“Mathematical Thinking Is the Key to Understanding AI” — Interview with Yurii Nesterov

Yurii Nesterov, world-leading mathematician and convex optimization pioneer, visited the Faculty of Engineering, discussing mathematics in the AI era, how engineers can adapt, and why logical, model-based thinking drives innovation.

 What advice would you give to students who are just starting their studies? How should they approach this rapidly evolving science?

Artificial intelligence is not as new as many people think. The idea appeared at the very beginning of computational mathematics — the term “artificial intelligence” itself was introduced in 1956. Since then, people have been developing systems that could already be seen as intelligent — for example, optimization programs for designing airplane wings or towers. These were early forms of AI, solving problems that previously required human intuition.

 

To truly work with AI, students must understand how to build solvable models. Computational mathematics teaches us what kind of models can be solved effectively — and this knowledge is essential.

 

How will AI influence or change the work of engineers?

AI should be seen as an advisor, not a decision-maker. It can propose solutions, but the final responsibility always belongs to humans. Artificial intelligence is a tool — a very powerful one — but it is not independent. The human must always remain in control.

 

 

Using AI efficiently requires specific knowledge — for example, how to give the best prompts. Where should students learn from?

We are only at the very beginning of learning how to use AI effectively. But one thing is already clear: artificial intelligence needs help. It depends on how you ask your question. Just like with people — the way you formulate a question determines how easy or difficult it is to answer.

 

To use AI well, you must understand what happens inside — how the system processes your query, where it searches for solutions, and how it generates responses. The goal is to make your questions as clear and precise as possible.

 

What kind of skills and mindset should today’s engineering students develop to use AI effectively?

Engineering is a problem-specific discipline. Electrical, computer, or mechanical engineers all face different challenges, but what unites them is the need for good models. A model must not only describe reality — it must also be solvable.

 

Unfortunately, in many fields today, people create complex models without understanding how to solve them. They assume that a computer can do everything, which is wrong. You must balance accuracy with solvability. And this requires mathematics. Many people in medicine, economics, or social sciences try to avoid mathematics — but that time is over. Mathematics will be everywhere.

 Mathematics also shapes the way we think. What do you mean by mathematical thinking?

Mathematical thinking means supporting your decisions with logical justification — and being able to accept others’ reasoning when it’s well-supported. You don’t need to be a mathematician; you just need the mathematical spirit.

Pure mathematics is very abstract — even dangerous for beginners because it deals with immortal problems. But mathematical spirit is about structure, logic, and reasoned thinking — skills that are essential in any field.

 

 

How can we teach mathematics effectively in the age of AI, when everything seems to move so fast?

We must be careful. Basic mathematics is actually very simple and logical—but continuous learning is crucial. If students miss key steps early on, it becomes confusing later.

 

Theoretical mathematics, on the other hand, is valuable because it teaches how to build comprehensive theories — starting from hypotheses, exploring consequences, and constructing logical frameworks. Even if the results are abstract, it teaches structured and logical thinking, which can be applied anywhere.

 

AI evolves extremely fast. How can anyone keep up with such rapid change?

Honestly, it is almost impossible. We are living through another technological revolution. The methods we use now — like training huge neural networks — consume enormous resources and will soon be replaced by more efficient ones. We’ve seen this before: in the 1980s, computers filled entire rooms, and within a few years, personal computers replaced them. 

 

The same will happen with AI. That’s why it’s not essential to master everything — just start using simple models, experiment, and learn to collaborate with these new tools. They open new possibilities — just like cars or airplanes once did. We just need to find the best way to use them.

 

 

Last update: 2025. 11. 20. 09:50