The Abel Prize ceremony 2026

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[00:00:07]Ladies and gentlemen, please rise for His Royal Highness the Crown Prince.

[00:00:27]Heat. Heat.

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[00:04:26]Oh, heat.

[00:05:11]Your royal highness, esteemed laurate, minister, mayor, your excellencies, ladies and gentlemen, welcome to the 2026 Abu Prize ceremony here in the University AA in Oslo.

[00:05:29]We are surrounded by some of Edward Monk's worldrenowned paintings. They are telling us the story of the university and the sciences.

[00:05:42]This is the home of the Able Prize.

[00:05:48]Opening the ceremony today, we heard I know an ang um a fantasy on music from Norway and Germany written especially for this year's laurate.

[00:06:07]He has been central in establishing the city of Bon as a center for mathematical excellence and Bon is also the city that gave us Beethoven and so we could hear echoes of Beethoven's symphony uh in this tribute and here in Norway we are celebrating the 150th anniversary of Edward Griggs's music to Henrik Ipsson's pergint and I'm sure many of you recognized Sulves my song and in the hall of the mountain king it guban's hope the prize was established by the Norwegian government in 2002 and is awarded by the Norwegian Academy of Science and Letters on behalf of the Ministry of Education and Research.

[00:07:00]Today we honor the 2026 Abel Prize laurate and his extraordinary scientific work in the field of mathematics.

[00:07:12]So please welcome president of the Norwegian Academy of Science and Letters, Professor Amalene Erikson.

[00:07:30]Your Royal Highness, Abel Laurate, Minister, Mayor, Ladies and gentlemen.

[00:07:39]The Abel Prize is named after the most famous Norwegian mathematician Nils Henrik Abel and recognizes pioneering and groundbreaking scientific achievements in mathematics.

[00:07:55]The Arbel Prize recognizes these achievements not necessarily for their applicability but for the fundamental insights they bring.

[00:08:06]These insights have an intrinsic value because they reveal the nature of the mathematical world.

[00:08:14]They reveal what is hidden for most of us. They reveal eternal truths that future generations can build on. Just like this year's laurate, Professor G Falting worked on insights and questions initiated almost 2,000 years ago by the Greek mathematician Dioantis.

[00:08:40]In a world where nothing seems stable, where the truth is politicized, the world of mathematics, of number theory, of dopantine equations show us something that is shared.

[00:08:55]Mathematics is a universal language.

[00:09:00]This also tells us something about the nature of basic research.

[00:09:04]Valuing basic research entails valuing knowledge not as a tool for something but for itself.

[00:09:13]When arble discoveries 200 years ago were valued and celebrated for their brilliance and beauty, there were no practical applications.

[00:09:23]Today, however, several of his discoveries lay the foundation for what we all do every time we turn on our computers.

[00:09:34]History has shown us time and again that the deepest breakthroughs come from curiositydriven inquiry.

[00:09:43]When researchers are free to explore fundamental questions, they lay the groundwork for advances we cannot yet imagine.

[00:09:54]Basic research expands the boundaries of knowledge and applications might or might not follow and sometimes they follow decades later.

[00:10:05]Mathematics underpins all of modern technologies from simulations of industrial processes to cryptography and data science.

[00:10:15]Supporting basic research is an act of trust in human curiosity and creativity.

[00:10:22]It ensures that future generations inherit not only solutions but entirely new ways of thinking.

[00:10:32]The Abel Prize has a dual purpose. In addition to celebrating the highest achievements in mathematics, it supports multiple activities to stimulate the interest in mathematics among children and youth. This sets the ABA Prize apart from other international prizes.

[00:10:55]Today we celebrate someone who has given us an invaluable gift.

[00:11:01]Professor G Fings has given us insights that expand our mathematical understanding.

[00:11:09]Today we give him something in return.

[00:11:13]The Arbel Prize values the invaluable, the fundamental insights into the hidden mysteries of mathematics. Thank you.

[00:13:05]Heat. Heat.

[00:14:06]Heat. Heat.

[00:14:28]Heat up here.

[00:14:54]Heat.

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[00:15:24]Shine you no more inspired by Scandinavian folk songs and performing it was Bickup Hari Johannes Leod or Pedik all students from young talents bara and the prize is a strong supporter of young mathematical talent and as president Erikson mentioned children and young people are really at the part of the Abel Prize mission to inspire a lasting interest in mathematics.

[00:16:00]The Abel Prize is awarded based on a recommendation from the Abel Prize Committee and this committee consists of prominent researchers in the field of mathematics.

[00:16:11]Please welcome chair of the Abble Prize Committee, Professor Helga Holden.

[00:16:28]So, Professor Holden, this year it's all about diaphin equations.

[00:16:33]Tell me more what is a dapantin equation. So when you try to solve an equation to compute the the interest on a loan or the time it takes to charge your uh car battery, you get the decimal number as an answer, but you round it off to an integer name say the croner amount of croner or the minute it takes and equations where integers or rational numbers are solutions are dantine equations.

[00:17:03]Could you give me a simple example?

[00:17:06]>> Yes. Let's take one example being this room. Fire regulations given maximum number of seats that can be in this room. But it doesn't specify the number of rows and the seats in each uh row.

[00:17:20]And to solve this, find the optimal solution for this is solving a dantin equation.

[00:17:25]>> Mhm. Another example is if you want to buy something and pay with the exact change. You have a 1 cron a coin, you have a 10 krona coin, you may have a 50 crroner bill and you have to find the right combination to add up to the exact amount you have to pay. In order to do that, you have to solve a dantin equations and if you have say five croners and 10 croners and the amount you have to pay is 17, you cannot do it.

[00:17:50]So this dantin equation has no solutions.

[00:17:53]Now it sounds a bit too easy almost.

[00:17:56]>> Yeah. I'm afraid you don't get the Hubble prize for paying with the exact change.

[00:18:01]>> So does this have any practical significance today?

[00:18:07]>> Yes. Dantine equations are at the foundation of everything we do when we have transactions on the internet and want to make them safe.

[00:18:15]>> So the more we know aboutin equations, the safer the transactions we do on the internet can be. And we want to avoid people to break the codes. So we want to know as much as possible about dantin equations.

[00:18:28]>> Thank you. And in a moment, Professor Helga Holden will explain the decision of the Nobel Prize committee. But first, let's get to know this year's laurate a little bit better.

[00:18:45]I guess the purpose of my life is to do well in mathematics.

[00:18:51]I liked it because the answers are definitely true or wrong. Not like in other fields like literature where you can have this opinion or that opinion.

[00:19:04]I was born in Ghingb which is in the German rus belt and my father was a physicist and my mother a chemist. Later I moved out. I studied in minster.

[00:19:20]I was a good student and I did my first research in minster. I had a teacher Nastold who was very nice.

[00:19:30]N told you somebody in Paris Spiro had some ideas about the model conjure.

[00:19:39]I learned from him and I thought some things were missing in his approach.

[00:19:48]I got a job in Bertal and I must be thankful for the university there that they had so much trust in me and well and then I worked on this spirro had the so-called kara class which didn't exist after some time you see clearly I invented a new tool the so-called the galler presentation and This did the job.

[00:20:18]Overnight I became a star in the profession.

[00:20:26]Mathematics usually there are noa moments. You often think you have solved something and then if you check it you find that you have overlooked something.

[00:20:37]So in this sense you only know after some time that it might have been an moment.

[00:20:45]I mean these days if you look back you can see clearly what makes the difference. At that time I guess it wasn't so clear to me.

[00:20:57]There was the option to go to the US. It was a happy time for me and I got married and soon I got my first daughter and then my second and so and also got the fierce medal. So it was everything at once.

[00:21:18]I like music although I have no talent for it and I like to go to the opera and I like to do gardening because uh there I don't have to use my brain but only muscle.

[00:21:37]Of course, after model, I had not time to retire. For each problem, you're solving two new ones. In the model proof, they were sort of handmade solutions as we say. And uh I worked on these fields trying to find better and more systematic proofs and I got some success. It was also a good feeling that after model you could still achieve things.

[00:22:09]The prize shows that people appreciate me. I'm proud of my proof of model but uh I feel good because I'm appreciated by the aring is a he's an outstanding mathematician towering figure in mathematics really and uh and and a very nice colleague.

[00:22:31]Yeah, >> he did some monumental work in the field of arithmetic geometry diaphan equations. Um by in particular by proving his maybe most famous theorems the model conjecture and uh went on to do really influential work in particular in per theory and other other subjects um that have also influenced my own work enormously.

[00:23:02]Well done.

[00:23:04]>> I'm working on a variant of the valind formula.

[00:23:08]>> I'm getting somewhere but the moment I'm stuck. If you get around something, you are happy for two days and then you are stuck again.

[00:23:20]The things I could do, I have done and I'm only left with the things I can't do. And I have no idea what to do. And the young guys shouldn't follow me but should do something else >> for a program or homologist.

[00:23:35]>> You always have to look for topics which are interesting and which you probably can have an impact. So the side of horse uh is considered by uh stones and uh >> if you start something new of course you first find walls where you bang your head against but sometime you learn how the wall is shaped and then you try to get around it and well and sometimes it works and sometimes it doesn't. If you are too realistic, then you know that you would fail. You always have to think this is a good chance you can do something to be an optimist.

[00:24:27]Your royal highness laurate. Ladies and gentlemen, equations are at the heart of mathematics. Indeed, we encounter them in everyday life. We use equations to compute travel times, taxes to calculate loans and interest rates and the list goes on. We are however here interested in equation where natural numbers that is the positive integers 1 2 3 etc or possible rational numbers that is fractions are solutions. These equations are called Dopantin equations named after the Greek mathematician Dophantis.

[00:25:05]Natural numbers are the most fundamental objects we have. In the words of the German mathematician Leopulandre is mentioned where God made the natural numbers all else is the work of man.

[00:25:23]We have already heard two examples of Dantine equations. Yet another example is the use of Lego bricks. If I'm tasked with constructing a given shape with Lego bricks, there are many ways to go about it, but all share this factor, I have to use an integer number of bricks, thus a diaphantine equation. While opinions may differ about the importance of Lego bricks, for modern society, the use of diaphin equations for cryptography and security is absolutely essential. This preserves for instance the safety on online trans uh trans transactions and the use of biometric identification.

[00:26:04]The solution of the fantine equations is the focus of this year's arel price.

[00:26:10]Consider the example of the length of the sides in a right triangle. According to Pythagoras theorem, the square of the length of the hypotenuse equals the sum of the squares of the two other sides.

[00:26:22]There are many indeed infinitely many integer solutions to this equation. Say 3 4 and 5 since 3^ 2 + 4^ 2 equals 25 as does 5^ 2. However, if you increase the power to three and look for solutions, you can prove that there are no integer solutions.

[00:26:42]In 1922, the British American mathematician Louise Modell boldly conjectured that for a vast class of Dantine equations, more precisely those of genus higher than two, there could only be a finite number of solutions, be that one, two, 27, a billion or indeed zero, that is no solutions, but it could never have infinitely many.

[00:27:08]The difference between say a billion or infin infinitely many may sound immaterial but for mathematicians the distinction is immense.

[00:27:17]The problem remained open for decades not because mathematicians didn't try but because it was intrinsically very hard. In the early 1980s the young and failless Gad falting decided to investigate the problem.

[00:27:33]It was then a sensation when in 1983 he succeeded in solving it showing that the conjecture of Modell was correct. Thus Modell's conjecture turned into Falting's theorem which states that there are finitely many rational solution to this vast class of equations.

[00:27:53]Falting's proof came as a big surprise to experts. First from the fact that it could be proved and second from the method used showing a special case of the Tate conjecture devised by John Tate the 2010 arbor laurate as well as the Shafare conjecture on his approach to proving the model conjecture.

[00:28:14]Around 10 years later, Andrew Wilds, the 2016 Abel laurate, subsequently showed that the firm my equation x to the n + y to the n= z to the n had zero solutions for n greater than or equal to 4. These equations constitute a special case of the equations conjectured by modell.

[00:28:34]Thus, while we knew that the firmi equation could only have finitely many solutions from falting's theorem, while showed that indeed there were no solutions at all.

[00:28:45]Shortly after falting proved Modell's conjecture, Paul Vua found another proof. In 1991, Falings adapted this proof to show a vast generalization of the Modell conjecture, namely the Modell Lang conjecture on subvarieties of a billion varieties.

[00:29:03]I make a small digression here and direct your attention to the word I just innocently used namely a billion.

[00:29:10]This objective is of course named after Neil Senriel as he together with Evista laid the foundation of what is now called mathematical group theory and here both a billion and the opposite nonabilian are central concepts and it has reached the ultimate level of acceptance in the mathematical community as it's written with a lowercase a before I end up sounding too chauvinistic I should add that it is of course an advantage that ar name is short and easy pronounce in any language but let me now return to our main focus to prove the model lang conjecture falting established the fantin approximation result known as falting product theorem indeed falting has made multiple fundamental contribution to several areas of mathematics let it suffice here to mention briefly his major contributions to paddic hodgej theory giving proofs of the main conjectures formulated by Tate and Fonten and extending its scope to nonabilian setting under the name of Padic Simpson correspondence.

[00:30:21]Gat fings is a towering figure in arithmetic geometry. His ideas and results have reshaped the field settling major long-standing conjectures while also establishing new frameworks that have guided decades of subsequent research. His exceptional achievement unite geometric and arithmetic perspectives and exemplify the power of deep structural insight. It thus gives us great pleasure and honor to award the 2026 our prize to G fings.

[00:30:59]I would now like to ask fings to come on stage.

[00:31:12]I now invite his royal highness the crown priest to present the 2026 arings.

[00:31:47]Your royal highness, minister, major, your excellencies, ladies and gentlemen.

[00:31:55]So I have to read this to get the right details.

[00:32:01]uh I was was very very much honored to get the ar prize. I've now uh at the beginning of my career and at the end I've gotten the two highest honors in mathematics and they make nice cornerstones of my career. When I started uh in mathematics, I didn't think about prizes like well there was only the Fields Medal, no AR prize and I just wanted to get a position where I could make a living from mathematics.

[00:32:35]So I've gotten come a long way. The Apple Prize shows Norway's big regard for science. Well, Norway has the for most of the time has been ruled by foreign kings and so the national heroes are not did not work by the sword but by the pen and uh in mathematics there's of course arel but there's also Lee and Zber which left their mark. We Germans have a bad reputation because we did many bad things. But Albert had a good time in Berlin. He published things in the K journal which gave this journal a tremendous start and his famous memoir was lost by somebody else.

[00:33:30]In my work of Modell I used the word used a billion varieties.

[00:33:36]So a billion varieties were a hot topic in the time when Abel studied them. Uh studied with started with elliptic curves. Uh which have also group structure and which is well this was also part of the theorem of model not the conjecture and uh more complicated curves. There's also a group a group but the group groups are called a billion varieties and they have higher dimension and they play an important role in well in my mathematics and mathematics in general and it's sort of it's a basic tool. It's like a train line maybe in the beginning it's an adventure to build it but once it's built you just take the train and worry with it. Maybe you late but use it as a tool. I had I had the good luck to be uh present at the inauguration of the arbor prize. This was in the year 2002 for the bsentennial.

[00:34:46]There was a conference and I was on the scientific committee. It was a very pleasant committee because there was a chairman Lordal who did all the work and we only had to say from time to time we fully agree what you do what you propose and uh and so I thought I should do some work for this committee and I I read Stupaul's book on AL and so I learned a lot about Norway at this time and also So uh we had a pilgrimage uh afterwards to Abel's birthplace at Fland and uh it was very nice. So I understood lots about Norway.

[00:35:36]Abel had to teach a hombo and also had to teach at minster who was a very nice professor and I remember I gave a talk on algebraic geometry and I attended it and soon I was the only listener but but so I got good advice from him. One advice was to read Gordon Deik which at that time well he was very active but some people didn't like him but I liked him because he while somebody said his work was locally trivial which meant that well he there were lots of sentences but each of them I thought well that's clear what does he make such a fuss but then at the end he had proven a big theorem and So I was very impressed.

[00:36:33]Well, I had some person some contact with Gordon, but this was later. And my teacher also had a friend bio in Paris who had ideas about the model conjecture and uh and I found them interesting. I thought well yeah as a young guy you always have to find topic to work on and you want something which is interesting and which is not too crowded and so I thought about ideas of model I could work on it. I would get something interesting, maybe not prove it, but uh I mean as a mathematician you are satisfied if you get some results.

[00:37:16]But then there was a surprise. I managed to prove it and then I became a star of the field overnight and then I I mean there was much excitement in Germany but uh I decided I wanted to go to the US and I went to Princeton which is a small town but I liked it and there I had a very good time. I got well I got married before I got my two daughters and also I got the Fields medal. So it was raining mana from heaven. And then uh but after 10 years I decided I wanted uh my daughters to be German. And so I came back to Germany and I got at the Maxplank Institute in Bon which was founded by professors.

[00:38:14]And I mention him because at in 2002 at the bicesentennial you also get an got an honorary degree.

[00:38:24]Uh so I profited from my work. Uh and I had a had a much better time than ever.

[00:38:34]Yeah, thank you very much.

[00:39:08]In the thine I must love for my star.

[00:39:35]Let us gl them on us.

[00:40:01]heart decision of life.

[00:40:27]Oh my shoo.

[00:40:56]Woo!

[00:40:59]Woo!

[00:41:23]la.

[00:41:53]Hya in Denber in the mountains um from the opereta the charters princess we heard Andrea Bunar on the piano musical director and percussionists Peten and the wonderful Cecilia Katrina Erdigorn.

[00:42:12]Now, please welcome back president of the Norwegian Academy of Science and Letters, Professor Amalin Ericson.

[00:42:31]I would like to extend my warmest congratulations to Professor G Fings, Abel Laurate 2026.

[00:42:42]Your scientific contribution to the field of mathematics is of great value to us. We appreciate your presence here today and are grateful for being able to celebrate together with you.

[00:42:55]I would also like to thank to take the opportunity to thank everyone who has contributed to the continued success of the Aral Prize. The International Mathematical Union, the European Mathematical Society, the H Highleberg Laurate Forum, the Arbel Price Committee, the Arold Board and the Mathematical Community, which have contributed to establishing a highly recognized international prize in mathematics.

[00:43:29]To the chair of the Ael board, Professor Ingri Glad, my warmest thanks for your dedicated work during the last four years.

[00:43:40]I also want to thank the chair of the Abel Prize Committee, Professor Helga Holden.

[00:43:47]You have been formative since the very beginning of the Abel Prize and you have ensured its success.

[00:43:56]Let me end by congratulating again uh the 2026 Abel la Laurate Professor Gart Fings. Thank you Heat. Heat.

[00:44:47]Heat. Heat.

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[00:47:06]Heat. Heat.

[00:47:52]Hey, hey, hey.

[00:47:58]Heat. Heat.

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