2006年阿贝尔奖得主78岁的瑞典数学家 Lennart Carleson教授将参加2006年国际数学家大会，并出席8月29日晚18:00举行的一个以“纯粹数学与应用数学是否正在分道扬镳？”为题的圆桌会议。这个会议有国际数学联盟主席John Ball主持，除了Lennart Carleson教授还有其他四位知名的数学家参加。这尽管是个老题目，但是它至今仍然如以往一样重要。2006年国际数学家大会执行委员会主席Manuel de León教授解释道，长久以来数学一直有所谓的“纯粹”与“应用”之分。这种区分常常带来偏见，比如，“纯粹”数学家们总是把自己封闭在自己的思想空间里，他们研究的数学没有一点儿用处；或者“应用”数学家们算不上是真正的数学家。

Lennart Carleson教授应该是一个“纯粹”数学家。他是因为 “他在平稳动力系统的调和分析和理论方面意义深远的贡献”而荣获2006年度阿贝尔奖。阿贝尔奖委员会认为“Carleson教授的工作永远改变了我们对分析的理解。他不仅证明了一些极其困难的定理，他证明这些定理时所引入的工具被认为和定理本身一样重要”。他的研究成果没有一项直接带来了实际的应用；然而，他的工作为一些应用领域的发展打开了一扇门，它们在这些领域起到的潜在推动作用，就如同以jpg格式存储的一幅相片一样实实在在。

    那么，Lennart Carleson教授将在圆桌会议上表述什么样的观点呢？Fernando Soria教授认为，他可能会借傅立叶猜想为例。这个猜想本身没有什么用处，但是他本人在研究这个猜想所采用的论证方法和技巧无疑构成了应用调和分析的一部分，而这对信号的数字化处理是非常有用的，类似的工作还用在数字图像的压缩中。

英文全文 The “Nobel for Mathematics” This Year at the ICM2006

Carleson will speak on the relation between pure and applied mathematiocs

Some years ago, during an informal meeting, a group of students and colleagues asked Lennart Carleson, the 78 year-old Swedish mathematician who has recently been awarded the Abel Prize, how he had managed to solve a particular problem. Carleson pondered for a moment and said, “I don’t know… If I came back in a second life and had to prove those theorems again…”. He did not finish the sentence. Fernando Soria, professor of Mathematical Analysis at the Universidad Autónoma de Madrid and present on that occasion, was always curious to know how Carleson would have finished the phrase. Now he will have the opportunity to ask him, since Carleson will be at the ICM2006 International Congress of Mathematicians to be held this August in Madrid.

Carleson will take part in the ICM2006 closing round table on August 29th (18:00) titled: “Are Pure and Applied Mathematics Diverging?”. The session will be chaired by the president of the International Mathematical Union, John Ball, and besides Carleson four other prestigious mathematicians researching in pure and applied mathematics will also take part. The subject they have chosen is a classical one, but as important and up-to-date as ever. “There has always been a ‘pure-applied’ frontier, a frontier often extended by prejudices such as ‘pure’ mathematicians are wrapped up in their own thoughts and don’t do anything useful, or that ‘applied’ mathematicians are not true mathematicians”, explains Manuel de León, chairperson of the ICM2006 Executive Committee.

Carleson’s scientific career would place him with the pure mathematicians. The Abel Prize, first awarded three years ago by the Norwegian Academy of Science and Fine Arts and worth 755,000 euros – the same amount as the Nobel Prize, which is not given for mathematics – was conferred “for his profound and fundamental contributions to harmonic analysis and the theory of continuous dynamic systems", in the words of the jury. None of these contributions have directly yielded practical applications. However, Carleson’s work has opened the door to the development of applied areas, fields which lie behind something as tangible as a photograph in .jpg format.

The problem Carleson was asked about in Fernando Soria’s anecdote concerned the Fourier Series. “In 1807, the French mathematician Joseph Fourier delivered a report … in which he stated that every periodic wave could break into an infinite sum of sines and cosines. Behind this statement lies the intuitive idea that all sounds are composed of the sum of duly amplified simple harmonics”, explains Soria. “This statement was controversial at the time and could not be demonstrated. Later, in the 20^th century, it was proposed as a conjecture”. This is the statement that Carleson proved. In a sense, says Soria, the award-winning Swedish mathematician ended up struggling against himself; he was convinced that the conjecture was false, and what he was really looking for was “a counterexample, a non-decomposable wave in harmonics”

So what position will Carleson adopt at the round table in August? It could be that the demonstration of Fourier’s Conjecture in itself will be of little use, but “the arguments Carleson used certainly form part of applied harmonic analysis, and are indeed very useful. They lie behind the digitalization of signals. Solutions similar to Carleson’s work are used for example in the compression of a digital image”, remarks Soria.