Elon Lindenstrauss was awarded the prestigious Fields Medal for his far-reaching advances in ergodic theory concerning the measure rigidity of higher rank diagonal actions in homogeneous spaces and its application in the analytical numbers theory. The Fields Medal has been awarded every four years since 1936 by the International Mathematical Union (IMU) during the International Congress of Mathematicians (ICM), and is viewed as the greatest honor which can be bestowed upon mathematicians under forty years old. The Medal is sometimes referred to as the equivalent of the Nobel Prize, which – as is commonly known – is not granted for achievements in mathematics.

Elon Lindenstrauss was one of the key plenary speakers at the 2011 Israeli-Polish Mathematical Congress which took place in Łódź, Poland, on September 11-15th 2011. Below you will find a transcript from the interview with Professor Lindenstrauss conducted by Aleksandra Cholewińska, a representative of Ericpol. This interview is part of a wider conversation, in which Mariusz Lemańczyk and Krzysztof Pawałowski from the Polish Mathematical Society also took part. The complete interview with Elon Lindenstrauss will be published in the Wiadomości Matematyczne (Mathematical News) journal in spring 2012.

Aleksandra Cholewinska, Ericpol: I’d like to ask a few questions more about how to promote mathematics rather than about the specifics of your work. This year, the International Banach Prize was awarded for the third time and I’d like to start with its patron. 18-year old Banach thought that everything there was to be discovered in the mathematics, had already been discovered, so there is no point studying it. A few years later he changed his mind completely and set new directions for this field. What do you think, how much it is there left to discover, will we ever be able to say we know everything about mathematics?

Elon Lindenstrauss: Actually, I didn’t know this about Banach. The belief, that everything there is to be discovered in mathematics, had already been discovered is a common misconception, that somehow I have encountered many times among people, and, of course, it is completely false. There are no limits to what we can know, we can always push the frontier more and more, and furthermore, build on what has already been discovered. I have heard a story about a colleague interviewed by some news organization. He told the interviewer about Euclid’s proof, given about 2500 years ago, that there exist infinitely many prime numbers, and was asked by the interviewer if the result is still true today…

That is a nice thing about mathematics – it never becomes obsolete. A theorem remains a theorem. The fact, that it is always much more to know, is not so surprising. You could always ask more questions, and – what’s important – more interesting questions. Somehow, the most wonderful thing is, that we can still manage this growth of information. All the knowledge we have gained since Euclid (realistically, in the last couple of hundreds of years) we have built on mathematics, we can still manage and use this knowledge effectively. Right now, I think it is a very good time for mathematics, there are lots of interesting ideas, new connections between different fields. We also see, that some conjectures, open for hundreds of years, now suddenly become solved, like the Fermat and Poincare Conjecture.

A.C.: Last year, at the Polish Mathematical Meeting there was a thesis, that biology is currently at the same level of development as physics was in the 19th century. Thanks to mathematics, biology could become even more advanced than physics is today. You’ve worked at the famous Institute for Advanced Study, where also Jon von Neumann, a good friend of Banach worked. Given your experiences from Princeton, how do you judge the possible uses of mathematics in other sciences, other fields?

E.L.: Mathematics and physics were in a way twins for a long time. They share a hundred years of fruitful interaction. Biology and mathematics – it is a much newer interaction. I am not very knowledgeable about the extent to which mathematics can be used in the context of biology. I am sure, that people with mathematical training could pick a good approach to do a lot of things. Mathematical training is a very healthy training, it is a sort of ability how to think in a clear and rigorous way, and apply criticism to what you do. So, this can be useful anywhere, including biology. It is also true, that nowadays in biology we have, in a sense, many things that you could translate into sequences of digits. Eg. DNA translates into sequences of digits. One might think that, potentially, you could use mathematics to analyze these things, but I have never worked in this direction, so I can’t give you an honest answer.

A.C.: In Poland, a country with good mathematics traditions, for a period of time maths was not compulsory for matriculation exams. Do you think it should be a subject only for those, who choose it, or for everyone? How should we teach mathematics in order to encourage young people? Stefan Banach said once, that maths is a sharp instrument, not suitable for children.

E.L.: It is another new thing I never heard about Banach. Still, it is certainly true that for many things one does, a certain amount of mathematical literacy is essential. Whether one wants to be an engineer, a biologist, any other type of scientist, a banker, or someone else from the finance industry, or software industry, you definitely need some sort of mathematical literacy. Certainly, it would be a good thing if people learn mathematics. I think it’s also an unfortunate fact, that many students view mathematics as an unpleasant subject, which it, obviously, isn’t. Of course, what they are given is not mathematics but a repetitive routine tribute, which is not so much fun and perhaps not super useful in any kind of discipline.

A.C.: It’s more about the way of teaching than the maths itself?

E.L.: I must say something that is trivial. Teachers should try to teach mathematics in an interesting way. It should be a part of what a student, who graduates from high school, should be expected to know. A little bit of mathematical literacy, as well as, some general literacy about the culture, about the government of the country, history, and other things that every knowledgeable citizen should feel comfortable with. Mathematics should be part of that , but not exclusively. I think it is right to say, that it is just one of the things people should learn.

A.C.: The mathematicians of Lwów used to meet in cafeteria, drink cognac and coffee, smoke cigarettes, pose questions and then write down solutions on tabletops, and later in the Scottish Book. Those meetings would last several hours, and as a form of teamwork would bring interesting, sometimes surprising results. What does a mathematician need in his work today and how does that work look like?

E.L.: Well, it’s a nice way to work – meet with friends over a coffee, share ideas, talk about this and that, and try to learn from each other. That’s definitely something which is very important to me. I think it’s wonderful to sit in the office, to work without any disturbance from outside, to deal with one problem after another. At the same time, I do like to work with other people, to share my ideas, to learn their point of view. To be an effective mathematician, you need time free of outside hassles, so that you can concentrate on what you do… I find, that I like to have, and I am fortunate to have, people that I enjoy talking to and trust. Likewise, they trust me and we share ideas. Basically, you don’t need much more than that – we don’t need laboratories, we don’t need anything very fancy, we need our books, we need our journals, we need…

A.C.:…a computer?

E.L.: The computer is an interesting and very powerful tool. Of course, one thing is that we use computers, like everybody else nowadays, to document what we do. We use them for email, to communicate, to access information. It is also true that sometimes one could use a computer as a research tool, just to check that something which should be true, really is. It’s even a useful tool in proofs that maybe would be very tedious or impossible to do, but are very simple to perform with use of a computer. So yes, it is an important tool but not indispensible, for some kinds of mathematical activity.

A.C.: Mathematicians are considered as one of the best jobs in the world. Is it a pleasure being a mathematician, or is it painful to always have to find a path into the unknown?

E.L.: It could be a very frustrating job. We work all the time. The moments, when we actually gain insight into something, when we suddenly understand something, that nobody understood before us, when we get these new ideas, that you can apply – these moments are very, very rare. In fact, most of the time you get very frustrated. So, it is quite a hard occupation. One of the ways to mitigate this, is that most of us teach. I believe teaching is a nice activity – it is not one where you have only a rare insight, but instead you work in a predetermined way. You get into a routine, some kind of continuous feedback from teaching. Of course, there are many good things about being a mathematician. You are really able to freely share ideas with many very smart people, it’s a beautiful thing, and I cherish being a mathematician.

A.C.: What are your goals in mathematics?

E.L.: There are some things that I really want to understand, some circles of conjectures that I would like to understand better. There are also many interesting results out there that I just would like to know.

A.C.: Mathematics is a tool for engineers. The Vice-President of Ericpol Telecom, Mr Marek Gajowniczek said, when awarding the Banach prize, that every good engineer must admire mathematics.

E.L.: Engineers use mathematics, and I think it’s extremely important that they understand the mathematics that they use. It’s very important, that when an engineer uses a formula, or an estimate, he needs to understand the meaning of it, and when it is valid. I think, one of the differences between a good engineer and a not-so-good engineer, is his ability to not just use mathematics, but to understand what he uses and why.

A.C.: What do mathematicians admire in the modern world? What do you admire?

E.L.: I am very curious about many things. I’d like to know how computers work, I’d like to know how things work in general. There are many interesting things that are happening in the world, changes taking place in societies. Knowledge is much more accessible than it was not so long ago. Definitely, this is something truly incredible!

A.C.: Prof Alex. Lubotzky says that mathematics is a most beautiful, exciting and challenging task, and when you’ve finished solving a problem it simply makes you happy. What would you wish to young mathematicians, who are just getting to know the subject in school, but will perhaps follow your footsteps in the future?

E.L.: The important thing for young mathematicians is to try to find some directions that they can be passionate about. If you aren’t passionate about a problem you can’t really work on it. You can’t focus yourself if you don’t have something you are passionate about. The best thing for people, let’s say for graduate students, is to find directions which really excite the imagination. I think it’s very important!

Works for the fourth edition can be submitted until 31 January 2012.

For the Prize can be submitted a doctoral dissertation, based on which a given author was granted a degree at a university located in one of the countries covered by the competition during the year of competition announcement and two years preceding the competition.
Only doctoral dissertations originally written in Polish or English, or such whose results were published or approved for publication in English, can be submitted for the Prize.

For more information about the competition:
• Contact form
• Prize Rules

The jury will announce the winner by the end of May 2012, and the award ceremony will take place in Krakow, on the 2nd-7th of July, 2012, during the 6th European Congress of Mathematics.

BanachPrize was founded in 2008 by the Polish Mathematical Association and Ericpol Telecom, a Polish IT company.

For the third edition 14 dissertations were submitted: 9 from Poland and the rest from the Czech Republic, Estonia, Norway, Sweden and Ukraine. The submitted papers represented a number of branches of mathematics, such as the theory of numbers, functional analysis, the set theory, differential equations, the complex analysis, or differential geometry. The winner was doctor Łukasz Pańkowski of the Adam Mickiewicz University in Poznań. The awarded dissertation, Joint universality theorems vs. Kronecker’s diophantine approximation theorem, was written under the supervision of Professor Jerzy Kaczorowski, PhD.
The Jury also nominated four others for the Prize: Mr Łukasz Kosiński (Jagiellonian University, Faculty of Mathematics and Computer Science), Ms Olena Naboka (National Technical University “Kharkov Polytechnical Institute”, Department of Higher Mathematics), Mr Tomasz Piasecki (Polish Academy of Sciences, Institute of Mathematics) and Mr Marcin Sabok (University of Wrocław, Institute of Mathematics).

The prize-giving ceremony of the fourth edition will coincide with the European Congress of Mathematics, which will be held in Kraków, on July 2-7, 2012.
The programme of the Congress maintains between lectures giving a broad overview of active mathematical disciplines and more specialized talks on recent results. During the Congress several prestigious prizes established by the EMS will be awarded. The Congress will also include round table discussions, poster sessions, and a cultural and social programme.

To see more, visit: http://www.6ecm.pl/

This is an open invitation to all those who are interested in making a difference!

Doctor Łukasz Pańkowski was awarded for his dissertation entitled ‘Joint universality theorems vs. Kronecker’s diophantine approximation theorem’, which was written under the supervision of professor Jerzy Kaczorowski, PhD.
‘The dissertation concerns analytical properties of so-called Riemann zeta function, which are directly connected with natural numbers’ arithmetical character, particularly with prime numbers’, said doctor Pańkowski. ‘I’d like to say that I’m greatly honoured with the Prize named after Stefan Banach – one of the greatest mathematicians ever’.

The International Banach Prize was established by Ericpol Telecom, the benefactor of the prize, and the Polish Mathematical Society. It reflects the appreciation for mathematics and the role it plays in the contemporary world, but it also is aimed at popularizing the scientific output of Stefan Banach and the Polish science in the world.

‘We would like Poland to be the technical development centre. We have to start form the very beginning to make it happen. The mathematics is the very beginning of all engineering sciences, therefore we strive to convince the society, that the mathematics is crucial for our future development’ explained Marek Gajowniczek, Vice President of Ericpol Telecom.

The IV season of the International Banach Prize competition is coming soon. The doctoral dissertations can be submitted till the end of January, 2012. The final of IV season will be held on the 2nd-7th of July, 2012 in Krakow, during the 6th European Congress of Mathematics.

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The Jury also nominated four others for the Prize:
Mr Łukasz Kosiński (Jagiellonian University, Faculty of Mathematics and Computer Science)
Ms Olena Naboka (National Technical University “Kharkov Polytechnical Institute”, Department of Higher Mathematics)
Mr Tomasz Piasecki (Polish Academy of Sciences, Institute of Mathematics)
Mr Marcin Sabok (University of Wrocław, Institute of Mathematics).

For this year’s season 14 dissertations were submitted: 9 from Poland and the rest from the Czech Republic, Estonia, Norway, Sweden and Ukraine.

- The submitted papers represented a number of branches of mathematics, such as the theory of numbers, functional analysis, the set theory, differential equations, the complex analysis, or differential geometry – concluded Professor Zbigniew Błocki, Member of the Jury. – The winning thesis of Łukasz Pańkowski concerned the greatest unsolved mathematical problem, the Riemann hypothesis. Among other things, the thesis contains generalised results of Voronin and Kaczorowski and Kulas related to the so-called universal character of the L-function. The main findings of the paper have been published in one of the leading journals dealing with the theory of numbers, “Acta Arithmetica” – he added.

 Mr Pańkowski’s dissertation was also highly appreciated by Ericpol – the founder of the Prize.

- The involvement of Ericpol in the organisation of the competition is another aspect of the extensive scope of collaboration of our company with the scientific circles as part of the strategic programme, Ericpol Science Ecosystem – explains the company CEO, Mr Jan Smela. – It is a vital area of our activity. The success of Ericpol owes it to the intellectual potential, methods of acquisition and practical application of knowledge. We want the prize to be an impressive highlight on the career path of people who are engaged in mathematical sciences and we want to reinforce the intellectual potential of the scientific milieu. It is our goal – stressed Mr Smela.

The prize-giving ceremony will take place in Łódź on 11-15 September 2011, during the Isreaeli-Polish Mathematical Meeting (http://imuptm.math.uni.lodz.pl/).

- In the meantime, we would like to invite all interested to participate in the 4th season of the International Banach Prize. It will be a great event, as the competition finals will coincide with the European Congress of Mathematics in Kraków to be held in July next year – says Professor Paweł Walczak, vice-president of the Polish Mathematical Society.

It is the aim of the competition to promote young, talented scientists and create an opportunity for the presentation of their achievement to the general public. Mathematics is universal, it knows no boundaries . by expanding each of the new seasons of the competition with new countries mathematics will reach wider circles, and not only academic ones.

‘All participants in our competition are very talented. Often it is pure abstraction, seemingly unrelated to real life, which is the subject of their research, yet it is owing to their achievement that the world and science can change so fast’, says Mr. Jan Smela, the President of Ericpol Telecom.

‘Our initiative is becoming increasingly interesting. The competition invites excellent work at an increasingly high level. This year.s season will provide a certain breakthrough, as our competition has already reached 90 mathematics centres in Europe’, adds Professor Stefan Jackowski, the President of PTM.

20 PhD theses were submitted for the last season of the competition, including 13 from Poland, 4 from the Czech Republic and one each from Hungary, Ukraine and Slovakia. The winner, Dr Jakub Gismatullin from the Institute of Mathematics at the Wrocaw University, was honoured with the prize of 20 000 PLN at the 4th Forum of Polish Mathematicians (1-3 July 2010 in Olsztyn). His work under the title “G-Compactness and Groups” was written under the supervision of Professor Ludomir Newelski. The jury also nominated 4 other people for the prize: Radosaw Adamczak (Warsaw University, Institute of Mathematics), Sawomir Dinew (Jagiellonian University, Institute of Mathematics), Paulina Grzegorek (Warsaw Polytechnics, The Institute of Mathematics and Information Technology) and Jan Stovicek (The Charles University, Prague, faculty of Algebra).

Works for the third season of the competition can be submitted until 31 January 2011.

The jury will announce the winner by the end of May 2011, and the award ceremony will take place in d, on 11-15 September 2011, during the Polish-Israeli Forum of Mathematics . The forum programme includes research conducted both in Israel and in Poland. There are plans to hold plenary sessions with specially invited lecturers, and other theme-based sessions, each co-chaired by an Israeli and Polish mathematician. This will be a second science forum organized by the Polish Mathematical Association in cooperation with a mathematical association from another country, in this case with the Israeli Mathematics Union. The First Joint International Meeting between the American Mathematical Society and the Polish Mathematical Society was held in Warsaw in 2007.

For more information about the competition:

• Contact form
• Information about the Jury
• Prize Rules

This is an open invitation to all those who are interested in making a difference!

Doctor Jakub Gismatullin was awarded for his dissertation entitled ‘G-compactness and groups’, which was sponsored by professor Ludomir Newelski. The dissertation refers to the model theory and is connected with the important section of algebra – the group theory. In his dissertation the author researched, among others, algebraic groups which through the representation theory were used in physics. The researched issues are used e.g. in theoretical informatics, when systematizing a huge amount of data.

‘For me the prize is a firm proof of the appreciation for the abstract subject of mathematics. It gives me a freedom to conduct research without worrying for everyday material needs. I hope that my dissertation will have an interesting influence on the development of science and become an exit point for dissertations of other mathematicians’ - said doctor Jakub Gismatullin.

The International Banach Prize was established by Ericpol Telecom, the benefactor of the prize, and the Polish Mathematical Society. It reflects the appreciation for mathematics and the role it plays in the contemporary world, but it also is aimed at popularizing the scientific output of Stefan Banach and the Polish science in the world.

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• Radoslaw Adamczak (University of Warsaw, Institute of Mathematics)
• Slawomir Dinew (Jagiellonian University, Institute of Mathematics)
• Paulina Grzegorek (Wrocaw University of Technology, Institute of Mathematics and Information Technology)
• Jan Stovicek (Charles University in Prague, Faculty of Algebra)

The scope of this year’s edition was extended and, besides Poland, Belarus, Lithuania and Ukraine, included the Czech Republic, Estonia, Latvia, Slovakia and Hungary. As in the previous year, 20 dissertations were submitted; however, the level and quality were much higher than last year. Thirteen of them were written by PhD students from Poland, four came from the Czech Republic, and one each from Hungary, Ukraine and Slovakia.
“The subject matter was extremely diverse. Most of the dissertations concerned pure mathematics – from the very foundations (set theory and model theory), through algebra, topology and functional equations and inequalities, to dynamic systems with ergodic theory, probability theory, differential equations and mathematical analysis in various forms. Several dissertations were based on the applications of mathematics in cryptography, hydrodynamics, image processing and selected areas of mathematical physics,” says Professor Pawel Walczak, vice-president of the Polish Mathematical Society.

The International Banach Prize is becoming increasingly recognised in the scientific mathematical community. ’But, this is just the beginning,’ Ericpol Telecom CEO Jan Smela emphasises. ‘Each year, we will try to make the competition reach further and be noticed by other scientific circles both in Poland and abroad.’

The International Stefan Banach Prize is contributing to a large extent to the propagation of mathematical sciences in the contemporary world. The fact that mathematics was an obligatory subject during this year’s maturity exam, the ‘Mathematics. You can count on it’ social campaign as well as numerous initiatives featuring young and talented scientists, following the examples of similar projects functioning in Western Europe, bear testimony to how important mathematical sciences are in the modern world.

The Prize is, above all, supposed to support young and exceptional talent, promote their achievements and encourage them to continue scientific work. The competition was established in 2008 on the initiative of Ericpol Telecom as a joint undertaking of Ericpol Telecom and the Polish Mathematical Society.

‘As an ICT company that makes use of state-of-the-art global technologies, we draw on the accomplishments of mathematical minds. Mathematics, known as the king of sciences, is indispensable for the development of almost every sphere of life. We wouldn.t be able to go far without it. By our participation in this initiative, we want to show the society that mathematics is present in our everyday life, we want to liven up its image and promote young and remarkable scientists,’ Jan Smela adds.

In 2010, The International Stefan Banach Prize is worth PLN 20.000. It is one of the most important mathematical awards in Poland. The official presentation to the winner will take place during the Fourth Forum of Polish Mathematicians held in Olsztyn from 1st to 3rd July 2010.

The next edition of the competition for the best doctoral dissertation begins in November.

The Prize, worth 20 000 PLN, is going to be presented to the winner at the 4th Forum of Polish Mathematicians in summer 2010.

The Prize was established in 2008 in a joint initiative of the Polish Mathematical Society and Ericpol Telecom, a large Polish IT company. The ceremonial signing was held in the Cloth Hall building right at the heart of the Main Market Square in Krakw, the home town of the renown Polish mathematician, professor Stefan Banach.

‘Young mathematicians should follow professor Banach’s example. At the start of his scientific career he had to cope with numerous obstacles, but thanks to the unique qualities of his mind and personality he never gave up and managed to become one of the best-known mathematicians in the world‘ – reminded prof. Stefan Jackowski, head of the Polish Mathematical Society, during the ceremony of signing the agreement which brought the Prize to life.

‘Without poetry or fine arts our world would be incomplete, however, without mathematics modern civilization would simply not exist‘, said Jan Smela, the president of Ericpol Telecom.

In total, 19 dissertations from Poland, Ukraine, and Latvia qualified for the first edition of the competition. The jury selected the best five – four finalists and the winner, Tomasz Elsner, PhD from the University of Wroclaw. His work, supervised by professor Lech Tadeusz Januszkiewicz, PhD, was entitled ‘The minimal surface theory in systolic spaces’.

The authors of the other four nominated papers were: Grzegorz Kapustka, PhD from the Jagiellonian University in Krakow, Pawel Konieczny, PhD and Filip Murlak, PhD – both from the University of Warsaw, and Piotr Przytycki, PhD from the Institute of Mathematics of the Polish Academy of Sciences.

Read more on the first edition here.

More information on professor Stefan Banach may be found here.

Applications for the 2nd edition of the International Banach Prize for outstanding doctoral dissertation may be submitted by January 31st, 2010 using the application form on this website.

The Banach Prize regulations are available here.

The Prize was established in 2008 by the Polish Mathematical Society and Ericpol Telecom and it is the biggest mathematical prize in terms of value awarded in Poland. It is worth 20.000 zlotys and was founded to distinguish outstanding mathematical research papers and appreciate the importance these sciences have nowadays.

The Prize was presented to the winner on June 30 together with nominations for other remarkable dissertations at the inauguration of the 3rd Forum of Polish Mathematicians held in Krakow.

In total, 19 dissertations on various subjects were submitted for the competition from Poland, Ukraine, and Latvia. The jury comprising representatives of the Polish Mathematical Society and the president of Ericpol – the Prize founder handpicked the best five. The authors of the five nominated papers were: Grzegorz Kapustka, Ph.D. (from the Jagiellonian University in Krakow,) Paweł Konieczny, Ph.D. and Filip Murlak, Ph.D. (both from University of Warsaw), Piotr Przytycki, Ph.D. (from Institute of Mathematics of the Polish Academy of  Sciences,) and Tomasz Elsner, Ph.D. (from University of Wroclaw). As has already been mentioned, the Prize went to Tomasz Elsner from University of Wroclaw., Ph.D. His work is entitled The minimal surface theory in systolic spaces and was supervised by professor Lech Tadeusz Januszkiewicz , Ph.D.

‘Polish Mathematical Society and Ericpol Telecom company together showed true commitment to organizing the event up to the highest standards. We are very happy that the business environment appreciates mathematics and has shown willingness to promote it‘ , said Stefan Jackowski, the head of the Polish Mathematical Society during the award ceremony.

‘Mathematics is not promoted on the first pages of newspapers or placed in the centre of politics but I assure you this is the axis of business. I hope that thanks to such initiatives it is going to be respected even more in Poland, and that the Prize will contribute to strengthening the role Polish mathematics plays in Europe and, at the same time, to popularizing the heritage of the genius Polish mathematician, professor Stefan Banach. My dream is that the next year edition of this contest will attract more women‘, said Anna Smela-Kjellin, the vice president of Ericpol Telecom.

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On behalf of the winner, the Prize was accepted by Tadeusz Januszkiewicz, the supervisor of the best dissertation.

The next edition of The International Banach Prize for a Doctoral Dissertation in the Mathematical Sciences for the academic year 2009-2010 is going to be extended to other East-European countries and EU member states: Hungary, Slovakia, Czech Republic, Latvia and Estonia.