Paul Ernest discusses the contrast between the beneficial side of mathematics and the dangerous uses and abuses of it.
There is a myth and mystique about mathematics that presents it as superhuman, present in the universe everywhere and at all times, irrespective of the existence of humans. Even though widely believed, in my view. When you work with mathematics in depth, the objects, relationships, and worlds it conjures up all seem real and almost alive, with solid properties like a rock or car. Similarly, if you spend years working with Shakespeare’s plays, they seem real and necessary. When Tolstoy finally finished writing Anna Karenina he burst out of his study in tears, crying “She is dead”. Human creations, whether films, books, laws, money, or numbers have a life of their own, a reality that exceeds any one person’s beliefs. They are enduring parts of human culture, passed on from generation to generation, preserved and extended.
Mathematical objects are different because they are bound together by rules of definition and logic. We can reimagine Anna Karenina with blonde hair without changing her character and story, but we cannot reimagine 1+1=3 without fundamentally changing the definitions of 1, 3, +, =, and the whole of arithmetic. Although in my view humans every mathematical theory has many rules and restrictions within them that bind each into a logical whole. Once we have set up such a system it is locked into place. The certainty of 1+1=2 follows from the basic rules and assumptions of arithmetic. In Ernest (1991) I demonstrate this for 2+2-4.
Such necessity makes mathematics seem superhuman, but this is an illusion. Needs, reasons and choices underlie every mathematical theorem and theory, but we too easily forget that human customs underpin the axioms and logical rules. The seeming objectivity means that many people assume that mathematics is neutral and above ethics and other human values. But seeing the world as made up of units learning to count them and inventing the means of calculating with the numbers was initiated in societies that wanted to control tax, tribute and trade, as well as charting regularities in the heavens. Thus, applied mathematics came first, long before scribes extended their virtuosity to create mathematics for its own sake.
Appliers of mathematics do so in the pursuit of social purposes and interests. Predicting the loads that bridges can bear, testing vaccines statistically, calculating taxes, working out who is entitled to state help, setting and marking exams, directing and controlling computers through software, etc., are all social applications of mathematics. These and many other uses are beneficial to society. But mathematics also has a dark side, and it can be misused in ways that are harmful. Three problematic mathematical usage types are mathwashing, harmful applications, and performative applications that change society with harm to some persons.
Mathwashing is the use of mathematics to make some policy, process or product look better than it is with the spurious authority of mathematics. The British Prime Minister announced that his government’s policy towards the Covid epidemic was based on a scientific formula CAL = N + R (Covid Alert Level = Number of infections + Rate of increase). This was mathwashing because the mathematical formula is not meaningful and cannot suggest any policy or response (Ernest 2020). Anybody can see, at the very least, that for a start, the Number of infections must be multiplied by the Rate of increase, not added. Another example of mathwashing is the claim in the large print of an advertisement that a handwash kills 99.99% of bacteria and viruses. But in small print, it also says “In laboratory condition. Testing in the field is 48% effective”. In each case, mathematics is not used to justify the claim but to add a spurious air of authority to it.

There are many harmful applications of mathematics. An obvious example is computer-controlled weapons used murderously by authoritarian regimes. Closer to home, a recent misuse was the deliberate application within the computers regulating the engines of diesel cars by VW and other manufacturers. These controlled the engine to give much lower measures of pollutants in the exhaust during laboratory test conditions than in similar usage on the road. Thus, the applications were deliberately deceptive and misleading.
Lastly, performative applications can be very damaging when they change the reality they are supposed to measure. They can result in changes to society with significant personal harm. A well-known example is the formula included in programs to trigger buying and selling of stock market shares. In the mid-’80s, Wall Street turned to the quants—brainy financial engineers—to invent new ways to boost profits. Their methods for minting money worked brilliantly. For five years, the Gaussian copula function looked like a real positive breakthrough, a piece of financial wizardry that increased profits. But it also increased risks. So much so, that it triggered the financial sell-off and crash that devastated the global economy in 2007. It is now known as the ‘Formula That Killed Wall Street’, and cost banks and countries around the world billions if not trillions of dollars (MacKenzie & Spears 2014).
Thus, mathematics has two faces, the smiling and beneficial face, and the scowling and harmful face. It is important that we teach our students, and ultimately all citizens in society, not to believe everyone using mathematics to make their claims. Learners and the public need to be able to question all the applications of mathematics around them, and not assume that they are all good. Just as we are skeptical of emails coming from unknown sources offering prizes and riches, so too we must be on our guard against math washing, harmful applications, and performative applications that change policies and damage society. To this end, mathematics teaching must add the very serious task of developing a critical citizenry to its overall aims and goals.

Prof. Paul Ernest
Emeritus professor of mathematics education at the University of Exeter, UK
References
Ernest, P. (1991). The Philosophy of Mathematics Education. London: Routledge.
Ernest, P. (2020). Unpicking the Meaning of the Deceptive Mathematics Behind the Covid Alert Levels. Philosophy of Mathematics Education Journal, No. 36 (December 2020). Retrieved on 8 May 2023 via https://education.exeter.ac.uk/research/centres/stem/publications/pmej/pome36/index.html
MacKenzie, D & Spears, T (2014). The formula that killed Wall Street: The Gaussian copula and modelling practices in investment banking. Social Studies of Science, Vol. 44, No. 3, pp. 393-417. Retrieved on 8 May 2023 via https://www.pure.ed.ac.uk/ws/files/15459604/Formula_final2.pdf