Will AI Push the Mathematization of Science and Technology?

The scientific revolution initiated by Galileo and Newton established mathematics as the language of science. Physical phenomena could be described by mathematical equations, allowing quantitative prediction rather than merely qualitative explanation.

But there has always been a fundamental obstacle: Formulating mathematical equations is one thing, solving them is another.

While mathematical models have been developed for an enormous range of physical phenomena, solving the resulting equations has often required extensive mathematical expertise, sophisticated numerical methods and substantial programming efforts.

As a consequence, much of science and technology still relies on empirical correlations, experimental databases and simplified models rather than direct computation from fundamental equations.

Artificial Intelligence (AI) is now changing this situation.

AI can increasingly construct numerical algorithms, generate computer programs and solve mathematical equations with limited human intervention. What previously required months of specialized computational work may become possible in hours or days.

This suggests a fundamental change in the division of scientific labor:

1. Human: Formulate the scientific question.

2. Human assisted by AI: Formulate the mathematical model.

3. AI: Solve the equations computationally, subject to verification.

4. Human: Evaluate the predictions against physical reality.

The main intellectual challenge thus shifts from solving equations to formulating the right equations.

This may have profound consequences.

Fields traditionally dominated by empirical methods may become increasingly mathematical and computational. Scientists and engineers may develop and test their own models rather than depend on specialized computational experts or commercial software.

Moreover, easy access to computation may expose weaknesses in established mathematical models and stimulate the search for better ones.

But computation alone does not guarantee scientific understanding. A precisely computed solution of an inadequate model remains inadequate. The physical meaning of the equations and their agreement with observation remain decisive.

Will AI therefore push a new mathematization of science and technology?

The answer appears to be yes, potentially on a scale comparable to the original scientific revolution.

The first mathematical revolution showed that nature can be described by equations.

The AI revolution may make it possible to systematically explore the consequences of those equations and thereby discover better ones.

The central question for future scientists and engineers will increasingly be not How do we solve the equations? but:

What are the right equations to solve?