1. INTRODUCTION. For geometers, Hilbert’s influential work on the foundations of geometry is important. For analysts, Hilbert’s theory of integral equations is just as important. But the address “Mathematische Probleme ” [37] that David Hilbert (1862– 1943) delivered at the second International Congress of Mathematicians (ICM) in Paris has tremendous importance for all mathematicians. Moreover, a substantial part of

As the nineteenth century drew to its close, David Hilbert (1862–1943), then regarded as a leading mathematician of his generation, presented a list of twentythree problems, which he urged upon the attention of his contemporaries. They have entered the folklore of professional mathematicians; even a partial solution of one of them has given its author(s) much prestige. Two compendia have reviewed progress to the date of their publication: [1] in the former Soviet Union, where study of the problems has been a speciality, and [4] in the United States. In addition, individual problems have been examined in various other books and special articles. Now, at the centenary of the lecture, it is opportune to compare the range of Hilbert’s problems against the panoply then evident in mathematics. Circumstances and Publications First, some details of the preparation and publication of the list are appropriate. The motivation was the Second International Congress of Mathematicians, held in Paris early in August 1900, which Hilbert was invited to address. He seems to have thought of the topic by December 1899, for Ivor Grattan-Guinness is professor of the history of mathematics

The coming century is surely the century of data. A combination of blind faith and serious purpose makes our society invest massively in the collection and processing of data of all kinds, on scales unimaginable until recently. Hyperspectral Imagery, Internet Portals, Financial tick-by-tick data, and DNA Microarrays are just a few of the betterknown sources, feeding data in torrential streams into scientific and business databases worldwide. In traditional statistical data analysis, we think of observations of instances of particular phenomena (e.g. instance ↔ human being), these observations being a vector of values we measured on several variables (e.g. blood pressure, weight, height,...). In traditional statistical methodology, we assumed many observations and a few, wellchosen variables. The trend today is towards more observations but even more so, to radically larger numbers of variables – voracious, automatic, systematic collection of hyper-informative detail about each observed instance. We are seeing examples where the observations gathered on individual instances are curves, or spectra, or images, or