International Congress of Mathematicians ICM2006
Press Kit
Index:

• This Summer Spain Will Host The Foremost Scientific Meeting In The World.
• The IMU General Assembly.
• Practical Information About The Congress.
• Parallel and Cultural Activities During The Congress.
• Scientific Content of the ICM2006 Congress.
• The Nobel Prizes in Mathematics.
• More Than 60 Satellite Congresses Revolve Around The ICM2006.
• The International Mathematical Union And The ICM Congresses.
• Mathematical Challenges Of The Third Millennium.
• Mathematical Production According To Country.
• But What’s The Use Of Mathematics?

International Congress of Mathematicians (ICM2006)
Dates: from 22 to 30 of August, 2006
Venue: Palacio Municipal de Congresos del Campo de las Naciones, en Madrid
Web: www.icm2006.org
Press: Ignacio Fdez. Bayo (610.908.224) y Mónica Salomone (649.934.887)

The XXV International Congress of Mathematicians ICM-2006 will be held in Madrid from August 22nd to 30th

THIS SUMMER SPAIN WILL HOST THE FOREMOST SCIENTIFIC MEETING IN THE WORLD

Some 5.000 mathematicians from one hundred countries are expected to attend

This summer Spain will host what is considered to be the greatest scientific meeting in the world owing to the number of specialists who regularly attend: The International Congress of Mathematicians (ICM2006). From 22nd until 30th of August, Madrid will welcome some 5.000 mathematicians from all over the world who will gather at the Palacio Municipal de Congresos in the Campo de las Naciones exhibition park to participate in the most important meeting of the International Mathematical Union (IMU). This congress has been held every four years for almost a century, and on this 25th occasion it will be held for the first time in a Spanish city. The previous congress, held in Beijing, was attended by 4,270 mathematicians from 101 different countries.
    Furthermore, this international event will be marked by the celebration of 60 smaller satellite conferences, which are due to take place in different countries over the next few months.  As the host nation, Spain will be the venue for 36 of these mathematical meetings, which will be held in 12 of the country’s autonomous regions, a fact that will attract even more attention from scientists worldwide to what is taking place in Spain at this time.  “This is the greatest mathematical event in the world, a huge mathematical fair where the most important advances are presented, where the most outstanding mathematicians of the last four years receive their awards, and where the current state of this science is debated”, says the chairperson of the Organizing Committee, Manuel de León.
    The week-long ICM2006 in the Campo de las Naciones in Madrid will host 20 plenary lectures and 169 invited lectures, divided into 20 scientific sections covering all mathematical fields.  The highlight of the congress will take place on the morning of August 22nd during the opening ceremony, when it is hoped that the Fields Medals, considered to be the Nobel Prize for Mathematics, will be presented by King Juan Carlos. Two more prizes will also be awarded, the Nevanlinna (for advances in mathematical aspects of information science) and Gauss Prizes, the latter a distinction that will be conferred for the first time for mathematical advances that have had the greatest impact on technological development and daily life. 

Weekly News Bulletin
Starting on April 10th, and during the following 20 weeks, a weekly bulletin containing news, interviews and information about the ICM and its satellite conferences will be issued.  The bulletin will be sent free of charge by electronic mail to journalists, the media, and to all those people and institutions are who interested in receiving it.  It can be obtained via the congress web page:
www.icm2006.org

The Three Axes of the Congress

Every ICM Congress has its own special international connotations.  The 1998 Berlin congress paid tribute to the victims of the Holocaust, while the General Assembly that year was held in Dresden and included a symbolic event in homage to the city.   Beijing 2002 marked a further step on China’s road to democracy and closer relations with the West; respect for human rights was a demand of the IMU, which throughout its history has stood by the principles of freedom and democracy. 
    Madrid 2006 also has its own special features.  The geopolitical situation in Spain is unusual, as is its history.  It is for that reason that three major axes of procedure have been set out for the ICM2006 in Madrid:

• The Latin American axis, which seeks to encourage participation from mathematicians belonging to countries in this region as a contribution to their development and to increase scientific collaboration.
• The Mediterranean axis, a revival of the Spain of the Three Cultures, an example of coexistence symbolized by the celebration of the meeting “Mathematics for Peace and Development” in Córdoba in July.
• The European axis, symbolized by the holding of the IMU General Assembly in Santiago de Compostela, with the Camino de Santiago or Road to Santiago as the channel for culture and science in the Middle Ages. 

With these three axes, the ICM2006 Madrid seeks to underline once again the universal role placed by Mathematics, a key factor in development, as the IMU and UNESCO showed by the declaring the year 2000 as the International Year of Mathematics. 

THE IMU GENERAL ASSEMBLY

Every four years, the International Mathematical Union (IMU) holds its General Assembly on the weekend preceding the ICM Congress.  The member countries of the IMU, which at present number 67, get together to take decisions that will affect the future of mathematics in the world during the coming four years.  The meeting is always held in the country responsible for organizing the congress, although in a different city. 
    In order to be a full member of the IMU and take part in the General Assembly, the member countries are required to possess a minimum mathematical potential.  With the purpose of helping developing countries to achieve the minimum level required to form part of the organization, the IMU carries out projects of international cooperation.  The IMU consists of five groups, numbered from I to V according to their level of mathematical development.  Group I is the elementary level and Group V the highest.  Indeed, the group number indicates the number of delegates from each country with the right to participate and vote.  Spain joined Group II in 1952; in the late eighties it moved up to Group III, and last year it was included in Group IV.  It hopes to join the highest group in 2007.   
    On the occasion of the ICM2006, the IMU General Assembly will be held in Santiago de Compostela on the 19th and 20th of August.  The choice of this Galician city is symbolic of the Road to Santiago, the route along which culture and science were spread during the Middle Ages in Europe.  This will be the first time that the IMU has assembled in Spain.  The chairperson of the IMU General Assembly Organizing Committee is Juan Manuel Viaño, dean of the Faculty of Mathematics at the University of Santiago.  
    Important decisions will be taken during this General Assembly, two of which will be the choice of host country for the next ICM in 2010, and the new election of the different IMU committees, for which many Spanish mathematicians will stand as candidates, both decided on the basis of increasing global representation on the IMU.  Furthermore, important issues such as education, research, cooperation, the history of mathematics, electronic communication and the digitalization of mathematical literature, among other topics, will be debated. 

PRACTICAL INFORMATION ABOUT THE CONGRESS

The congress of the International Mathematical Union, due to take place in Madrid from August 22nd to 30th, is the 25th to be celebrated in the history of the organization and the first to be held in Spain.  Judging by the number of scientists expected to attend (approximately five thousand), it will be one of the greatest scientific events ever to have taken place in the country.  A budget of three million euros has been assigned to cover its organization. 
    The proposal to organize this congress in Madrid arose jointly from the scientific societies representing Spain in the IMU, and whose members include some 8,000 Spanish mathematicians. Outstanding mathematicians from several Spanish universities form the Executive Committee for the congress, chaired by Manuel de León with Carlos Andradas as general vice-chairperson.
    The congress will be preceded by the IMU General Assembly, which will be held on August 19th and 20th in Santiago de Compostela.
  The inaugural ceremony and the following sessions will take place at the Palacio Municipal de Congresos in the Campo de las Naciones exhibition park in the capital of Spain.  
    Throughout the week of the congress 20 plenary lectures and 169 invited lectures will be held, divided into 20 scientific sections and covering all mathematical fields from the history of mathematics to its popularization.  More than 60 parallel satellite conferences will be held in other Spanish cities (Zaragoza, Sevilla, Barcelona, etc.) and abroad. 
    For the first time since its participation in such events, Spain will be represented by nine official speakers. 
    The Press Office will be responsible for facilitating the task of the accredited media representatives during the days of the congress.  

PARALLEL AND CULTURAL ACTIVITIES DURING THE CONGRESS

 SCIENTIFIC CONTENT OF THE ICM2006 CONGRESS

In order to plan the programmes for the different ICM Congress sessions, the International Mathematical Union appoints a Scientific Committee consisting of about a dozen members whose names are not made public until the congress is over.  The organizing country is traditionally allowed to propose one or two of its own members to stand on this committee.  On this occasion, two Spanish scientists have been appointed as members.
    The most eagerly awaited sessions of this congress are the Plenary Lectures, which will be given by 20 specially invited renowned mathematicians, among whom will be Juan Luis Vázquez, the first Spanish mathematician to receive this recognition.
(The details of each lecture can be found at: /scientificprogram/plenarylectures/)
The main body of scientific content is concentrated in the 169 lectures included in the 20 sections into which the International Mathematical Union has divided this congress.  All the speakers are chosen and invited by the Scientific Committee. 
(Details of the lectures in each section can be found at: /scientificprogram/sectionlectures/)
Furthermore, there will be short communication, poster and the presentations of mathematical software sessions. The period set for submissions in these sessions ended on March 30th, and the review procedure for these submissions will last until the end of April.  It is estimated that some 1200 such submissions will receive approval.  
Lastly, eight special sessions will also be held, which will include round table and panel discussions as well as magistral lectures. Among these, it is worth mentioning the Emmy Noether Conference in memorial of this brilliant mathematician, which will be given by a leading woman mathematician.

(The programme for these sessions can be found at: /scientificprogram/specialactivities/)
The weekly news bulletin will be issued from April 10th and during the following 20 weeks will provide information about the scientific content of the congress and the most relevant participants.  Those who wish to receive this bulletin should consult the congress web site: www.icm2006.org

The 20 Sections of the ICM2006

• Logic and Foundations
• Algebra
• Number Theory
• Algebraic and Complex Geometry
• Geometry
• Topology
• Lie Groups and Lie Algebras
• Analysis
• Algebraic Operators and Functional Analysis
• Ordinary Differential Equations and Dynamic Systems
• Partial Differential Equations
• Mathematical Physics
• Probability and Statistics
• Combinatorics
• Mathematical Aspects of Computational Science
• Numerical Analysis and Scientific Computation
• Control Theory and Optimization
• Applications of Mathematics in the Sciences
• Education and Popularization of Mathematics
• History of Mathematics

THE NOBEL PRIZES OF MATHEMATICS

On August 22nd, 2006, during the ICM2006 ceremony of inauguration, one of the most important events in the world of mathematics will take place in Madrid: the award of the Fields Medals, the highest scientific accolade in this discipline.  In addition to these prestigious awards, the Nevanlinna Prize will be awarded, and for the very first time the Gauss Prize.
    The Fields Medals are awarded every four years on the occasion of the international congresses of mathematicians in recognition of the most outstanding achievements during that period.  With a profile of Archimedes on one side and on the reverse the inscription “Transire Suum Pectus Mundoque Potiri” (To transcend the spirit and take command of the world), these medals struck in gold are as prestigious as the Nobel Prize, with the difference that according to an unwritten rule they can only be awarded to mathematicians under the age of 40 (on January 1st of the year of the congress).  The medals are named after the Canadian mathematician John Charles Fields (1863-1932) and have been awarded since the International Congress held in Oslo in 1936.  A Spanish mathematician has never been awarded this medal.  A maximum of four Fields Medals can be awarded at each congress. 
    The Nevanlinna Prize has been awarded every four years since 1982 in recognition of the most outstanding achievements for aspects of mathematics in the Information Society (such as computational science, programming languages, cryptology, analysis of algorithms…).  This award consists of a gold medal bearing the profile of Rolf Nevanlinna (1895-1980), Rector of the University of Helsinki and president of the International Mathematical Union (IMU), who in 1950 took the initiative of introducing computation into Finnish universities.
    The Gauss prize, which in Madrid will be awarded for the first time, is to be conferred for those advances in mathematics which have made the greatest impact on technological development and daily life.  It is named after Carl Friedrich Gauss (1777-1855), nicknamed the ‘Prince of Mathematics’ and considered one of the most outstanding mathematicians of all time.  In 1801, Gauss propounded the revolutionary idea of calculating the orbit of the asteroid Ceres, which after being discovered disappeared in the firmament.  Thanks to Gauss’ so-called ‘least squares” method, Ceres was rediscovered.   

•     This award consists of a medal with the figure of Gauss on the top side and a curve symbolizing the orbit of Ceres on the reverse side, which includes a circle (Ceres) and a square (the method).

MORE THAN 60 SATELLITE CONGRESSES REVOLVE AROUND THE  ICM2006

In their book The Matematical Experience (published in Spanish under the title “Experiencia matemática”, by Labor, Barcelona, 1988), Philip J. Davis y Reuben Hersh estimate that there must be about 3.000 specialized and sub-specialized areas within the universe of mathematics.  They also estimate that each year sees the appearance of some 200.000 new theorems.  Obviously, no one is capable of keeping abreast of all these fields, nor can they possibly check the validity of all the theorems propounded. 
    Unlike the case of the other principle scientific disciplines, the complexity of mathematics does not prevent the ICM congresses from being held.  There is room for all this wealth of content in the congresses, although in many cases communication among the specialists in different fields is complicated, not so say impossible, particularly when it comes to the in-depth study of a question.
That is why it is essential for conferences to be held for each specific speciality, and the ICMs act as a catalyst for many of them, which take place at venues and times close to the main congress. 
    On this occasion, the ICM 2006 has broken all records, since the number of satellite conferences will exceed 60, each one of them organized independently by separate committees (see:
/satelliteactivities/listofsatellites/).
     Several thousand mathematicians are expected to attend these satellite conferences (in addition to those who will attend the ICM), which will be held throughout the summer, the first beginning on June 28th in Coimbra, Portugal, while the last will end on September 29th in Pamplona.
   36 of these conferences are due to be held in Spain, which together with the ICM itself provide the country with a unique opportunity of promoting its own research activity and familiarizing mathematicians from all over the world with the work being carried out in our country. 

Number of Satellite Conferences by Country:

Information about all these satellite conferences can be obtained at:
/satelliteactivities/listofsatellites/

THE INTERNATIONAL MATHEMATICAL UNION AND THE ICM CONGRESSES

The history of the “world summits” of mathematics goes back to the end of the 19th century with the creation of the national mathematical societies.  One of the people who did most to bring about the union of mathematicians was the German Georg Cantor and his fellow countryman Felix Klein, who in 1893 raised the cry of “Mathematicians of the world, unite!”.
    The first international congress of mathematics was held in Zurich in 1897, during which 208 specialists from 16 countries took part.  The official languages were French and German.  It was on this occasion when the objectives for this type of meeting were established: to stimulate relations between mathematicians of different countries; to deliver reports on contemporary mathematical subjects, and to foster cooperation in fields such as terminology and bibliography. 
    The second meeting, which took place in Paris in 1900, was particularly memorable because David Hilbert gave his historic lecture Mathematische Probleme, during which he outlined the principle mathematical problems to be tackled in the 20th century, a series of twenty-three challenges that would  provide the incentive for the next one hundred years. 
    During the following congress, held in Rome in (1908), the need to establish a permanent body to ensure coordination between congresses became clear.  Likewise an international organization for the improvement of the teaching of mathematics at secondary school level was set up: el ICMI (International Commission of Mathematical Instruction).
    The congress scheduled to be held in Stockholm in 1916 was cancelled due to the First World War. 
    At the following congress in Strasbourg in 1920 it was agreed to create the International Mathematical Union (IMU), but with the exclusion of the nations defeated in the First World War (Germany, Austria, Hungary and Bulgaria), a discriminatory measure that led to the suspension of the Union’s activities in 1932. 
    Attempts to reestablish the IMU during the 1930s were unsuccessful.  Nevertheless, in 1936 the Fields Medals, the highest honour in mathematics, were awarded for the first time.  This event, together with the ICMI, helped to fill the vacuum left by the suspension of the IMU.
     At the 1950 congress held in Cambridge, England, a vote was taken to reconstitute the organization without any exclusions, and the following year the IMU resumed full activity.  Spain joined the IMU one year later, in 1952.
    From that time on, and in spite of the tensions created by the Cold War, the IMU has continued to function without interruption to the present day. 
    In 1992, the IMU approved the Rio de Janeiro Declaration for the celebration of the year 2000 as the “International Year of Mathematics”, to commemorate the centenary of the second congress held in Paris. 
    The Beijing congress in 2002 was the first to be held in a developing country, and at the General Assembly held prior to the congress in Shanghai, Madrid was chosen to be the host city for the next ICM. 

The IMU is currently composed of representatives from 67 countries.  Its structure is divided into five groups or levels, according to the contribution of each member country to advances made in mathematical science.  Spain is presently situated at the fourth level and aspires to form part of the fifth group, which is the highest in the structure. 
    The goals of the organization are to promote cooperation among mathematicians and to provide backing for its international congresses.
    These congresses have become the foremost international event in mathematical science.  During the different sessions of the congress the basic advances in mathematical research are presented and the most outstanding mathematicians are honoured by awards.  Except for the periods during which the two World Wars were fought, the congress has been held every four years since 1900, during which time the number of participants has continued to increase.  The 1998 congress in Berlin was attended by 3,446 participants; the 2002 congress in Beijing attracted more than 4,000, while the congress this year in Madrid is fully expected to exceed this figure. 

List of The 24 ICM Congresses Held to Date:

• Zurich (1897)
• Paris (1900)
• Heidelberg (1904)
• Rome (1908)
• Cambridge. G.B. (1912)
• Strasbourg (1920)
• Toronto (1924)
• Bologna (1928)
• Zurich (1932)
• Oslo (1936)
• Cambridge, USA (1950)
• Amsterdam (1954)
• Edinburgh (1958)
• Stockholm (1962)
• Moscow (1966)
• Nice (1970)
• Vancouver (1974)
• Helsinki (1978)
• Warsaw (1982, held in 1983)
• Berkeley (1986)
• Kyoto (1990)
• Zurich (1994)
• Berlin (1998)
• Beijing (2002)

MATHEMATICAL CHALLENGES OF THE THIRD MILLENNIUM

Mathematical problems are the quintessence of the discipline.  Because they involve strategic conceptual challenges, these technical barriers constitute potential breakthroughs for enhancing the capacity of mathematical language.
That is why the major problems still awaiting solution are so important.
    Seven of these problems were identified in Paris by the Clay Foundation in the year 2000.  They are known as the “Millenium Prize Problems” because the Foundation is offering a million dollar prize for the solution of each separate problem. 

• P versus NP
• The Hogde Conjecture
• The Poincaré Conjecture
• Riemann’s Hypothesis
• The Existence of Solutions to the Yang Mills Equations and the Mass Gap
• The Problem of the Existence of Solutions to the Navier-Stokes Equations and  their Differentiability
• The Birch and Swinnerton-Dyer Conjecture

MATHEMATICAL PRODUCTION ACCORDING TO COUNTRY
(1994 – 2004, Source: ISI Essential Indicators)

BUT WHAT’S THE USE OF MATHEMATICS?

An overwhelming majority of mathematicians would say that mathematics are beautiful in themselves and that they are their own justification.  But mathematics are also important, not to say necessary.  They could be called the invisible science; part of their importance arises from the fact that they are behind many aspects of daily life, at once hidden and essential.  They are also the engine of change; there is no aircraft, no robot, no computer … no future technology without mathematics.  Here are just a few examples:

• Should I take the umbrella today? Mathematics play a vital role in weather forecasting.  For this purpose the atmosphere surrounding the planet is divided into imaginary boxes with sides 50 kilometres long and dozens or hundreds of metres high.  Data on the climate in these boxes is taken by means of satellites and meteorological stations and the variables entered into powerful computers where they are combined with the laws of dynamics and physics in a process of complicated calculations in order to forecast the behaviour of the weather over the next few days.  For predictions in the long term, the interaction of the atmosphere with the oceans, and the ice caps with the biosphere, are incorporated into mathematical models similar to those used in this process in order to study the possible effects of climate change.    
• I’m sorry, I don’t speak Spanish. Sometimes considered a universal language, mathematics are also vital for the automatic translation of all languages, from French to Zulu.  This is possible because computer programmes for translation are based on statistics and probabilities as well as on enormous data bases of words in order to come up with the correct translation of every term.  
• Picking up the telephone.  Dialling a number and speaking with someone on a cell phone is much more complicated than it seems. The GSM (Global System for Mobile Communications) standard alone, which enables one receiver to connect with another, consists of more than 5,000 pages of technical specifications.  Mathematics and algorithms not only simplify this process, they are also fundamental to each of the steps comprising every call; the transformation of the voice into numerical series, its transmission by Hertzian waves, the encryption of the call, and the different radio frequencies of each operator… 
• Protected Comunication. How can a telephone conversation be encrypted to prevent it from being overheard by other people?  Or how can a credit card be made secure?  Since the Second World War, in which mathematics played a decisive role in the decryption of secret messages, this science has been a key factor in many security systems used today on a daily basis.  Many of these systems are based on the RSA protocol, which is founded on the idea that although extremely long figures can be constructed from prime numbers (N = p x q), it is very difficult to find the factors p y q if only N is known.
• Bid and win.  What do you have to do to make the most of bidding at an auction?  Game Theory, created by the Hungarian mathematician John von Neumann between 1920 and 1940, analyses the different players and the different strategies for anticipating their preferences.  For example, in a symmetrical situation in which the different players are all following the same train of thought, a bidder must seek maximum benefit while knowing that the others are following the same strategy as he or she. 
• Is this skyscraper going to fall?  Numbers have also enabled complex mathematical models to be developed for the computer representation of practically any solid or fluid with the aim of simulating the way it behaves in reality.  In other words, these models are a way of predicting the future, and have already been used for analysing the stability of skyscrapers and bridges in earthquake conditions, or for simulating the landing of space probe on a distant planet.  Attempts are currently being made to reproduced organs of the human body by computer in order to be able to predict how a patient will respond to surgery in an operating theatre. 

• The chances of developing cancer.   Many diseases are determined by hereditary factors, which means that a person carrying a particular gene may be predisposed to suffering from a certain illness.  This is the case with the BRCA1 gene, whose mutation was discovered in 1990 and is involved in a high percentage of cases of women suffering from breast cancer.  In order to isolate this gene, researchers were obliged to carry out many statistical analyses on people from the same family groups.    
• From Jurassic Park to Star Wars.  Creating toy models that come to life on the cinema screen or making an audience grip their seats under imminent attack by a Tyrannosaurus Rex is in large part possible thanks to mathematics.  Many of the most amazing special effects in feature or animated films are a combination of pixels and geometrical shapes created mathematically by means of computer programmes. 
• Reliving the past.  Reconstructing a broken vase is never an easy task.  But what happens if the vase is hundreds of years old and must be put together again from hundreds or thousands of small, incomplete and jumbled fragments, without an overall notion of what the vase was like originally?  Mathematics are also an indispensable tool in archaeology, since they enable surfaces of all kinds to be reconstructed, even including parts of the human body using a few ancient remains.  The available parts are digitalized and included in computer programmes that recompose the object virtually by means of geometry, combinations and statistics. 
• Protecting the environment.  The combination of mathematics and ecology enables us to understand the complex interactions of nature.  With the help of algebra, numerical simulations, stochastic processes, differential equations and statistics, many models can be created for determining for example the extent of territory required for conserving a particular animal population, or at what rate an invading species of plant is propagated.   
• Music and literature.  Whether it be an opera by Mozart or a guitar riff by Keith Richards, all the music stored on a CD is made up of long series of zeros and ones.  But this is far from being the only relation of mathematics with music and with art.  Musical composition is closely linked with mathematics, the same as many paintings and works of art.  Mathematics is also present in many classical works of literature, such as “Alice in Wonderland” or “Gulliver’s Travels”.  And in the case of Borges, who studied mathematics for several years, the traces of this science can be found in all his work, especially in his story “The Aleph”, which refers to a mathematical theory stating that the sum is not necessarily greater than the parts.