Announcing Science’s Third Great Transition

In 1960, physicist Eugene Wigner wrote what many consider one of the most profound scientific papers of the 20th century: “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” He revealed how Mathematics haunts physics in a most uncanny way.

Wigner marveled at how perfectly mathematics describes physical reality. Newton’s laws, quantum electrodynamics, relativity – all use elegant mathematical formulas that predict physical behavior with extraordinary precision.

The fact that abstract math, developed in the minds of humans, so perfectly describes the physical universe is, as Wigner put it, “a wonderful gift which we neither understand nor deserve.”

Many times in physics, solutions dreamed up by mathematicians decades or centuries before suddenly show themselves to be precisely applicable.

Everyone in science accepts this, to the point where many define science itself as the imperative to reduce everything in the cosmos to equations.

But there’s twist to the story. Stuart Kauffman, Sy Garte and I just published a new paper in the journal Entropy. It’s called “The Reasonable Ineffectiveness of Mathematics in the Biological Sciences.”

Biology Rewrites the Mathematical Playbook

While physics bows obediently to mathematical formulations, biology stubbornly resists them. For decades, scientists have battled with this perplexing reality. Many deny it outright, suffering from what we call “physics envy” – desperately trying to force biological complexity into neat mathematical boxes.

It doesn’t work. Now there’s an indisputable reason why: In 1931, Kurt Godel proved that mathematics cannot explain mathematics. Recent papers by myself, Stu Kauffman and others extend this principle to biology.

Take evolution. The concept of “fitness” in natural selection is circular. We define fitness by what survives, then explain survival by fitness. There is no mathematical “law of evolution” that predicts how species will adapt and change. Stuart Kauffman proved using mathematical Set Theory that such a law is not merely difficult but impossible.

There are no equal signs in biology

Biology doesn’t operate in equilibrium like physics; it’s constantly creating, adapting, and inventing new possibilities that no equation could have encoded.

This isn’t just a practical limitation of our current knowledge. Biology transcends the limits of computation itself. Our thesis is not a matter debatable scientific data; it is a mathematical proof. Any assumption that the universe is entirely mathematical trucks in a mind-bending contradiction that Kurt Godel unearthed in 1931.

David Chalmers famously introduced the Hard Problem of Consciousness in the 1990s. This philosophical puzzle asks how subjective experience (feeling pain, seeing red) emerges from physical brain processes. To date we have no physical explanation for our experience of being.

Biology has its own Hard Problem: How do living cells make choices that cannot be reduced to algorithms?

When flatworm embryos are exposed to barium, a chemical they’ve never encountered in evolutionary history, their heads explode. Then they generate new barium-resistant heads within hours. No algorithm could possibly predict this specific adaptation. Flatworms do not have an “in case of barium” subroutine in their DNA. These worms are exercising agency, making choices from an indefinite set of possibilities.

This means: Biology doesn’t simply obey mathematics; it creates mathematics. Organisms perform induction which by definition creates new mathematics as they adapt to their environments.

“We believe humans really are choosing which scientific theories are good or bad, and our dogs really are choosing whether to urinate in the living room or back yard.”

The Power of Heuristics

If we can’t reduce biology to equations, how do we make progress? The answer isn’t more data – it’s asking superior questions and choosing more elegant models.

A heuristic is an educated guess that works well enough in practice, even if it’s not perfect or mathematically precise. A great heuristic is incredibly powerful.

In business strategy, Bruce Henderson’s Growth-Share Matrix divides businesses into just four categories (Stars, Cash Cows, Question Marks, and Dogs), providing a powerful framework that bypasses enormous underlying complexity. I’ve been teaching Henderson’s “Star Principle” to my business clients for a decade. Similarly, physiologist Denis Noble points out that simple metrics like blood pressure, heart rate, height and weight tell a doctor more about her patient than an entire genome analysis.

The most powerful scientific tools are not larger datasets, but ingenious heuristics that demand we wisely choose very small data sets and well-posed questions to solve specific problems. This fact will only prove itself more central as the AI age advances.

The Third Transition in Science

The world is in birth pangs as everyone knows. AI is transforming the Internet; we are experiencing swings of economic cycles; and we’ve also entered what Stuart Kauffman calls a “third transition” in science.

The first was the Newtonian paradigm with its ‘clockwork universe’. The second came with quantum mechanics and its probabilistic nature. Now, biology forces us beyond both into a new framework that can accommodate life’s creative freedom.

This transition doesn’t diminish the achievements of mathematical biology. Rather, it places them in a wider context, reminding us that nature’s creativity transcends any single formalism.

By recognizing the reasonable ineffectiveness of mathematics in biology, we open ourselves to a more humble, wonder-filled science. We acknowledge that the world is not merely a theorem to be solved but a creative process unfolding in ways that cannot be fully prestated or predicted.

This isn’t a failure of science but an invitation to expand its horizons – to develop new concepts and frameworks worthy of life’s endless forms most beautiful.

The world is not a theorem. And that is why science will forever perplex and amaze us with its wonders.

Read our new paper “The Reasonable Ineffectiveness of Mathematics in the Biological Sciences.”

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Watch the podcast conversation with Sy Garte that gave birth to this paper.

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