The explosion of mathematics

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The explosion of mathematics

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Foreword – Mireille Martin-Deschamps and Patrick Le Tallec (pdf format 35 kb)
The weather – Claude Basdevant (pdf format 200 ko)
Weather or climate prediction is not an easy task. It involves the modeling of many phenomena of different natures, and the intervention of several sciences, from mathematics to biology, via computer science, physics or chemistry.
The bottom of the mobile phone – Daniel Krob (format pdf 512 ko)
The mobile phone is now a relatively ordinary object. Who has never seen a cell phone or telephoned with it? But few people have a thought for the science and technology involved.
Encryption and decryption: communicating safely – Jean-Louis Nicolas (pdf 169 kb)
In today’s world, where telecommunications are crucial, cryptography is a major issue. It has also become a complex science, which can not do without high-level mathematicians.
Controlling a complex world – Pierre Perrier (pdf format 232 ko)
Whether it is the maneuverability of an aircraft, the mechanical strength of a complicated structure or the management of car traffic, progress in these areas does not come solely from purely technical inventions. It is also born of abstract research, like the mathematical theory of control.
The bellows theorem – Étienne Ghys (format pdf 192 ko)
A ruler, a pencil, cardboard, scissors and glue: it does not take much to give mathematicians pleasure and pretty problems – the study of which is often revealed, afterwards and unexpectedly, useful in other trades.
Find a gene responsible for cancer – Bernard Prum (format pdf 104 ko)
The developments of modern biology, and in particular those of molecular genetics, require new mathematical tools. Example with statistics and its role in the search for a gene linked to breast cancer.
Wavelets to compress an image – Stéphane Mallat (format pdf 122 ko)
Whether digitally stored in computer memories or traveling over the Internet, images take up a lot of space. Fortunately, it is possible to “condense” without altering their quality!
Preventing the waves from making noise – Daniel Bouche (format pdf 165 ko)
How to escape detection by a radar? What is the optimal shape of a sound barrier? Can ultrasound images be improved? To receive a satisfactory answer, these questions require advanced theoretical analysis.
When art rhymes with math – Francine Delmer (format pdf 286 kb)
Mathematics does not inspire scientists. Many artists have drawn from them some of their works. The converse is sometimes true too, as in the case of perspective, where art has shown the way to geometric theories.
From DNA to Node Theory – Nguyen Cam Chi and Hoang Ngoc Minh (pdf format 188 KB)
The biological activity of the DNA molecule depends in particular on its arrangement in space and the way it is twisted – things that fall within the purview of the mathematical theory of nodes.
The philosopher and the mathematician – Pierre Cassou-Noguès (format pdf 344 ko)
Throughout their history, philosophy and mathematics have maintained a close and enigmatic relationship. We should go back to Plato in the Greek world and to Descartes at the dawn of the modern era. Let us mention here two great figures of the twentieth century, David Hilbert and Edmund Husserl.
How to streamline auctions? – Jean-Jacques Laffont (pdf format 327 kb)
Thanks in particular to the Internet, auctions are becoming widespread. The modeling of these sales processes makes it possible to define the optimal rules and strategies for their use.
Econometrics to sell wines or bonds – Philippe Février and Michael Visser (pdf format 181 ko)
Great wines or treasury bills are auctioned. But what type of auction should I practice? To find out, we complete the general modeling of auctions by econometric studies.
The puzzles of the airlines – Jean-Christophe Culioli (pdf format 124 ko)
The organizational and planning problems faced by an airline are similar to those encountered in other industries. Operational research, which concerns tens of thousands of mathematicians and engineers around the world, strives to solve them at best.
11-dimensional geometry to understand Genesis? – Maurice Mashaal (pdf format 239 kb)
Physicists have long aspired to a theory capable of encompassing all elementary particles and all their interactions. For fifteen years, they have a serious track.To explore it, they have to navigate highly abstract spaces where even mathematicians have not yet ventured.
Internet: modeling traffic to better manage it – François Baccelli (pdf format 298 kb)
Specialists in communication networks strive to understand the statistical properties of the data traffic they have to carry. The management of these networks and their development depend on them.
The price of financial options – Elyès Jouini (format pdf 143 ko)
The world of finance fixes the price of options by means of formulas that have been obtained through relatively recent mathematical work. The search for better formulas continues … and this does not concern only the stock market!
Communicating without errors: the correcting codes – Gilles Lachaud (pdf format 202 ko)
To detect and correct the inevitable errors that affect the exchange of digitized information, digital coding specialists are calling for abstract methods that fall under algebra or geometry.
Rebuilding surfaces for imaging – Jean-Daniel Boissonnat (pdf format 176 ko)
Reconstructing a surface by knowing only some of its points: a problem that is often encountered, whether it is geological exploration, archiving of archaeological remains, medical or industrial imagery.
Mathematicians in France and around the world – Jean-Pierre Bourguignon (pdf 244 kb)
Until the end of the 19th century, “geometers”, as the mathematicians used to call them, were few in number. In a century, their ranks have been considerably strengthened. Today, they face a profound change in their discipline.
How to become a mathematician? – Maurice Mashaal (pdf format 227 kb)
Long years of learning and obvious talents are needed for those who want to do basic research in mathematics. But enthusiasts have at their disposal several training courses, with varied opportunities.
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