Quotes (archive)

Quote of the month (September 2023)
‘‘To see a World in a Grain of Sand
And a Heaven in a Wild Flower
Hold Infinity in the palm of your hand
And Eternity in an hour
’’Auguries of Innocence lines 1-4 Blake 1803

Quote of the month (August 2023)
‘‘A mathematical formula does not explain love, but it can carry a charge of love.” p. 241 Frenkel 2013

Quote of the month (July 2023)
‘‘Most of everyday life is spectacularly nonlinear; if you listen to your two favourite songs at the same time, you won't get double the pleasure. … By contrast, peanut butter and jelly are better together. They don't just add up — they synergize.” p. 279 Strogatz 2020

*As taken from a phenomenal voyage through the history of calculus written by Steven Strogatz.

Quote of the month (June 2023)
‘‘The ultimate goal would be to prove instability in our own solar system. “I wake up in the middle of the night thinking about it,” Clarke said. “I would say that would be the real dream, but it would be a nightmare, wouldn’t it? Because we’d be screwed.” Clarke 2023

Quote of the month (May 2023)
‘‘The procedure ordinarily used consists in neglecting, in the differential equations … all the terms of higher than first order … The only attempt, as far as I know, at a rigorous solution belongs to Poincaré, who, in the remarkable memoir … ‘Sur les courbes definies par les equations differentielles’ … considered questions of stability for the case of second order systems … the methods he used allow much more general applications and could still lead to many new results. This will be seen in what follows, for, in a large part of my researches, I was guided by the ideas developed in the above-mentioned memoir.’’ Lyapunov 1892*

*From the introduction of the translated edition.

Quote of the month (April 2023)
‘‘We show in this paper that in constructing a theory for the most elementary class of control problems defined on spheres, some results from Lie theory play a natural role. In particular to understand controllability, optimal control, and certain properties of stochastic equations, Lie theoretic ideas are needed. The framework considered here is probably the most natural departure from the usual linear system/vector space problems which have dominated the control systems literature.’’ Brockett 1973 p.1

Quote of the month (March 2023)
‘‘… Formel konnte ich im Verlauf einer im Sommer 1928 in Göttingen von mir gehaltenen Vorlesung durch Heranziehung gruppentheoretischer Begriffe unter dem Einfluss von Fräulein E. Noether wesentlich durchsichtiger und einfacher gestalten.’’ Hopf 1928 p.127

Quote of the month (Febr 2023)
‘‘Major open problem
I suspect that the question about the major open problem in control and systems theory is meant in the way mathematicians think of open problems, as Fermet's last theorem, the Riemann hypothesis, or the invariant subspace conjecture. If the question is meant in this sense, then it is both an inappropriate and an irrelevant one. Usually such open questions are readily answered, often after reformulation, or quickly abandoned. The art in control theory is to shape new questions, to introduce new concepts, to build new paradigms.’’ Willems 1995

*From a very inspiring paper: Survey on the state of systems and control by Blondel, Gevers and Lindquist.

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