Romania nearly had its first Abel laureate in 2025 – mathematician George Lusztig came close to winner Masaki Kashiwara

[FROG ZEW]

 

When the Norwegian Academy of Science and Letters announced Masaki Kashiwara as the 2025 recipient of the Abel Prize – often referred to as the “Nobel of Mathematics” – the spotlight naturally turned to his groundbreaking work in algebraic analysis and representation theory. But what the public may not have seen was how close the final decision had been. Behind the scenes, another name stood shoulder to shoulder with Kashiwara: George Lusztig, a Romanian-born mathematician whose towering influence in the field has shaped the landscape of modern mathematics.

 

‘The work of the Abel Prize winner this year is very, very closely related to the work of George Lusztig’, says Olivier Schiffmann, a French mathematician and external expert for this year’s Abel Committee. In an interview with Edupedu.ro, Schiffmann, who is Professor at Paris-Saclay University and Director of Research at the French National Centre for Scientific Research (CNRS), offered rare insights into the internal logic and nuances behind one of the most prestigious decisions in the world of mathematics.

Both Kashiwara and Lusztig are luminaries in the realm of representation theory, a branch of mathematics that investigates symmetries using algebraic tools. According to Schiffmann, ‘In representation theory I think it is fair to say that Lusztig is the number one’. Yet the committee ultimately leaned toward Kashiwara, not necessarily for greater brilliance, but for the breadth of his influence: ‘The difference between them was a small one. I think that the Abel Committee decided to go for Kashiwara because he also worked in algebraic analysis. Basically, Kashiwara worked in two areas and Lusztig was very, very influential in one’.

 

Masaki Kashiwara / Foto: The Abel Prize 2025

 

Kashiwara’s contributions, detailed in the official citation, include his development of D-module theory – an algebraic framework for tackling partial differential equations – as well as his formulation of the Riemann–Hilbert correspondence and the discovery of crystal bases in quantum groups. His work is a bridge between algebra and analysis, theory and application, geometry and logic.

 

But Lusztig’s achievements are no less monumental. ‘He founded an area which is now called geometric representation theory’, Schiffmann explains, referring to the way Lusztig brought deep geometric intuition into the study of abstract algebraic structures. His theories reach even into number theory, enabling mathematicians to understand how groups behave over finite fields – a crucial aspect of modern cryptography and coding theory.

 

Born in 1946 in Timișoara, Romania, George Lusztig is one of the most influential Romanian-born mathematicians, internationally recognised for his contributions to representation theory and algebraic groups. A professor at MIT since 1978, Lusztig has authored over 250 research papers and a widely cited monograph on quantum groups, says West University of Timișoara (UVT) in a presentation.

 

George Lusztig / Foto: captură Youtube.com/ Tom Rocks Maths

 

His collaboration with David Kazhdan led to the Kazhdan–Lusztig polynomials, now essential tools in the field. He also pioneered the use of intersection cohomology in representation theory and co-founded the theory of canonical bases in quantum groups – a concept closely linked to the work of Masaki Kashiwara.

 

Their paths converged and, at times, competed. ‘There was a competition between the two. Because they defined the same objects. So it’s always a question – who discovered first the very important thing called canonical basis?’ Schiffmann says. While Lusztig may have arrived at the concept earlier, Kashiwara’s contributions extended the theory into new terrain.

 

That a Romanian-born mathematician was so close to winning the Abel Prize is no surprise to those familiar with the country’s long-standing mathematical tradition. ‘Romanian mathematics is really very strong’, Schiffmann affirms. He cites not only Lusztig, but also Ciprian Manolescu, another Romanian mathematician of international renown, as emblematic of the country’s intellectual depth.

Still, challenges remain – particularly when it comes to keeping top talent engaged in Romania. Schiffmann notes that while Romania excels in nurturing young mathematical minds through olympiads, maths clubs, and programmes like APEX, ‘the main point is the salaries’. Many top scholars, though tied emotionally and intellectually to their homeland, are inevitably drawn to better-funded institutions abroad. ‘It’s very hard to compete’, he says, ‘but what Romanian mathematicians who come back enjoy is the vibrant community’.

 

As the mathematical world turns its gaze toward next year’s Abel Prize, the story of 2025 remains a poignant reminder of the thin line between recognition and near-miss. For now, Kashiwara wears the Abel laurels. But for many, including Schiffmann, George Lusztig’s moment may only be a matter of time.

 

The following is the full interview with Olivier Schiffmann, conducted by Edupedu.ro:

Edupedu.ro: Could you tell us more about this year’s finalists? What were they appreciated for and what are the main discoveries or contributions that brought them into the final selection?

 

Olivier Schiffmann: The Abel Committee works like this as far as I know: it asks people for nominations and I think this year the topic they chose was representation theory. Or maybe they were looking for someone who works in the representation theory field. And in representation theory there are two obvious candidates: MasakiKashiwara who won the Abel Prize and George Lusztig, who is Romanian and was a professor at MIT. Very close work related to Kashiwara is the work of George Lusztig.

 

The work of the Abel Prize winner this year is very, very closely related to the work of George Lusztig. The difference between them was a small one. I think that the Abel Committee decided to go for Kashiwara because he also worked in algebraic analysis. Basically, Kashiwara worked in two areas and Lusztig was very, very influential in one area. In representation theory I think it is fair to say that Lusztig is the number one.

Olivier Schiffmann / Foto: APEX-Maths 2024

 

Edupedu.ro: From your perspective, was it a surprise for the international math community to see a Romanian researcher as a finalist in such a prestigious competition?

 

Olivier Schiffmann: No. I think that certainly Lusztig is such a towering figure in Mathematics. I would expect him to win the Abel in a few years. The next years might be a hard time because they would change topics every year. Certainly I think that, once the topic goes back to representation theory, Lusztig will be an obvious candidate. I do not speak for the committee, but he is a strong candidate.

Romanian Mathematics is really very strong. There was a very strong contender for the Fields Medal a few years ago, Ciprian Manolescu, and he was rumoured to be on the short list because of his work in topology. In science, I would say Mathematics is where Romania is the strongest and definitely he was very strong.

Edupedu.ro: In your view, how can countries like Romania better support world-class mathematical research? What do you think it should do better?

Olivier Schiffmann: What is already done is very well and this is highschool training, but also math clubs, the IMAR [n.r. the Institute of Mathematics of the Romanian Academy], the APEX School Camp we are trying to run but there are other that are more olympiad oriented. When I come at APEX I see a lot of highschool students and early university students who come and listen to seminars – there’s a very good sense of community in mathematics. At least in Bucharest, I cannot speak about other cities because I don’t know.

 

What it would take to keep them… We see that they often come back. They don’t stay, they come back for a few weeks, a few months. For instance, right now, Ciprian Manolescu is at IMAR for a few months, this is really a world-class mathematician who’s a professor at Stanford and he decided to come back for a few months. And so I think the sense of community remains throughout the career, but it’s very hard to compete against the salaries.

 

I think the main point is the salaries. I think what Romanian mathematicians who come back enjoy is the fact that there are many students, a vibrant community. So it’s really pleasant to come back here and you have seminars and you have students and you can talk to lots of people and encourage the younger generation. But of course, salaries are what I think one would need to increase. We have the same problem in France. Best professors get an opportunity to go to places – it could be England, it could be Germany, the United States, Japan, Korea where they get much higher salaries.

 

Edupedu.ro: Can you explain a little bit for our public that might not be specialized on this topic regarding mathematics – in simple terms, of course – what did Masaki Kashiwara research and what did the Romanian one research? What were their theories about, their research about?

Olivier Schiffmann: MasakiKashiwara worked in two areas that he was able to connect. One is the area of differential equations, even partial differential equations who have many variables. He was able to develop an algebraic way to to think about partial differential equations. The name of the theory is D-Module. D-Module is an algebraic way to deal with differential equations. And that really completely  changed the way people think about differential equations, as it allows you to use all the fancy techniques in algebra and especially the revolutionary work in algebraic geometry Alexander Grothendieck, the famous french-german mathematician. It is one of the areas Romania is the strongest.

 

He [Masaki Kashiwara] was able to transfer all the techniques from algebraic geometry to analysis and partial differential equations. And that really changed the landscape. And then he was able to use that to study group representation. It means we have a group and you want to realize elements of the group in terms of matrices. So that two multiplied elements of the group correspond to the multiplication of the matrices. We want to understand how a group can be realized in all the different ways in terms of matrices. This way you can understand the group much better.

So the example that I’d like to give is the following: imagine that there is a picture on the wall, an old fresco that comes from ancient times but unfortunately it was essentially all broken, except for maybe a 20 degrees sector. Everything is destroyed except the 20 degrees sector, which you can see, but you know you have extra information that the whole picture remained the same if you rotated it by 20 degrees. And so if you have just two pieces of information, just a very small part of the whole picture, which is this 20 degree sector, and you also know that by rotating you remain the same, then you can reconstruct everything. You rotate your 20 degree sector, you get 40 degrees altogether, and then you rotate again, and so on. So the idea is that using symmetry of something, you can recover the entire space by knowing just a little thing.

 

You know that there’s a group of symmetry, then from a small part you can recover everything. That’s how symmetry is important: it’s important in physics but you can also study directly for mathematics

 

That’s the area in which Kashiwara and Lusztig worked and that’s the area in which Lusztig is definitely the best in the world. What Lusztig was able to do was to use some very deep geometric intuition to study groups. So that’s, you know, groups belong more to algebra. But Lusztig was able to use geometry to study groups. So he founded an area which is now called geometric representation theory. And using that, he was able to even study groups in very, very almost number theory problems.

 

For advanced: we can also talk about finite field modulo – modulo 5, modulo 11, modulo prime number. This is a very number theoretic setup, but you can work with groups over a finite field. So you can look at how a group can be represented using matrices over finite fields. You have a group, and now you want to realize it’s not a matrix with real or complex coefficients, but the coefficients of the matrix, you want them to belong to, say, Z modulo 11Z. This is really number theory.

 

This is now a mixture between groups and number theory. And it’s a very important area for number theory and Lusztig was really able to develop that theory very, very much. So there are lots of conjectures and theorems of Lusztig that explain how you can study groups over finite fields. And then the two mathematicians, Kashiwara and Lusztig – their work intersects in a theory of so-called quantum groups. These are also groups, but not quite groups, inspired by physics.

 

Both Lusztig and Kashiwara worked on quantum groups and they had very strong results there and actually there was a competition between the two. Because they define the same objects. So it’s always a question – who discovered first the very important thing called canonical basis? And so I think they share the discovery. Maybe Lusztig a little bit earlier, Kashiwara also did some other things but anyway there was competition between the two.

 

Sursa

Edited March 29 by FROG ZEW