very well. After school tutoring for 1-2 hours every day is the norm in Asian countries.

  4. Lowered expectations (e.g. DIE: Diversity, Inequity, Exclusion). Diversity [dogma] (e.g. racism, sexism, ageism) breeds adversity.

    1. Why on earth would anyone think that diversity, equity and inclusion are positive for society? They aren’t. Multiculturalism isn’t positive. Equal outcomes without equal effort is not positive. Inclusion the pathological is detrimental. Only sociopathic Narcissistic elements of society want such changes so that they can openly prey upon the majority.

      1. “Multiculturalism isn’t positive”

        Sure it is.
        I like eating food from different cultures.
        I like looking at art from different cultures.
        I like talking to people from different cultures.

        If you don’t, what a loss.

  5. Let’s wrap this up. Give Ukraine all the weapons that the United States and NATO would use themselves if at war with Russia. The Ukrainians should be given the means to invade Moscow and capture Putin themselves, as if NATO were doing it. The sooner it gets wrapped up, the sooner Tucker will stop crying like a baby about it. Isolationishts are stupid. They won’t let you extinguish a fire, so the fire gets bigger, so there becomes an even greater need to extinguish it, and so the cycle continues.

    1. It is extremely dangerous to corner failing global powers. Especially one with half the nukes in the world.

      Ukraine is not and never has ben in the US national interests.
      While that does nto mean we allow Russia to crush it under his boot, it certainly means we do not risk global nuclear war over it.

      Russia will collapse soon – with or without our help. There is no reason to risk nuclear war to accomplish what is inevitable.
      The US should be more interested in how do we deal with the collapse of Russia – a country with half the nukes in the world.
      Within the next decade that is likely.

      30 years ago we SHOULD have been trying to build bridges with Russia and Putin – trying to bring them into the west rather than trying to isolate Russia. You can blame Clinton and Shrub for that. And to a lessor extent Obama.

      1. Russia won’t collapse. It’s making more money than ever thanks to Biden’s sanctions. It’s forging stronger foreign ties again due to O’Biden.

        1. While I share your distaste for the Biden regime, that does not alter facts.
          Russia’s peach GDP was 2.2T – about 1/10th that of the US in 2013.
          In 2021 GDP was 1.7T estimated 2023 GDP is 1.5T.

          Sanctions have required Russia to dip heavily into its currency reserves.
          While it was prepared for Sanctions and had “sanction proofed” its economy – that is accomplished by burning through its reserves.
          It will exhaust all reserves in 9-18 months – at which point either its economy collapses or it MUST be able to borrow money on the international market – which so long as sanctions are in place it can not do.

          Separately Rusia is in almost the worst demographic position of any country in the world. It has a rapidly declining population and no way to recover.

          Regardless of this War Russia is in trouble – facing a failing economy within the next decade.

          Biden’s stupidity does not change Russia’s fundimental problems.

    2. You know Russia gets about as much support from the left as the right. Well, you don’t know it. I can tell by your comment that exploring the reality of complex situation is not your forte. Someone screams and you join the unthinking herd in ‘oh, look at Tucker Carlson.’ Whopee!

      A small group of Leftists about the same size as the small of people on the right, in America,and around the world, also support Russia. And if we’re going to point fingers, Bush wanted Ukraine in NATO and leftists shut that down. So this blood is on your hands. Had the left not stabbed Ukraine in the back, there’d be no war today.

      1. Just around the time Biden started to think how much money he could take in, if the right setup was accomplished. Then his son was available and game on. Untouchable…

    1. It doesn’t.

      But people who use or teach math may.

      Also, historically, the Greeks are not the only ones to have invented (or discovered) math.

      1. Yes, affirmative discrimination: Diversity [dogma], Inequity, Exclusion (DIE) that targets men, women, and “our Posterity” based on color judgments, class-based bigotry, is a clear, present, and progressive problem.

        Yes, historically, human discoveries are attributable to a global climate characterized by diversity of individuals, minority of one.

  6. If the students don’t get a good foothold on math (and reading) in the lower grades, it can become more difficult as they move up in the grades. I heard a story recently (post-Covid school shutdowns). It was the teacher’s turn to be observed and evaluated. She was working on a page in the math book with the students. The observers determined that she should be farther along in the book, even though the students were having a problem grasping the concept being studied. Is this why they they grow to not like math? They are pushed forward? Is that fair to any of the kids. Because they have problems reading, will there need to be some equity developed for kids who can’t read? There are word problems in math. Again, were they pushed along without spending time helping them, figuring out the best way that “each” student learns and then group them together to make it easier for them to learn? I am losing patience with elitist college professors and administrators.

      1. One of the sponsors of all these events is from the Tulsa Ok area, on the other side of town. Before about 2 years ago I had never heard of Clay Clark or the rest of them.

        Come to find out here & in many other areas we’re all pushing for the same type things, a return to a just USA Constitutional Republic of Liberty & Freedom.

        Much like Prof Turley & the 1 Million plus Peaceful People that showed @ the stop the steal rally on J6.

  7. Letting people into fields that rely on math and the ppl don’t know math will hurt outcomes from those professions. This isn’t tennis where the elite make the games scoring so complicated only the initiated can keep up. This is abacus math! Which logically can not be racist….And even if it is at root that pupils don’t get taught properly in primary school. That’s a primary school problem not…..a professional problem handled bymaltrication standards to a university.. .

  8. JT reports on and discusses many things that he disagrees with, but I have never heard him disagree on the basis of communism or worry about a communist threat. So why are people around here constantly bringing up communism and a communist threat when discussing the issues raised by JT?

    1. Concerned Citizen – Communism seems to be used as a place-holder for marxism. A political scientist could probably give a nuanced difference, but many of the news items the Professor comments on are in some way a manifestation of cultural marxism. Cultural marxism has some similarities to economic marxism, with the difference being that the class divisions are not along economic lines, but in terms of race, ethnicity, sexual orientation, and the like. A good, if brief, introduction to the topic can be found here:

      https://docsandlin.com/2018/04/23/cultural-marxism-simply-explained/

    2. “So why are people around here constantly bringing up communism . . .”

      That is actually a good question.

      Communism is a form of dictatorship based on Marx’s political theory. But that pertains to politics. The issues in this post (and others like it) are far deeper than politics.

  9. As far back as Marx and Engels, Communists recognized that they’d never replace Western Society by force. It’s long been understood that destroying capitalist societies would require our institutions to be destroyed.

    Professor Leyva, et al are simply advancing that theory . . . and we’re letting them!

    1. About as evil as it can possibly get. Liberal press is pathetic for not reporting it. Then again they had zero interest in the Kermit Gosnell trial in Philadelphia. For them, any corruption, no matter how abject, that casts doubt on their narrative is not worth reporting.

    2. Diogenes,
      Horror story is right.
      I do hope those men are found guilty, and get the max time.
      Sick. Seriously sick.
      Note, these sick predators are NOT a reflection of the LBGetc (I cannot keep up with all the . . . whatever) community.
      Gays Against Groomers are, clearly by their name, against this kind of sick behavior.
      As should everyone.

      1. Thank you .

        The fight against peodophiles – and policies that empower peodophles.
        The fight against teaching our kids nonsense is NOT a fight against homosexuals or transsexuals.

        The fight against CRT and similar racist BS is not a fight against minorities.

        I have gay friends whose families were incredibly harmful to them as kids.
        That unfortunately does not alter the fact that government is worse.

        Recently an FTM trans teen was removed from her family because they were unaccepting.
        After which she ended up being Trafficed – Twice.

        To the extent that government has any role it is to mitigate from the outside the harm of bad parents.
        It is not to co-parent, or take over parenting.

        Charles manson is the product of government parenting.

        With all respect to those working in foster care or other services for children with no parents or bad parents,
        the record of govenrment – or foster care is much worse than that of parents.

        One of the common failures of the left is to find a problem – life is fully of problems and to presume that
        Government stepping in will be an improvement.
        Just be cause we have a real problem – does not mean that government involvement will not make it worse.

        We do not not and I do not care what the causes of Homsexuality or Transexuality are. We do not know if they are genetic, or environmental, or a choice. And I do not care.

        They are NOT however normal – +- 2 std from the mean, and we should quit pretending they are.

        Everything that is not normal is not inherently bad.
        But accomidating abnormality that is not inherently bad often encourages abnormality that is inherently bad.

        1. JohnBSay: Your first two sentence/paragraphs are very good, and important to remind others of.
          Coming from a large metropolis, I likewise have gay friends, and they do NOT join in all this nonsense; for that reason, they remain closeted. Too bad, because they and like are the ones we all should hear from.

          1. I have some friends like yours.

            Frankly based on my own friends – you would guess that straight white males are a tiny minority.

            Unfortunately many of my friends who are gay or minorities – while not the idiots that so many on the left here are,
            Are too supportive of this nonsense.

            One of the things that disappointed me as a strong supporter of Gay rights was how quickly many close friends turned from victims to oppressors.

            You have the right to mary, to adopt, you need no longer be affraid of getting raided by the police and jailed.
            You can hold a security clearance.

            Why is it that you give a $hit that some christian fundimentalist will not bake you a wedding cake or build you a webt site ?

            Leave the people you call bigots alone – or you will become what you you hated.

            I have said repeatedly that we live in the least racist, least homophobic, least transphobic, least discriminatory country in the world, at the least descriminatory moment in time.

            We should be celebrating how close we have come to Martin Luther Kings dream – rather that trying to F’it all up.

            But we are not. We are in the midst of a mess driven by the extreme left that strongly resmbles the Chinese Cultural revolution replayed as a farce. Most of the remaining “culture war” issues will sort themselves out on their own over time – without government.

            Private businesses will convert to multiple self contained genderless restrooms.
            Most of us will try to call woke young people whatever it is they want – so long as it is not too insane, and so long as we are not FORCED to.
            In the long run most will grow out of this nonsense. as things like a family, a home, a good job become more important.

            Dress as you like. If you are an adult – have surgery, take drugs.

            There are a few problems that are harder – that are likely to be solved in ways the left does not like.

            DO NOT F#$K with the kids.

            I would do most anythign to support my kids but if they were still teens, there is no way in H311 that I would be rushing them into surgery or injections if they thought they were trans.

            And the right place for a teacher that wants to sex up 3rd graders is jail.

            No M2F trans should not be competing in womens athletics.
            No pre-operative M2F trans do not beleong in womens and girls lockerrooms.

            Finally – to varrying degrees – because we are not all the same we are not going to have universal acceptance.

            Grow up and get over it.

            The best way to acheive tolerance is to be tolerant of those who you think are not tolerant of you.

            I learned alot when I brought my daughter home from China.

            A few people were openly hostile. I was attacked by a small number of people who had no problem berating me for not adopting a white kid from the US. But these a**holes were pretty rare. Many many people came up to me and inarticulately and inartfully asked sometimes invasive questions. These were not hateful bigots. Sometimes they were people who were curious or contemplating adoption themselves, and a white guy with a chinese child screams I am and adoptive parent.
            By far adopting my daughter connected me to many many more wonderful – if sometimes inarticulate people than bigots.
            Thre were minor problems – because my kids did not want to be the center of attention all the time.

            I also found that having two asian kids really opened up minority communities to me.
            It changed the way ramdom black or hispanic people on the streets would relate to me.
            Minorities were far more likely to smile at me in the grocery store or say hello.

            It also had a dark side – minorities were more likely to be open with me regarding race.
            I have had far more black people say incredibly biggoted things to me about asians – sometimes with my kids nearby,
            Willing to be open with me – because my kids are minorities, but oblivious to the fact that it was MY CHILDREN they were talking about.

            In the end I find the biggest difference between those I know on the left and those on the right,
            is that those on the left are oblivious to their own biggotry – only seeing it in conservatives,
            and think they are better than everyone else.

            Just to be clear – my friends – the people in my life come in all different races, orientations, politics,
            you take your friends how they come, or you do not have that many friends

  10. Imaginary numbers. Political coefficients. Farrakhan’s Theorem. Unequal angles are congruent. Forced dis-integration. Obama transforms. Diversity calculus. Malthusian redistributions. Sexual derivatives. The null hypothesis.

    The new field of progressive mathematics. Where everyone qualifies for an advanced degree. But we all regress below the mean.

    1. EDKH: Just in case you didn’t know, imaginary numbers are part of the complex numbers while the null hypothesis is used in a common form of statistical reasoning.

      Just being pedantic.

      1. Very good, David! You correctly called out a list of woke nonsense bookended by two real concepts. Somebody knows their math.

        Unlike so many students whose mathematics education is corrupted by tangential issues.

              1. They call it the Royale with Cheese. They got the metric system there. They wouldn’t know what the f#ck a Quarter Pounder is.

                But, like their confederates at Vanderbilt, they are at the forefront of progressive thought. QED.

        1. The most basic imaginary number, “i,” is defined to be the square root of -1. All other imaginary numbers can be expressed as a multiple of i, just as real numbers can be expressed as a multiple of 1. If your response is that -1 has no square root, imaginary numbers were invented to define its square root, because it’s useful in pure math, and then it turned out to have applications.

          Imaginary numbers and real numbers are both subsets of complex numbers, and they are often used in combination (e.g., 1 + i). If you do an internet search on how are complex numbers used in the real world, you’ll find a number of lay discussions. Among other things, they’re used in various kinds of engineering.

        2. The term “Imaginary” is an unfortunate one, as the things quantified by imaginary numbers are just as real as, for instance, negative numbers. At first glance, how can you have less than zero? But then you realize that they allow you to combine two opposite concepts in a single number: profit and loss, overshoot and shortfall, growth and shrinkage.

          Imaginary numbers complement real numbers in a similar, though less obvious way. In electric circuits, capacitance and inductance show up as imaginary resistance. Conductive materials show up as having an imaginary component to their permittivity, making electromagnetic waves peter out. Similar to the way negative numbers let you gather opposite physical concepts under one number, imaginary numbers extend that to certain related, yet orthogonal concepts.

          1. DaveL: Fascinating. Thank you.

            So is it right to say that “i” is a variable, the value of which is always a negative number? That would fit with this: “they allow you to combine” — as algebra is the math of integration.

            It seems that “i” is a correlative concept, in that its meaning depends on positive numbers. Is that right?

            “profit and loss:” So the “i” symbolizes *both* the profit and loss, even when the result is a positive number? Or does the “i” symbolzie both profit and loss, but only when the result is a negative number?
            “. . . show up as imaginary resistance.” It seems that “imaginary” in this context does *not* mean fantasy or Casper the ghost. Rather that it means a negation, as in a force that depletes. Is that correct? If so, then I assume that drag can also be symbolized by an “i.”

            Your examples are clear and terse. Thank you, again.

            1. i is not a negative number. Negative numbers are a subset of real numbers. Imaginary numbers are not a subset of the reals.

              i = squareroot(-1)

              If you think of reals as being on a number line (the x-axis), the imaginary numbers are perpendicular to it (the y-axis), so that 1 + i gives you a location in a plane, analogous to the (x,y) coordinate (1,1). As Dave noted, one of their applications is to waves, because you cannot capture wave motion just with the x-axis; you need a plane to illustrate wave motion.

            2. “i” is not a variable, it is a constant. There’s no real number which, multiplied by itself, gives -1, so we imagine such a quantity exists and call it “i”. It’s best not to think of it as any kind of force or other such poetry – it’s a number, a number that, multiplied by itself, gives you -1, that’s all.

              It’s not a negative number, but the way it fits with and extends the real numbers is similar to how negative numbers fit with and extend the positive numbers. When I spoke of profit and loss, I was talking about the way negative (not imaginary) numbers combine with positive numbers to describe two opposite phenomena is a single quantity. Imaginary numbers combine with real numbers to do something similar. They allow phenomena that seem oddly related to be grouped together under a single quantity.

              As with negative numbers, imaginary numbers also make mathematics itself more unified and elegant, turning a collection of exceptions and special cases into universal rules. For instance, without negative numbers you can do 3 + 4 – 5, but not 3 – 5 + 4 while following a consistent order of operations. But if you’re willing to go into negative numbers, they both work and yield the same result. Similarly, without imaginary numbers, x^2 + 4 = 0 has no solutions, but x^2 – 4 = 0 has two: but with complex numbers both have two solutions. In fact any similar equation with just powers of “x” and constants (a polynomial, it’s called) has exactly as many solutions as the highest power of “x”.

              1. You know what’s really sad?

                That a generation of young people won’t have the opportunity to learn about complex numbers. Let alone other, more accessible mathematical concepts that would teach them critical thinking skills and help them advance their lives and careers.

                Instead, math educators like Luis Levya spew forth nonsense. Yet another hidden cost of the woke plague that has overtaken academics.

                1. What bunk. There are generations of math teachers teaching the current generation math. They range from crappy to excellent, just like the teachers of any other generation. Some students will learn about imaginary numbers in HS and others won’t, just as occurred in your generation. Others will learn about them in college, just as occurred in your generation.

                  The things that actually most stand in the way of good teaching are the facts that (a) it’s hard to learn to teach well (as you not only need a strong subject matter knowledge but also a knowledge of students as learners, an ability to interact effectively with students, parents, administrators, other teachers, …), and (b) our society devalues it, insulting teachers with stupid sayings like “those who can, do; those who can’t, teach,” and telling bright STEM students that they should work in industry rather than teach.

                  1. That’s a nice sentiment, but it doesn’t square with the subject of this post. Judging by the comments above, some of Turley’s readers have had the privilege of a strong math education. It is easy forget that many students aren’t to lucky.

                    Luis Levya and the Vanderbilt School of Education aren’t helping the situation. They aren’t celebrated for teaching the new generation of teachers how to teach math. They are celebrated for teaching the division and resentment. The politics of long division.

                    Time, energy and resources diverted from far more challenging, productive and enlightening subjects. Sadly, it doesn’t seem to be an aberration. Wouldn’t it be far more productive if classroom time were spent on actually teaching math?

                    WARNING: Teacher trained at the Vanderbilt School of Education.

    2. First the communists infiltrated the law schools, then the social sciences and arts, then the stems. The sickness has pushed everyone beyond what they can tolerate. I look forward to the retaking of our education system — the one so many students worldwide were striving to get accepted by.

      1. Who would’ve thought we’d ever see STEM get corrupted by woke politics? But, here we are. The system is far too corrupt for change from within. We need fundamental change. Fundamental reform. And to strip universities of their privileged, tax exempt status.

  11. Well, yes. I know of important mathematics from East Asians and South Asians but not Southeast Asians. None from Arabs or sub-Sahara Africans, ever. For that matter, none from Latin America. Ditto Iceland.

    1. David – are you sure about the none-from-Arabs part? I thought algebra was an Arab invention. Even the name is Arabic – al jabr meaning completion or the reunion of broken parts.

      1. Kansas Elder, yes. Algebra comes from Persians. The Arabs just adopted it. Similarly, the so-called Arabic numerals with the place system for representing numbers comes from India. The Arabs just adopted it.

    2. @david

      Who do you think the South East Asians were back then? Moghuls, who were Muslim. You are also leaving out ancient Egypt, and, and and. Mathematics is a continuum that has nothing to do with the subject’s ignorant 21st century identity dogma, nor the modern dem party’s. They have coopted based on their own limited knowledge, or fully aware and gaslit, for their own benefit. I have come, for myself, to term this ’21st century colonialism’, it is nearly exclusively employed by privileged democrats/progressives regardless of nationality, and it is the height of irony that in doing so they think they are ‘decolonizing’ anything whatsoever. As I said earlier, these people are turnips. All they are capable of is projection, appropriation, and irrationality. Then again, some are likely just nefarious.

      1. I like your answer, “Mathematics is a continuum.” I start at zero and work from there. Zero, first used in India, preceded Mohammed by half a century and was long after the algebra of the Egyptians and Greeks. If I wish to go back in history, I choose the birth of man and his ten fingers.

    1. In woke-world anyone who claims two plus two equals four is the racist. They don’t value inclusiveness and diversity because they leave out the possibility that two plus two could equal 5 or 7 or negative-pi.

  12. “I don’t blame you. I blame the person that hired you.” An old saying that fits the crisis at Vanderbilt to a tee.

    Levya’s graduate training and focus is in mathematics education. He is an assistant professor in the Department of Education in Vanderbilt’s Peabody College. Levya’s job is teaching – or should we say indoctrinating – future math teachers. Terrifying when you think about it. He has been amazingly successful in his career. But you can’t blame Levya. He is doing what he is paid to do.

    Camilla Persson Benbow has chaired the Department of Education at Peabody College for the last twenty-five years. Dating back to last century. Benbow enjoys the fruits of a lucrative position and the security of tenure. Ironically enough, her academic focus is on identifying gifted children and the development of mathematical talent. Yet, as an administrator, Benbow has presided over the devolution of a once proud department into one focused on the woke, political indoctrination of generations of teachers.

    How do we stop this madness? This failure of leadership? Through fundamental change and reform of our academic institutions. Institutions that, by the way, are exempt from paying their fair share of taxes. By holding administrators like Camilla Benbow accountable for the destruction of academic standards in their departments. Through the loss of their jobs. By replacing them with competent administrators who reward academic excellence free from the constraints of political ideology.

    BTW, in an excellent comment below, honeslawyermostly offers a warning label for bridges and other structures: CAUTION- designed by a Vanderbilt engineer.

    May I offer a corollary aimed at protecting schoolchildren and their parents? WARNING – Teacher trained at the Vanderbilt School of Education.

  13. “IF YOU CAN KEEP IT”
    ___________________

    What Fresh Hell finally awakens and bolsters the resolve of the “sleeping giant?”

    When does the worm turn and roust Americans?

    When do Americans take back their restricted-vote republic under the Constitution and neutralize that which is disparate, incongruous, irrelevant, immaterial, superfluous and unassimilable?
    _____________________________________________________________________________________________________________________________________________________

    “The [Communist Manifesto] dictatorship of the proletariat.”

    – Karl Marx
    _________

    “[We gave you] a [Constitutional, restricted-vote] republic, if you can keep it.”

    – Ben Franklin
    ___________

    “But when a long train of abuses and usurpations, pursuing invariably the same Object evinces a design to reduce them under absolute Despotism, it is their right, it is their duty, to throw off such Government, and to provide new Guards for their future security.”

    – Declaration of Independence, 1776

    1. When does the Supreme Court free Americans and begin the implementation of the severe limitations and restrictions on government, and the clear and evident meaning and intent of the Constitution and Bill of Rights?

  14. Professor Turley, The Joint Mathematics Meeting involved numerous sessions/lectures over the course of several days. Are you concerned only with this one math lecture or are there others we need to worry about?

    1. This strikes me as a session associated with the SIG-RME (Special Interest Group – Research in Mathematics Education)

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