Mathematics & The Imposing Your Beliefs Fallacy

Mathematics & The Imposing Your Beliefs Fallacy

I blush as I write the truism that it is possible, given obvious reasons, that anybody anywhere might discover or hit upon a mathematical truth. Any body. Even NPR listeners. Even DIE commissars. Even, yes, female professors.

I blush because this is not only obvious, but it is idiotically obvious, and when you are forced to write something idiotically obvious, you cannot escape a sting to your conscience.

You felt it, too, that hot stab of inflamed hackles, if you were a woman or a white-knighting beta male and you read the obvious statement that even women professors can discover mathematical truths. He must mean it isn’t true!, the constantly aggrieved internally emoted, Which is why he wrote it was true!

Which brings up the difference between might and likely. Because if you emoted in that fashion you fell out of the likely camp and into the might. Let that pass for the moment.

Let’s instead discuss why you and I are forced onto this dismal subject, and why we have say things that should “go without saying”.

But first a small thought experiment. Which of these three sentences give you the most cringe?

  1. Of course men can discover mathematical truths;
  2. Of course women can discover mathematical truths;
  3. Of course Indigenous and First Nations peoples around the world can discover mathematical truths.

Well, it’s no secret. There is no cringe for the first sentence, given the (again, obvious) observation that nearly all the most important mathematicians were and are men. I say obvious because everybody who cares to think about this know this. The sentence becomes a banality.

There is some cringe with the second sentence, the level according to how earnestly Equality is believed. There is in many minds the question Why is he saying this? By which they mean, what motive do I have. They ask themselves this because they know it is false that the most important mathematicians were and are women. But they also know they should not want this to be so. And so anybody who brings up the “disparity” in this underhanded way must be against Equality, or that they seek to discourage women from discovering mathematical truths.

But that is like arguing a man who said “The sun rises in the east” is against rotational freedom and works actively in preventing the sun rising in the west.

The third sentence I borrowed in part from lady professor Rowena Ball, from Australia. There is no cringe in the third sentence. Instead, many will find themselves nodding along with it. They do this because they know there have been very few “Indigenous and First Nations peoples around the world” who have been among the most important mathematicians. Yet, one feels, like with women, there have been certain anti-mathematical obstacles put into the paths of these fine people; obstacles which, when removed by Education, will allow Indigenous mathematicians to flourish.

Doubtless this is so in some cases. There may be a Ramanujan hiding among some Aboriginal tribe, just waiting for the right government grant to come along and free him—or her—to theorize. Of course, this might be a bad example, because Ramanujan’s genius was readily recognized under less than ideal circumstances. And he rose to prominence at a time in which the near totality of feverish craving for uncovering hidden gems did not yet exist; indeed, something like the opposite was the case, or so we are always told we must believe.

Now our Ball would, the linked article indicates, certainly enjoy uncovering a few gems. But it seems she has formed the tacit premise that gem searching has been going on for some time now, and without much success. And so the real problem must be in the definition of what counts as a gem.

Indigenous societies haven’t contributed much to mathematics as it is traditionally understood, but that is because they “often excel at non-numerical mathematics”. Like?

One interesting example that we are currently investigating is the use of chiral symmetry to engineer a long-distance smoke signalling technology in real time,” Professor Ball says. “If you light an incense stick you will see the twin counter-rotating vortices that emanate ? these are a chiral pair, meaning they are non-superimposable mirror images of each other.”

A memoir by Alice Duncan Kemp, who grew up on a cattle station on Mithaka country in the early 1900s, vividly describes the signalling procedure, in which husband-and-wife expert team Bogie and Mary-Anne selected and pulsed the smoke waves with a left to right curl, to signal “white men”, instead of the more usual right to left spiral….

To create and understand these signals, you have to be a skilled practical mathematician, Professor Ball says.

To which the only rational response is, No, you don’t. You can be utterly ignorant on the workings of internal combustion engines, not having a clue what a piston is or how it might function, and still be able to drive a car. Yet if you were to cruise past Ball, she would say “There goes a mechanical engineer.”

Incidentally, one also wonders if in addition to the chiral-paired smoke signal for “white men” there is another for “mathematicians.” Or is that considered a redundancy?

Here are two more important truths, both as obvious as the truth with which we began: (1) All of mathematics has not been discovered; (2) Many discoveries to come will arise from unexpected directions.

For instance, a great many interesting things were learned from the Mayan base-20 mathematical system after it became known. (And, by coincidence, has curious connections with Ramanujan’s thesis on highly composite numbers; i.e. those numbers with lots of divisors.)

So it remains possible that a form of mathematics, as yet unknown to the larger world, is operating quietly or in secret among “Indigenous and First Nations peoples”, a form that will in time become better known. But it won’t be of the chiral-smoke signal type, because that is an ordinary (to us) mathematician noticing a new application of ordinary (to us) mathematics.

The mistake egalitarians make is easy to identify. It is the opposite of the one a man makes when he observes only men who are taller than their mates, and concludes, falsely, that therefore all men are taller than all women. Ball argues that of all the mathematicians she knows the great majority are not “Indigenous and First Nations peoples”, and concludes, falsely, that therefore “Indigenous and First Nations peoples” are equally adept at mathematics as other groups.

To prove this, as said, she needs to redefine what mathematics means. And to do that she invokes the Imposing Your Beliefs Fallacy (blog, Substack). Which she does by “decolonizing”.

“Mathematics is a universal human phenomenon, and students of under-represented and minority groups and colonised peoples are starting to be more critical about accepting unquestioningly the cultural hegemony of mainstream European-based mathematics,” says Professor Rowena Ball from the ANU Mathematical Sciences Institute…

“Mathematics has been gatekept by the West and defined to exclude entire cultures. Almost all mathematics that students have ever come across is European-based,” she explains. “We would like to enrich the discipline through the inclusion of cross-cultural mathematics.”

Somebody or some group must gatekeep and impose their beliefs on what mathematics is, by setting its limits and purposes. One can, à la Ball, say that mathematics is whatever anybody wants it to be, but that makes it nothing. You reading this now is “mathematics” if you are a Victim. Ball is right that almost all mathematics in European-based, and that the people in this system (who now come from many races) continue to impose these beliefs on the practice of mathematics. She is being absurd and libelous to say that mathematics is “defined to exclude entire cultures.” No, it is not.

The author of the article says, “Here, in Australia, we are still in the early stages of the decolonisation journey. There is a curiously persistent trope that Aboriginal and Torres Strait Islander peoples had only rudimentary mathematical knowledge, despite widespread evidence to the contrary.”

Dividing through for the nauseating effeminate language (“decolonisation journey”), the author makes the same egalitarian error. There is no such evidence of mathematical equality, therefore equality must actually exist, she says.

What else can you say to such an absurd mistake except that is it absurd?

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  1. Gwyneth

    We are witness to the devolution of intelligence and common sense into absurdity and ridiculousness. While, on the one hand, it is pathetic and troubling, on the other, it does have a certain element of entertainment.

  2. McChuck

    Twits gotta twitter. Her mutterings have no more content than of a dog howling at the moon.

  3. JH


    Which of these three sentences give you the most cringe?

    NONE of them is cringe-inducing. All are proven facts.  

    I asked “Why is he saying this’? I asked the question out of curiosity.   I have always believed that the most important mathematicians include both men and women. (Though it was not true back when women were denied education.)  Just Google.

    Anyhow, what makes an important mathematician? Hard work? Great collaborators? Great PhD students?  Luck?

    It seems that you often somehow connect everything to your definitions of equality and DEI. While I think that the contents of higher-level abstract mathematics is culturally neutral, Prof. Ball’s points are that there are values in how Indigenous societies historically used mathematics and that she hopes to grow a cohort of Indigenous students in mathematics. Well, people can have different understandings of the same thing.

    From the link referred to in this post:

    Indigenous societies often excel at non-numerical mathematics, she says.

    “One interesting example that we are currently investigating is the use of chiral symmetry to engineer a long-distance smoke signalling technology in real time,” Professor Ball says. “If you light an incense stick you will see the twin counter-rotating vortices that emanate ? these are a chiral pair, meaning they are non-superimposable mirror images of each other.”

  4. Briggs


    It may seem to you that “JH” is an alternate persona of mine (much as how some think I am really Ianto Watt), or that JH and I collaborated on that response to sneakily prove every point made in my article, but I assure you it is not true.

  5. JH

    Weird comments. I give up, Mr. Briggs. All I can say is that I am no mind reader like you.

  6. Hagfish Bagpipe

    Professor Ball:

    “But in many Indigenous societies, mathematics is lived from when you are born to when you rejoin your ancestors. It’s about formalised relationships within human society and with every element of the environment. Everyone is taught them. And the levels go up from birth to adulthood, as you are ready for more knowledge. This mathematics permeates every aspect of life.”

    Hey! I’m a mathematician! Step aside Briggs — when I swoop down a ski slope I am doing hyperbolic geometry, when I drive my car I am expostulating on gravitational thermodynamics, and when I empty my bowels I am extracting food’s prime numbers and leaving behind number two. This is great! I used to think I was a math dunce, but now I see I’m akshully a math genius. Thanks Professor Ball!

  7. Briggs


    I bet your hair was blowing gently in the wind when you wrote that.

  8. Mark Docherty

    “Incidentally, one also wonders if in addition to the chiral-paired smoke signal for “white men” there is another for “mathematicians.” Or is that considered a redundancy?”

    I slapped my knee so hard, I became an expert in Newton’s three laws of motion.

  9. Rudolph Harrier

    About ten years ago educators started to realize that they could get higher pass rates in mathematics classes if they taught something other than mathematics but pretended it was still mathematics. Thus you got things like “Calculus and sustainability” where you would be shown an analysis of climate data that used derivatives and asked whether this meant climate change was human caused and a serious threat. If you said “yes”, full marks for you and this obviously proves that you understood the calculus used in the analysis. (Okay, that may be a bit hyperbolic, but if you look through many of the actual projects most of the “math” consists of doing things like fitting curves using excel with far more questions about why we should be concerned about the environment than taking or interpreting derivatives.) There are many possibilities for “math and” such as “math and social justice”, “math and intersectionality.” Ball is just trying to exploit this through “math and DIE,” but I saw people doing similar things a decade ago. (I remember a project where the educator talked about how Polynesians built boats, and then said that this meant that they must be engineers on par with the modern west. Therefore instead of learning to work with equations students could build a boat using traditional methods to meet their mathematics requirements.)

    Despite mathematics having a lot of prestige in terms of name value in modern society, there is very little interest in actually doing mathematics. Even many data science programs are doing all they can to throw out as much mathematics as possible. You’d think that they would need at least Linear Algebra, Discrete Mathematics and some Calculus based Statistics. Some do this, but many programs are trying to get by on the Stats 101 class for gen eds and maybe Calculus I, though I think many of them would like to only require remedial college algebra. One trick that they like to do in particular is to have a lot of mathematics “elective” credits which can also be fulfilled with specialized data science courses, with things being set up so that students can (and in practice do) fulfill the “mathematics” electives without taking a single course taught by a mathematician.

  10. Cary D Cotterman

    I think “JH” is really a Lou Costello or Stan Laurel invented by Briggs, to provide himself some comedic nonsense he can shoot down.

  11. We have so many examples of why the Victorians built all those insane asylums and why it was very wrong to close them and adopt the “care in the community” nonsense.

  12. Milton Hathaway

    JH: I feel your pain. As a pedantic engineer, I speak a different language (terminology and especially philosophy) than the host and many of the denizens of this blog. When one doesn’t speak the language, the first thing one must do is attempt to translate what’s being said into terms one can wrap one’s mind around.

    For today’s subject, my translation is “math is equations; if there are no equations, it ain’t math”. I get this. An intuitive understanding of chiral symmetry and air currents is certainly admirable, but “to engineer a long-distance smoke signalling technology in real time” is a non-sequitur. With the possible exception of the fictional MacGyver, there is no “engineering” in real time, and since the indigenous folk aren’t using equations, it isn’t math. Math and engineering aren’t easy, so it’s understandable that people who have invested years of their life to acquire the skills to be employable are going to chafe at the comparison. When one boards a plane for a flight, the assumption is that the aeronautical design is engineered and not intuited, and the mathematical analysis used actual equations.

    I remain unconvinced by a healthy percentage of the proclamations made in this blog, but I always appreciate a sincere explanatory effort, and I often learn something new, if not unintended.

  13. Johnno

    To unwrap this bird’s thinking, you need only remember that most of our credentialed fellows subscribe to the atheist creation fable know as material and biological evolution; a fanfic that defies all mathematical odds. Even if you were to demonstrate, with every handicap and benefit of the doubt, that the odds of a functioning eyeball tripping it’s way into existence alone requires far more more time to chance than anything they are willing to generously ascribe to the age of the entire universe, the a priori dogma kicks in, that given we all have both our eyes here, then of course it must have happened, so the math must be wrong!

    Likewise, once we get all the white dinosaurs out of the way, THE SCIENCES ™ shall flourish and spring forth from the indigenous tribes! And once a coalition of beings with intelligence, ability, and the will to do it are in place to overcome these odds, they’ll prove us wrong! Currently they are at the speaking phase, bringing this new light upon the darkened sphere of mathematics!

    I look forward to the Fall!

  14. NLR

    It was better for math (and science as well) when it was its own autonomous subject. There wasn’t much prestige in the sense of that word now, but there was respect and it was left alone.

    Isaac Newton used to go on walks and would draw geometrical diagrams on the ground with his walking stick. Many of the other fellows of Cambridge didn’t care about math themselves, but they respected what Newton was doing enough that they walked around the diagrams.

    If it was just about math itself, you wouldn’t have people trying to take it over. Better for the subject long-term to be left alone and respected, than prestigious and wealthy.

  15. Faith

    JH (does that stand for Jolly Huckster?)

    You could just take the word “reader” out of your last sentence and you’d be nearer the mark.

  16. You know, there’s a tribe called Piraha, in Amazon, and they think numbers are stupid. Consequently, they don’t count, and consequently, they don’t KNOW how to count. Who needs counting! \o/ (Apparently, even trade works fine for them without counting. No, I don’t know how they manage to do that. Maybe they’re transcendent beings who percieve the inner matter of other people with their third eyes? ¯\_(?)_/¯ )

    Also, for all we know, the “Indigenous and First Nations peoples” produce luminaries like Newton and Liebniz every century or so. It just sucks for them that calculus has already been invented. xD It’s a bit hard to be a genius mathematician when Europeans already wrote down all the easy fun stuff. 🙂 Nowadays, all you have is to either invent the 50th proof for some 600-year old theorem, or else write 500-page proofs for extremely obtuse stuff that only 5 people in the entire world care about. The days of Euler’s constant are far behind us.

    And another thing is that it might be that, in ages past, there were great mathematicians among the “Indigenous and First Nations peoples” (which presumably includes black Europeans, you know, 50,000 years ago), it’s just that nobody wrote all that down. 🙂 Even if you’re an amazing genius and prodigy and “discovered the truth of Collatz conjecture”, what good is it if you didn’t write it down because you lived 47,000 years before writing was invented?

  17. Kip Hansen

    I may be mistaken, but didn’t much of our “European” mathematics emanate from Babylon and Egypt?

    That’s hardly European.

  18. JH

    Milton Hathaway,

    Thank you for taking the time to respond to me.

    “1+1=2” seemed easy, until I was asked to PROVE mathematically that 1+1=2 in a real analysis class. Rowena Ball , obviously knows more math than me and Briggs and you and I respect her appreciation for the Indigenous math.

    For trying to grow a cohort of Indigenous students or black students or Asian students,  Dr. Ball is perceived as trying to achieve equality of certain definitions, and as if she has committed a grave sin.  Based on my experience, a professor with such goals is often very good at explaining hard math concepts in simple ways and processes DEI skills that help create a conducive learning environment.  (I have gone through DEI training, which is an enriching leadership training emphasizing on how to communicate thoughtfully without prejudice toward people of different opinions, cultures and color. People who complained about the training are usually old grumpy men who believe their ways of dealing with students are the way.)

    Let me remind you that professors have nothing to do with undergraduate admission. Equality of Briggs’s definition is not within the reach of professors. Regardless of what kind of students they are, professors have to do their best to educate them.

    If you want to let the media decide what DEI is based on a few half-true reports of bad cases by bad actors, it is your choice.  

  19. JH

    What is the advantage of having a cohort? I am the academic advisor of a cohort of actuarial majors. Amy (name changed) is responsible for responding to all my inquiries, instructions, and requests such as help with the recruiting endeavors. She just finished her sophomore year passed two SOA exams, and is currently doing an internship in an insurance company. She double majors in math and actuarial science. She has no media addiction problem. She came up with the ideal of volunteering 2 hours per week to help fellow cohort students study for the exams that she already passed, in addition to 15 hours of work. A cohort mentality. A person with DEI skills. One of best students that I have ever had. She shall go far because of her work ethics and leadership skills. No, going to graduate school is not her thing. The vast majority of students do not go to college to become a genius such as Briggs, so claimed by Faith.

    If an anecdote could prove an thing, as Briggs likes to do (Ha), what does this prove? Women students are smarter and have better work ethics. (And more female students in a math class is no longer uncommon.

    Now, compare what Amy is doing and what some people are doing in this post!!!

    If a woman researcher wins a prestigious math prize, Briggs probably would claim that the only reason she gets the prize is because she is a woman.  (Since I don’t really know Briggs and have not read this blog for quite a few years, I am mind-reading and guessing here, hence the word probably.) PROVE me wrong by providing me with a post in which he praises women academics in STEM.  A counterexample, that is.

  20. JH


    Very funny. I understand your comment and question were meant to insult me. No worries. Insults do not affect me. If I am wrong, I welcome corrections. (I always try not to become a perceived enemy of a woman. Not knowing your sex, I will assume you are a woman based on your name or alias ‘Faith’.)

    My Grandpa took the naming of his offspring very seriously. He believed that a name is a seed of a self-fulfilling prophecy and carries his hopes and dreams for his offspring.

    You are right. God forbid that I have a mind like Briggs… or you. This fact makes me happy and would my Grandpa too.

    IF you are not Briggs, how do you make a judgment about Briggs’s mind? Can you critically review his publications?

  21. Briggs


    It’s not just math. Do not get sick.

    So when it came time for the admissions committee to consider one such student in November 2021—a black applicant with grades and test scores far below the UCLA average—some members of the committee felt that this particular candidate, based on the available evidence, was not the best fit for the top-tier medical school, according to two people present for the committee’s meeting.

    Their reservations were not well-received.

    When an admissions officer voiced concern about the candidate, the two people said, the dean of admissions, Jennifer Lucero, exploded in anger.

  22. Rudolph Harrier

    Based off the evidence that we have, it is a rational decision to try to get a white or Asian doctor instead of a black, American Indian or Hispanic doctor.

    That’s not to say that there are not good doctors of those latter races. The trouble is that there are many bad doctors of those races, and unlike whites and Asians, the bad doctors are not screened out. Thus if all you know is the race, you will have a much higher quality of doctor on average by choosing a white or Asian doctor.

    This is one of many situations where the only rational response to “anti-racist” measures is to discriminate by race.

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