In the AI era, mathematics still needs the human mind
AI has changed mathematicians’ work with remarkable speed.
“As recently as last spring, AI tools were making mistakes in advanced mathematical reasoning, but their results improved considerably over the summer,” says Mikko Salo, 47, Professor of Mathematics at the University of Jyväskylä:
AI has now reached a level where it can provide substantial help with mathematical reasoning and proofs.”
In recent weeks, Salo has discussed in the media how AI is affecting mathematics research and its findings, as well as the opportunities and risks it presents.
As AI models grow more powerful, what will happen to mathematics?
According to Salo, AI software has improved so much that any errors it makes are becoming difficult to spot.
Methods for detecting errors have also improved, however,” he says.
“Until now, checking that a mathematical argument is correct has required considerable human effort. AI can now help convert a mathematical proof written in ordinary language into a version that a computer can verify. For example, a proof translated into the Lean programming language can be compiled and checked for correctness.”
Even so, uncertainty remains:
“The situation is changing rapidly,” Salo says. “It is still unclear how mathematicians will work in a couple of years, let alone further into the future.”
AI needs human guidance
As AI becomes more widely used, the need for specialists with a deep understanding of mathematics continues to grow. With more tools available for using AI, we need people who understand the foundations of mathematical theories, how mathematics can be applied and what it aims to achieve.
In short, human guidance remains essential.
Alongside expertise and understanding, mathematical creativity is also needed, Salo says. In his view, AI cannot yet combine these qualities.
Researchers are still needed to ask the right questions, ensure the quality of the results and communicate the findings to other researchers and the public.”
According to Salo, this human input enables new ways of thinking, insights and innovations. It also ensures that earlier researchers receive proper credit and that citations point to genuine previous work.
Faster results for the research team
Salo has secured highly competitive European Research Council (ERC) funding for 2026–2031 – his third ERC grant. The €2 million grant will allow his team to focus on inverse problems research for five years. The project aims to solve inverse problems involving partial differential equations and geometry.
The rapid advances in AI also appear to be accelerating the work of Salo’s research team.
When we were writing this funding application in 2025, it was far from clear that these tools would be so good by now,” Salo says.
“We will achieve our intended results sooner than we expected. That makes publishing the results and communicating them to the research community and the public more important than ever.”
Using inverse problems research to find drinking water
The study of inverse problems is a major field of mathematics. Its methods are already used in medical imaging, including X-rays, ultrasound and magnetic resonance imaging, as well as in measurements of the Earth’s crust.
In an inverse problem, the aim is to work backwards from a known effect to determine its cause. Researchers study the mathematical foundations and methods that make this possible.
My research concerns phenomena modelled by wave equations, including those involved in exploring the Earth’s crust to locate minerals or groundwater,” Salo says.
“Access to drinking water is an important issue in many parts of the world.”
Salo’s work is currently being put into practice at the Natural Resources Institute Finland in Laukaa, where researchers are testing the use of sound waves to locate groundwater.
Finland has a strong inverse problems research community
Salo currently leads an inverse problems research group that is part of the national Flagship of Advanced Mathematics for Sensing, Imaging and Modelling (FAME).
His Jyväskylä group was also part of the Centre of Excellence in Inverse Modelling and Imaging, funded by the Research Council of Finland, in 2018–2025.
Finland has a strong inverse problems research community that formulates and investigates interesting mathematical questions in areas such as imaging,” Salo says.
In Jyväskylä, the research focuses particularly on mathematical models for medical and seismic imaging and the associated theory of inverse problems. The group specialises in theoretical research. Salo’s team comprises nearly twenty researchers, teachers and doctoral students.
According to Salo, the University’s strength in inverse problems research is also reflected in its rankings. In the Shanghai Ranking’s latest ranking of academic subjects, the University of Jyväskylä was the highest-ranked university in Finland for mathematics.
Publishing, participating and maintaining a strong international presence really do make a difference,” he says.
Does this success and reputation also help attract students to study mathematics?
“Jyväskylä attracts motivated students,” Salo says. “Sooner or later, students will inevitably encounter AI in mathematics too. They also need guidance on using AI in their studies.”
From national-level gymnast to mathematician
Salo completed upper secondary school in Rovaniemi. After earning a master’s degree and undertaking postgraduate studies in the United States, he completed his doctorate at the University of Helsinki in 2004.
He moved to Jyväskylä in 2013 to take up a professorship in mathematics.
As a young person, Salo competed at national-team level in artistic gymnastics. One of his children now also practises gymnastics.
"Jyväskylä offers good opportunities for gymnastics too,” says Salo, who also enjoys a variety of physical activities himself.
His family likes living in Jyväskylä. Everyday life and getting around the city are easy.
We manage without a car in our daily lives,” Salo says.
“For the autumn holiday, we took the train to my hometown of Rovaniemi. It is a pleasant way to travel.”
“I was already interested in mathematics and computing at upper secondary school, and programming was a hobby,” Salo recalls. “The programming tools available could not do everything I wanted. Mathematics imposed no such limits – the only limit is your imagination.”
Today, Salo and his team are putting that mathematical creativity to successful use in Jyväskylä.
