2006年国际数学家大会关注21世纪数学发展方向

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2006年国际数学家大会关注21世纪数学发展方向
（转自2006年国际数学家大会官方网站）

    在15世纪达芬奇曾经说过：“如果一门科学它没有被注入数学的理论，那么它就不能被认为是一门科学。”

2006年5月3－4日在西班牙马德里召开了题为21世纪的数学专题会议。该专题会议是由国际数学家大会与西班牙皇家科学院共同举办的。国际数学联盟主席John Ball教授，和两位菲尔兹奖得主，Alain Connes教授（1982年获奖） 和 Efim Zelmanov教授（1994年获奖）, 将参加会议。

尽管两位菲尔兹讲得主的工作属于基础数学范畴，但是Alain Connes教授的工作在理论物理中有很大的用处，而Efim Zelmanov教授与西班牙同行合作的工作再一次表明一些现代数学的美之间源于包括密码学在内的应用领域。

Avner Friedman教授的工作属于应用数学。他将讲述生物和医学给数学带来的新的挑战，其中包括破解基因密码，理解蛋白质折叠机制，预测传染病甚至肿瘤形成发展方式。数学在解决这些实际问题中起到决定性的作用。

人工智能带给数学的挑战同样引人瞩目。西班牙数学家Luis Mª. Laita de la Rica教授将介绍机器可以做什么和不可以做什么。奥地利数学家Walter Schachermayer教授将介绍金融数学。会议上还安排了非数学家的报告。来自西班牙的科学家Jordi Bascompte教授将讲解数学如何可以帮助人们研究生物的多样性，而他的同胞 Amable Liñán教授将介绍如何设计能更有效地燃烧的发动机。

来自法国著名CNRS高等科学研究所的所长数学家Jean Pierre Bourguignon将最后一个做报告。

英文全文
What Kind of Mathematics Will We Need in the 21st Century?

Two Fields Medal Winners Will Try to Answer This Question at the ICM2006 Antechamber Symposium

Leonardo da Vinci said it in the 15th century: “A science cannot be considered as such unless it is impregnated with mathematics”, a statement that is still valid today.

Current science and technology must be nourished by mathematics in order to make any advances. But this is an arrow that flies in both directions at once: mathematics also grows according to the new problems constantly being thrown up by the world. So it is not out of place to ask: What will mathematics be like in the new millennium? What questions will it have to tackle? Some of the most outstanding contemporary mathematicians have agreed to share with us their reflections on the subject during the symposium “Mathematics for the 21st Century”, due to be held on the 3rd and 4th of May at the Ramón Areces Foundation in Madrid. John Ball, president of the International Mathematics Union (IMU), and two Fields Medal winners will attend what is considered to be the antechamber to the 2006 International Congress of Mathematicians (ICM2006), which will be held in August in Madrid.

The programme for the symposium at the Ramón Areces has been designed to provide a floor for both the kind of mathematics “that though focused on themselves give rise to spectacular developments, and those that are nourished by the natural world and new technological challenges” explains Manuel de León, one of the co-ordinators of the symposium and chairperson of the ICM2006 Executive Committee.

Alain Connes and Efim Zelmanov, who were awarded the Fields Medals in 1982 and 1994, respectively, belong to the basic mathematics group, but Connes'; work has proved to be of great usefulness in theoretical physics, while Zelmanov, who collaborates with Spanish mathematicians, has remarked more than once on the “beauty” of some of the current mathematical problems arising directly from applications, such as cryptography.

For his part, Avner Friedman, of the Ohio State University (U.S.A.), will be representing applied mathematicians at the Areces symposium, where he will speak on a subject that is expanding rapidly: The New Mathematical Challenges Posed by Biological and Medical Sciences. Decyphering the genome; understanding how proteins are folded; predicting the development of an epidemic and even of a tumour all of them problems in which mathematics has a vital role to play.

Of equal current concern are the challenges posed by artificial intelligence. Luis Mª. Laita de la Rica, from Spain, will speak on What Machines Can and Cannot Do, while Walter Schachermayer, from Vienna, will deliver a talk on financial mathematics. There will also be talks by non-mathematicians; Jordi Bascompte, of the Estación Biológica CSIC at Doñana, will explain how mathematics can contribute to the study of biological biodiversity, and Amable Liñán, winner of the Príncipe de Asturias Prize, will deal with the problem of developing more effective combustion engines.

In short, as Manuel de León, and Manuel López Pellicer of the Royal Academy of Exact, Physical and Natural Sciences, explain, the symposium will offer an “overview” of present-day mathematics “which will range from classical problems such as Poincaré';s Conjecture, probably one of the central themes of the ICM2006, to the relations between mathematics and biology, as well as with computation, engineering, industry and finance. And last but not least, the continual two-way relation with the physical sciences, which has done so much to shape both the world today and our vision of the universe”.

The closing talk will be given by the French mathematician Jean Pierre Bourguignon, director of the prestigious Institute of Higher Scientific Studies of the Centre National de Recherche Scientifiique (CNRS).

The symposium is organized in collaboration with the Spanish Royal Academy of Exact, Physical and Natural Sciences