Solved and Unsolved Problems

[摘要] The column in this issue is devoted to fundamentals of mathematicalanalysis.Mathematical analysis (or simply analysis) is an enormous fieldand arguably one of the most central in all of mathematics, appearingin the most abstract of research as well as an extremely wide rangeof applicable areas like physics, engineering, finance, sociology andbiology, to name just a few.In mathematics, in principle, one can study two categoriesof structures and phenomena: discrete1 and continuous. Generallyspeaking, the study of the continuous lies at the heart of analysis. Theorigin of analysis as an independent field of mathematics traces backto the 17th century, with the discovery of the differential by IsaacNewton, and Gottfried Wilhelm Leibniz playing a central role in itsgenesis. We must note, though, that several important mathematical concepts of analysis were introduced even earlier. For example,the concept of an integral traces back to Eudoxus (ca. 390–337 BC)and Archimedes (ca. 287–212 BC). Some of the central generativediscoveries of analysis arose from the effort to answer fundamentalquestions in disciplines such as astronomy, optics and engineering,as well as from the effort to determine mathematical methods forthe calculation of areas, volumes, centres of gravity, etc., for boththeoretical and practical applications.