We live in an age intoxicated by numbers. Big Data, AI and quantum computing promise to make science faster, sharper and more objective than ever. We count, model, predict, optimise. On paper, it looks like the triumph of reason. And yet, beneath the glow of dashboards and equations, a quieter question lingers: do numbers alone bring us closer to reality — or just to ever more elegant shadows of it?
To understand why data-driven science holds such power today, we must look beyond technology—and return to an older, deeper fascination with mathematics itself. From Pythagoras and Thales to Planck and Einstein, the history of science is also the history of our fascination with mathematics — its beauty, its power, and its blind spots.
Mathematics in Science: The Beauty and the Blind Spots
Humans are deeply drawn to structure, and few structures feel as comforting and beautiful as mathematics. There's a quiet thrill in following a complex proof to its clean conclusion, in watching order emerge from seeming chaos. This appeal to harmony has ancient roots.
Think of Pythagoras and Thales, whose mathematical inquiries were not just utilitarian but philosophical. To them, numbers revealed something about the cosmos itself—symmetry, proportion, order.
Later thinkers would echo this sentiment. Albert Einstein articulated this tension more clearly than most: a deep admiration for mathematical beauty paired with an unease about its seductive power:
"The most incomprehensible thing about the world is that it is comprehensible."
This sense of wonder, however, was never free from doubt. Einstein was acutely aware that mathematical elegance could mislead as much as it could illuminate. He admitted that he was fascinated by the beauty of mathematics, but also cautious. As he confessed:
"As a young man, my fondness for mathematical luxury had led me astray."
This unease culminates in one of his most enduring questions:
"How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?"
Taken together, these remarks capture a recurring tension that runs through the history of science: mathematics appears both as a miracle and as a risk—beautiful, powerful, and never entirely innocent.
Yet the very beauty that makes mathematics so powerful also makes it dangerous—especially when elegance begins to substitute for understanding.
When Numbers Aren’t Enough: The False Security of Quantification
The problem, then, is not mathematics itself, but the quiet belief that numbers can absolve us from interpretation. Mathematics is powerful, yes. But it is not infallible, nor is it sufficient.
This becomes painfully clear when we look at issues like the replication crisis in psychology or p-hacking in medical studies. Here, numbers are bent—consciously or unconsciously—to serve hypotheses. They no longer reveal the truth but obscure it.
Worse still, even rigorous and honest statistics can be misleading. The elegance of a model doesn’t guarantee that it corresponds to the real world. Quantification gives us confidence, but not always insight. As Max Planck famously said:
"Science cannot solve the ultimate mystery of nature. And that is because, in the last analysis, we ourselves are a part of the mystery we are trying to solve."
This humility is often missing in today's data-driven climate.
The Limits of Measurement in Human Sciences
The challenge of applying mathematical methods becomes particularly clear in the social sciences. Here, human behavior resists quantification. Emotions, decisions, cultural patterns—these are difficult to capture in variables and distributions.
Despite this, there's a push to treat sociology, psychology, or even philosophy: measure, predict, repeat. But the complexity and fluidity of human experience call for interpretive, qualitative approaches just as much as quantitative ones. On the limitations of statistics in the humanities in this article.
If quantification struggles most visibly where human meaning is concerned, this should not reassure us too quickly—because similar tensions are now emerging even in the hardest of sciences. Even in physics—the crown jewel of mathematical modeling—serious doubts are emerging.
Quantum Uncertainty and the Discomfort of Not Knowing
Consider the trajectory of modern physics. The early 20th century saw the rise of quantum mechanics, a theory that revolutionized our understanding of particles, probability, and causality.
Yet over time, more mathematically abstract theories—such as string theory—began to dominate. These are breathtaking in their formal beauty, yet often unfalsifiable.
String theory functions here less as a technical case study than as a philosophical warning: when mathematical coherence risks becoming self-sufficient, empirical friction begins to fade.
Physicist Lee Smolin criticizes this shift, noting that many current approaches in theoretical physics prioritize mathematical elegance over empirical testability. The result is a kind of metaphysical drift, where the math becomes more real than the reality it's meant to describe.
In such moments, we risk losing what science originally was: a spirit of inquiry driven by curiosity, not certainty. In antiquity, science and philosophy were intertwined.
Thales and Pythagoras were not just proto-mathematicians—they were wonderers. For them, numbers were gateways to awe, not systems of control.
"Mathematics is the music of reason,"
said James Joseph Sylvester, a 19th-century mathematician. But music is not only notes—it's silence, resonance, interpretation.
The Rise of AI and Quantum Computing: More Data, Same Limits
AI and quantum computing do not resolve these tensions—they amplify them. Advocates of AI and quantum computing argue that the limitations of traditional models will soon be overcome.
These technologies process more data, faster, and with greater precision. But here we must recall a basic truth: more is not always better.
Quality and quantity are not interchangeable. You can read a thousand summaries of a novel and still miss the meaning that a slow, thoughtful reading would reveal. The same applies to science. Machines accelerate analysis, but they do not replace insight.
We are tempted to believe that faster computation leads to deeper knowledge. But the danger lies in mistaking speed for understanding.
So What If Not Numbers?
It’s easy to criticize—but what then is the alternative? This is not a call to abandon mathematics. It is not a rejection of precision, but a call to re-embed it within judgment, context, and wonder. Rather, it is a plea for humility. For re-integrating intuition, context, and critical reflection into our scientific practices.
We need methods that reclaim science's roots: not only in calculation, but in contemplation. Not only in precision, but in presence.
"The essence of mathematics lies in its freedom,"
wrote Georg Cantor. But freedom must serve something beyond itself.
Perhaps it is time to return—not backwards, but deeper—to that ancient wonder, to that mix of observation and awe, where asking the right question was as important as finding the correct answer. ➡️ On the ancient roots in this timeless episode
Final Thoughts: Maths as Map, Not as Territory
So, do numbers matter in science? Of course they do. But not alone. They are tools, not truths. Maps, not territory.
We must remain vigilant against the seduction of neatness, the illusion that complexity can always be reduced to clarity. The real world is messy, surprising, and alive.
Let us not forget that even the most brilliant equation must be interpreted by a curious, thinking, questioning human mind. The glow of our screens is not the light of understanding—but it can guide us, if we remember that every map still requires a traveler.
References
Cantor, G. (1883). Grundlagen einer allgemeinen Mannigfaltigkeitslehre. [Foundations of a general theory of manifolds.] Leipzig: Teubner.
Einstein, A. (1954). Ideas and Opinions (original texts selected by Carl Seelig, English translation by Sonja Bargmann). New York: Crown Publishers.
Floridi, L. (2014). The Fourth Revolution: How the Infosphere is Reshaping Human Reality. Oxford: Oxford University Press.
Ioannidis, J. P. A. (2005). Why most published research findings are false. PLoS Medicine, 2(8), e124. https://doi.org/10.1371/journal.pmed.0020124
Planck, M. (1932). Where Is Science Going? (J. Murphy, Trans.). New York: W.W. Norton & Company
Russell, B. (1919). Introduction to Mathematical Philosophy. London: George Allen & Unwin.
Sylvester, J. J. (1869). A plea for the mathematician. Nature, 1(5), 162–163.
Wigner, E. P. (1960). The unreasonable effectiveness of mathematics in the natural sciences. Communications on Pure and Applied Mathematics, 13(1), 1–14. https://doi.org/10.1002/cpa.3160130102
Few of these aspects are results of the profound conversations with HBS Puar.
Authored by Rebekka Brandt