Mathematics in the Crosshairs: The Love-Hate Affair with Rigorous Education

Reflections on Pickover’s Mathematical Devotional and the Enduring Value of Algebra and Geometry

Bernard le Bovier de Fontenelle

The July 13 entry in Clifford A. Pickover’s The Mathematical Devotional features an excerpt from Bernard le Bovier de Fontenelle’s 1699 treatise Of the Usefulness of Mathematical Learning. Fontenelle, writing at the turn of the Enlightenment, defends the pursuit of mathematical knowledge not only for its practical applications but also for its intrinsic intellectual merit. “People very readily call useless what they do not understand,” he writes, noting the curious tendency of the uninitiated to dismiss abstract study as vain speculation. His observation is as incisive today as it was more than three centuries ago.

Contemporary society is locked in a paradoxical relationship with rigorous education, particularly in mathematics. We valorize innovation, data science, and technological sophistication, all of which are undergirded by mathematics, yet we continue to see a steady erosion in the public’s mathematical fluency. Algebra and geometry, long considered the foundational languages of rational thought, are now often viewed by students and even policymakers as arcane relics, burdensome hoops through which teenagers must leap before graduation. Albeit that politicians and policymakers rarely dare articulate such views in public. Their sense of survival depends to some degree upon not sounding too sophomoric.

This trend is not merely anecdotal. The National Assessment of Educational Progress (NAEP), sometimes called “the nation’s report card,” reveals a disconcerting decline. In the most recent data, average mathematics scores for 13-year-olds fell to their lowest levels in decades. The proportion of students demonstrating proficiency in algebraic reasoning or geometric understanding has dropped precipitously. Such metrics are not just academic; they portend long-term consequences for civic life, workforce readiness, and scientific advancement.

Why the disdain for these subjects, then, when their utility remains as vital as ever?

Fontenelle offers one possible explanation: revenge. “People very readily call useless what they do not understand.” This psychological insight remains strikingly relevant. Students frustrated by abstraction, adults alienated by their own poor schooling, and commentators skeptical of “geeky” learning—all too often seek refuge in dismissiveness. What they cannot master, they render moot.

Yet as Fontenelle argues, the divisions between “useful” and “theoretical” knowledge are artificial and misleading. In his day, navigation depended almost exclusively upon astronomy; astronomy relied on optics; optics, in turn, stood upon geometry. Our global navigation to this day depends upon a constellation not of stars but of satellites and GPS depends upon mathematics.

The practical world is scaffolded by layers of theoretical structure. Consider your smartphone: its existence depends not only on engineering (itself dependent upon mathematics) but also on mathematical modeling, signal processing, and algorithms born of theoretical inquiry decades prior.

So, what is lost when we devalue the rigorous study of algebra and geometry?

First, we lose a disciplined mode of thinking. Geometry teaches logical progression, spatial reasoning, and deductive clarity. Algebra cultivates symbolic manipulation and abstract generalization—the very skills required to engage with patterns, systems, and change. These are not only tools for scientists or engineers; they are tools for citizens navigating a complex and data-saturated world.

Second, we forfeit cultural continuity. Mathematics is a humanistic endeavor, a historical conversation stretching from Euclid to Descartes to Emmy Noether. To truncate it for the sake of expediency is to rob future generations of their inheritance. Just as we defend the teaching of Shakespeare for its aesthetic and ethical value, so too should we defend the mathematical canon for its intellectual and cultural richness.

Finally, and most dangerously, we risk creating a society divided not just by wealth but by epistemology. A mathematically literate elite will continue to steer industries, influence policy, and interpret the world, while an innumerate majority remains vulnerable to manipulation and misjudgment. The democratization of reason requires mathematical education. In advanced mathematics, we delve into such concepts as countable and uncountable infinities, with some students wondering how applicable such nuances might be.  I offer just the number of probability and statistics errors posted on commercial and social media as approaching uncountable infinity asymptotically, admittedly with tongue firmly pasted to cheek.

Fontenelle's defense, quoted by Pickover, reminds us that the deeper layers of mathematics—those seemingly remote from everyday experience—are in fact the wellsprings of innovation. The cure is not to dilute our curriculum but to elevate our understanding. We must resist the seductive ease of calling “useless” what we have failed to comprehend and instead strive to rekindle respect for the rigors of learning.

Algebra and geometry are not mere academic hurdles; they are the architecture of thought. In neglecting them, we impoverish not only our intellects but our future.