How Should AI Transform Mathematics Education at Technical Universities?

Prompt to chatGPT:

• What mathematics should future scientists and engineers learn when AI can do essentially all the mathematics for them?

Response by chatGPT:

The rapid development of Artificial Intelligence, now capable of advanced mathematical computation, symbolic reasoning and increasingly sophisticated theorem proving, makes this question urgent.

Mathematics education at technical universities is still largely based on a pre-computer tradition, with extensive training in symbolic manipulation, analytical solution techniques and formal proofs. Students spend years acquiring skills that computers can already perform, with AI now extending automation into mathematical reasoning itself.

Why continue spending years teaching students to do what AI can do in seconds?

What Is the Alternative?

The purpose of mathematics education at technical universities should be to develop an understanding of how mathematics can be used to describe, predict and investigate physical reality, rather than primarily training students to perform mathematical operations.

This suggests a curriculum centered on three activities:

1. Mathematical Modeling

Formulating physical laws and engineering problems as mathematical equations, understanding the underlying assumptions and identifying the limitations of mathematical models.

2. Computation and Simulation

Using AI to construct numerical methods, solve equations, perform simulations and investigate physical phenomena. Students should be able to address substantial problems in mechanics, electromagnetism, fluid dynamics and other sciences from the beginning of their studies.

3. Verification and Understanding

Evaluating the accuracy, stability and physical relevance of computed solutions through mathematical analysis, error estimation and comparison with experiments.

The emphasis shifts from performing mathematical operations to understanding what mathematical models and computations actually tell us about the world.

What Mathematics Remains?

Fundamental concepts of calculus, linear algebra, differential equations and probability remain important, but primarily as tools for understanding models and computations.

Extensive training in analytical solution techniques, symbolic manipulation and routine proofs can be substantially reduced.

The traditional progression

Mathematical techniques → Mathematical theory → Applications

can be replaced by

Physical problems → Mathematical models → AI computation → Verification and understanding.

This would allow mathematics education to become shorter in its traditional components while considerably richer in scientific content.

The central objective would no longer be to train students to perform mathematics, but to educate scientists and engineers capable of using mathematics to understand and investigate reality.

Connection to Body&Soul

This reform has a direct connection to the Applied Mathematics: Body&Soul program developed around 2000 by Kenneth Eriksson, Claes Johnson and Don Estep at Chalmers and Colorado State University.

Body&Soul proposed replacing traditional mathematics education with a synthesis of numerical computation (Body), mathematical analysis (Soul) and mathematical modeling of physical reality.

The computer revolution made it possible to replace extensive hand calculation with numerical computation, allowing students to address meaningful scientific problems much earlier in their education.

The AI revolution now takes this development one step further.

AI can increasingly perform not only numerical computation (Body), but also symbolic reasoning and mathematical analysis (Soul).

Thus, the original Body&Soul vision of mathematics education centered on computation, understanding and applications becomes even more relevant.

The computer revolution made Body&Soul possible. The AI revolution makes its underlying educational reform increasingly necessary.

The question is no longer whether technical universities should reform mathematics education, but how quickly they can replace a curriculum dominated by mathematical techniques with one centered on modeling, computation and understanding physical reality.