Mathematical problems in classical physics
Mathematical problems in classical physics
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经典物理中的数学问题
DOI：
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
V. Arnold
中科院分区：
文献类型：
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作者：
V. Arnold
数学是那些暂时不流行的理论物理领域的名称。不流行的好处是，它提供了对成熟的数学模型进行严格和深入研究的可能性。一个沉睡的“物理理论”可以被表述为一系列具有数学猜想的精确数学含义的陈述。这样的假设可以被证明或反驳。在许多情况下，数学问题出现这种方式是非常困难的，进展相当缓慢。在未探索的领域中获得新的结果要容易得多。因此，大多数研究人员都小心翼翼地避免对旧的经典问题进行任何思考。
Mathematics is the name for those domains of theoretical physics that are temporarily unfashionable. The advantage of being unfashionable is that it presents the possibility of the rigorous and deep investigation of well-established mathematical models. A sleeping “physical theory” can be formulated as a chain of statements having exact mathematical meaning of mathematical conjectures. Such conjectures can then be proved or disproved. In many cases the mathematical problems arising this way are very difficult, and progress is rather slow. It is much easier to obtain a new result in an unexplored domain. Hence, most researchers carefully avoid any thinking on the old classical problems.