Sam Baron, a philosophy prof at Australian Catholic University, whose specialty is the philosophy of mathematics, argues in a new paper that mathematics is not a human invention. It gives structure to the world we live in. We simply observe it.
So do many life forms, it seems. He offers an example:
There are two subspecies of North American periodical cicadas that live most of their lives in the ground. Then, every 13 or 17 years (depending on the subspecies), the cicadas emerge in great swarms for a period of around two weeks.
Why is it 13 and 17 years? Why not 12 and 14? Or 16 and 18?
One explanation appeals to the fact that 13 and 17 are prime numbers.Sam Baron, “Pythagoras’ revenge: humans didn’t invent mathematics, it’s what the world is made of” at The Conversation (November 21, 2021)
What if predators have life cycles (or population dips and spikes) of 2, 3, 4, 5, 6, 7, 8 and 9 years?
When a cicada with a 13-year life cycle comes out of the ground, none of its predators will be out of the ground, because none of 2, 3, 4, 5, 6, 7, 8 or 9 divides evenly into 13. The same is true for 17.Sam Baron, “Pythagoras’ revenge: humans didn’t invent mathematics, it’s what the world is made of” at The Conversation (November 21, 2021)
The idea that our world is fundamentally mathematical is not a new one. It was advanced by, among others, the ancient philosopher Pythagoras (ca. 570 to ca. 490 BC), best known for the Pythagorean theorem. But as we learn more about nature, where so much is geometrically patterned and/or based on significant numbers, Baron says, “Pythagoreanism is being rediscovered in physics.”
In the past century physics has become more and more mathematical, turning to seemingly abstract fields of inquiry such as group theory and differential geometry in an effort to explain the physical world.
As the boundary between physics and mathematics blurs, it becomes harder to say which parts of the world are physical and which are mathematical.Sam Baron, “Pythagoras’ revenge: humans didn’t invent mathematics, it’s what the world is made of” at The Conversation (November 21, 2021)
For example, we can say, if we like, that the cicada is wholly physical. But if it were not for that insect’s habit of unconsciously incorporating prime numbers into its reproductive life, there might not be many cicadas around. We can’t do without the abstract math.
Meanwhile, there are number of unsolved problems in mathematics:
Just one of the seven Millennium Prize Problems named 21 years ago has been solved
Twenty-one years ago this week, mathematicians released a list of the top seven unsolved problems in the field. Answering them would offer major new insights in fundamental mathematics and might even have real-world consequences for technologies such as cryptography.
But big questions in math have not often attracted the same level of outside interest that mysteries in other scientific areas have. When it comes to understanding what math research looks like or what the point of it is, many folks are still stumped, says Wei Ho, a mathematician at the University of Michigan. Although people often misunderstand the nature of her work, Ho says it does not have to be difficult to explain. “My cocktail party spiel is always about elliptic curves,” she adds. Ho often asks partygoers, “You know middle school parabolas and circles? Once you start making a cubic equation, things get really hard…. There are so many open questions about them.”Rachel Crowell, “The Top Unsolved Questions in Mathematics Remain Mostly Mysterious” at Scientific American (May 28, 2021)
Curiously, in a world that depends on mathematics — and offers intriguing math problems to ponder — in recent years, some educators have turned against math. They proclaim it to be an instance of white male supremacy because, in recent centuries, most mathematicians have been men of European ancestry (though historically, that is a phase, not a rule).
In September, Mind Matters News offered an update on the war on math education. Here are some other recent developments:
➤ The California Math Framework claims “We reject ideas of natural gifts and talents … and the ‘cult of the genius.’” (Howard Blume, Los Angeles Times, May 21, 2021) which leads the to advocate eliminating accelerated math classes for exceptionally proficient students before Grade 11. The research basis for the decision has come in for considerable skepticism. (Richard Bernstein, MercatorNet, October 27, 2021)
➤In April, Virginia also moved to eliminate all accelerated math courses prior to Grade 11. The Department of Education’s web site announced goals such as “[i]mprove equity in mathematics learning opportunities,” and “[e]mpower students to be active participants in a quantitative world,” and “[i]dentify K-12 mathematics pathways that support future success.” (Sam Dorman, Fox News, April 22, 2021) How eliminating advanced courses for students who would benefit from them would further any of these goals is unclear.
➤ It’s not just an American thing. The largest Canadian province, Ontario, is reorganizing math instruction along the lines that math is subjective, not objective: We are told that it“has been ‘used to normalize racism and marginalization of non-Eurocentric mathematical knowledges,’ and explains that taking a ‘decolonial’ and ‘anti-racist approach’ to teaching math will outline its ‘historical roots and social constructions’ to students.” (Denette Wilford, Bryan Passifiume, Toronto Sun, July 12, 2021). The new approach will also end streaming.
One issue raised in Canada is the fact that, for cultural reasons, students from Eastern Asian backgrounds tend to excel in math, so ending streaming will disproportionately affect them.
➤ In Nevada, Truckee Meadows Community College upheld disciplinary actions against math prof Lars Jensen for protesting “a new curriculum structure that essentially allows remedial math classes to count for college credit.” (Christian Schneider, College Fix, November 16, 2021).
➤ California both exemplifies and spells out the trend most clearly:
The framework recommends eight times that teachers use a troubling document, “A Pathway to Equitable Math Instruction: Dismantling Racism in Mathematics Instruction.” This manual claims that teachers addressing students’ mistakes forthrightly is a form of white supremacy. It sets forth indicators of “white supremacy culture in the mathematics classroom,” including a focus on “getting the right answer,” teaching math in a “linear fashion,” requiring students to “show their work” and grading them on demonstrated knowledge of the subject matter. “The concept of mathematics being purely objective is unequivocally false,” the manual explains. “Upholding the idea that there are always right and wrong answers perpetuates ‘objectivity.’ ” Apparently, that’s also racist.Williamson M. Evers, “California Woke Zealots Try to Cancel Math Class” at Independent Institute (May 19, 2020), also published at the Wall Street Journal
Perhaps we all need to recall something: The Iron Ring of the Canadian engineers is said to have been forged from the steel of a bridge that collapsed and cost 75 lives. The Ring is intended as a warning, not a training manual. It turns out that in the real world, right or wrong answers in math do matter.
You may also wish to read: Yes, there really is a war on math in our schools. Pundits differ as to the causes but here are some facts parents should know.
Further dispatches from the war on math (September 14, 2021) Discussions of social policy where math is relevant can be useful. But a student who does not understand how an equation works will fail at both math and social policy.