Quotes (archive)

Quote of the month (Jan 2023)

‘‘Wrong results are the rhythms of human research. We still beat the creativity of machines by a safe margin, thanks to our ability to produce wrong results.’’ Sepulchre 2022

Quote of the month (Dec 2022)
‘‘The ultimate proof of our understanding of natural or technological systems is reflected in our ability to control them.’’ Liu, Slotine and Barabási 2011

*As heard during this inControl podcast.

Quote of the month (Nov 2022)
‘‘Think geometrically, act computationally.’’ Krener 2022

*This was part of a phenomenal series on the history of control.

Quote of the month (Oct 2022)
‘‘All current indications point toward the conclusion that seeking a completely general theory of nonlinear systems is somewhat akin to the search for the Holy Grail: a relatively harmless activity full of many pleasant surprises and mild disappointments, but ultimately unrewarding. A far more profitable path to follow is to concentrate upon special classes of nonlinear problems, usually motivated by applications, and to use the structure inherent in these classes as a guide to useful (i.e., applicable) results.’’ Casti 1982

Quote of the month (Sept 2022)
‘‘This was the key step in my study of these metrics but this result was not found in quite such a simply way. At first, I stumbled around using individual component equations rather than differential forms to look for a useful coordinate system. It was only after I had found this that I realized that using differential forms from the start would have short-circuited several days analysis.’’ Kerr 2007

Quote of the month (Aug 2022)
‘‘Most applied mathematicians agree that determinants should rarely be used in serious numeric calculations.’’ p. 320 Axler 2015

Quote of the month (July 2022)
‘‘Beautiful as the considerations of the previous sections [on the finite-dimensional Morse inequalities] are, it is clear that to Morse they were mainly “results along the way” to his real goal—a corresponding theory in the calculus of variations.’’ p. 926 Bott 1980

Quote of the month (June 2022)
‘‘We need to focus far more energy on understanding and explaining the basic mental infrastructure of mathematics - with consequently less energy on the most recent results. This entails developing mathematical language that is effective for the radical purpose of conveying ideas to people who don’t already know them.’’ p. 8 Thurston 1994

Quote of the month (May 2022)
‘‘La voie la plus courte et la meilleure entre deux vérités du domaine réel passe souvent par le domaine imaginaire.’’ Hadamard 1945

Quote of the month (Apr 2022)
‘‘La topologie est précisément la discipline mathématique qui permet la passage du local au global.’’ Thom 1971

Quote of the month (Mar 2022)
‘‘… if such rough equations are to be of use it is necessary to study them in rough terms …’’ Conley 1978 p. 1

Quote of the month (Feb 2022)
‘‘The Committee which was set up in Rome for the unification of vector notation did not have the slightest success, which was only to have been expected.’’ Klein 1908 p. 63

Quote of the month (Jan 2022)
‘‘It is a curious fact that while the subject of differential equations is often taught in the driest ’'cookbook’’ way and loathed by students as the dullest drudgery, at the same time those who have penetrated to its inner core are frequently moved to rhapsodies of praise.’’
Hirsch 1984 p. 22