737 KB0 KB200820262024Hladnik, Milanštevilka:1letnik:71str. 6-27ISSN:0473-7466COBISSID_HOST:208271107URN:URN:NBN:SI:doc-ERWPSMAWslDruštvo matematikov, fizikov in astronomov SlovenijeObzornik za matematiko in fizikoFuchsovi sistemiHilbertov 21. problemlinearne diferencialne enačbematematikaRiemannov problemsingularnostiProfesor Plemelj in reševanje Hilbertovega 21. problema|It may be less known to the reader that the process of solving Hilbert’s twentyfirst problem did not end in 1908 with the publication of Plemelj’s solution which was considered definitive for almost seventy-five years. In addition to the basic mathematical explanation and Plemelj’s approach to the problem, the article, which avoids complex proofs, briefly describes further research, which at the end of the 20th century led to a surprising turn with the discovery of counterexamples and different conclusions. In the opinion of the author of this paper, the new findings do not diminish the importance of Plemelj’s work and his pioneering role in solving the problemBralcu je morda manj znano, da se reševanje Hilbertovega enaindvajsetega problema ni končalo leta 1908 z objavo Plemljeve rešitve, ki je skoraj petinsedemdeset let obveljala za dokončno. Poleg osnovne matematične razlage in Plemljevega pristopa k problemu je v članku, ki se izogne zapletenim dokazom, na kratko opisano nadaljnje raziskovanje, ki je ob koncu 20. stoletja privedlo do presenetljivega preobrata z odkritjem protiprimerov in drugačnih dognanj. Po mnenju avtorja tega prispevka nova spoznanja ne zmanjšujejo pomena Plemljeve pionirske vloge pri reševanju problemaTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaDruštvo matematikov, fizikov in astronomov