Goro Shimura quote: “The Fourier expansion of an elliptic modular form has been fruitfully utilized in various arithmetical problems as well…”

“You see, some mathematicians have clear and far-ranging. "programs". For instance, Grothendieck had such a program for algebraic geometry; now Langlands has one for representation theory, in relation to modular forms and arithmetic. I never had such a program, not even a small size one.”

Jean-Pierre Serre (1926) French mathematician

An Interview with Jean-Pierre Serre - Singapore Mathematical Society https://sms.math.nus.edu.sg/smsmedley/Vol-13-1/An%20interview%20with%20Jean-Pierre%20Serre(CT%20Chong%20&%20YK%20Leong).pdf

“A person's ability to see problems from various points of view and then determine solution steps is not a form of ordinary intelligence in general, but a form of wisdom.”

Titon Rahmawan

“Symbolical algebra adopts the rules of arithmetical algebra, but removes altogether their restrictions: thus symbolical subtraction differs from the same operation in arithmetical algebra in being possible for all relations of value of the symbols or expressions employed… all the results of arithmetical algebra which are deduced by the application of its rules, and which are general in form, though particular in value, are results likewise of symbolical algebra, where they are general in value as well as in form: thus the product of a^{m} and a^{n}, which is a^{m+n} when m and n are whole numbers, and therefore general in form though particular in value, will be their product likewise when m and n are general in value as well as in form: the series for (a+b)^{n}, determined by the principles of arithmetical algebra, when n is any whole number, if it be exhibited in a general form, without reference to a final term, may be shewn, upon the same principle, to the equivalent series for (a+b)^n, when n is general both in form and value.”

George Peacock (1791–1858) Scottish mathematician

Vol. I: Arithmetical Algebra Preface, p. vi-vii
A Treatise on Algebra (1842)

“Tony Cairo [English abstract sculptor] and I tried to collaborate at several points and it hasn't been successful. As a matter of fact, recently Tony has made sculpture that I have painted. He has to make the sculpture before I can paint it. That means that the form is taking precedence – that the material takes precedence as a form, rather than color establishing the form. It's not going to well but I'm working on it. There's something about color that is so abstract that it is difficult for it to function in conjunction with solid form... Color has properties of weight, density, transparency, and so forth. And when it also has to be compatible with things that have an actual density, a given form, it's very difficult.”

Kenneth Noland (1924–2010) American artist

Source: Color, Format and Abstract Art' (1977), pp. 99 – 105

“This monograph is about the current status of the faculty psychology program; not so much its evidential status (which I take to be, for the most part, an open question ) as what the program is and where it does, and doesn't, seem natural to try to apply it. Specifically I want to do the following things: (1) distinguish the general claim that there are psychological faculties from a particular version of that claim, which I shall call the modularity thesis; (2) enumerate some of the properties that modular cognitive systems are likely to exhibit in virtue of their modularity; and (3) consider whether it is possible to formulate any plausible hypothesis about which mental processes are likely to be the modular ones. Toward the end of the discussion, I'll also try to do something by way of (4) disentangling the faculty jmodularity issues from what I'll call the thesis of Epistemic Boundedness: the idea that there are endogenously determined constraints on the kinds of problems that human beings can solve, hence on the kinds of things that we can know.”

Jerry Fodor (1935–2017) American philosopher

Source: Modularity of Mind (1983), p. 1-2

“A liberal education forms… a single body. Those, therefore, who from tender years receive instruction in the various forms of learning, recognize the same stamp on all the arts, and an intercourse between all studies, and so they more readily comprehend them all.”

Vitruvius book De architectura

Source: De architectura (The Ten Books On Architecture) (~ 15BC), Book I, Chapter I, Sec. 12

“Adversity presents itself in various forms from mild to the intensive extreme. Therefore, each form necessitates a different approach that matches or exceeds the intensity in the moment.”

Gandolfo – (RJ Intindola)

1989

“In today's volatile world, organizational design is an everyday, ongoing activity and challenge for every executive, whether managing a global enterprise or a small work team. Globalization, worldwide competition, deregulation, and ever-new technologies drive the ongoing reassessment of the organization. The executive response has been many new forms of organizational design: virtual, learning, modular, cellular, network, alliance, or spaghetti – to name a few. New organizational forms challenge old ways of organizing for efficiency and effectiveness. Yet fundamental design principles underlie any well-functioning organization. Organizations still require a formal design.”

Richard M. Burton (1939)

Richard M. Burton, ‎Børge Obel, ‎Gerardine DeSanctis (2011). Organizational Design: A Step-by-Step Approach. p. 3

“In today's volatile world, organizational design is an everyday, ongoing activity and challenge for every executive, whether managing a global enterprise or a small work team. Globalization, worldwide competition, deregulation, and ever-new technologies drive the ongoing reassessment of the organization. The executive response has been many new forms of organizational design: virtual, learning, modular, cellular, network, alliance, or spaghetti – to name a few. New organizational forms challenge old ways of organizing for efficiency and effectiveness. Yet fundamental design principles underlie any well-functioning organization. Organizations still require a formal design.”

Gerardine DeSanctis (1954–2005) American organizational theorist

Richard M. Burton ‎Børge Obel, ‎Gerardine DeSanctis (2011). Organizational Design: A Step-by-Step Approach. p. 3

“I regard the whole of arithmetic as a necessary, or at least natural, consequence of the simplest arithmetic act, that of counting, and counting itself as nothing else than the successive creation of the infinite series of positive integers in which each individual is defined by the one immediately preceding; the simplest act is the passing from an already-formed individual to the consecutive new one to be formed. The chain of these numbers forms in itself an exceedingly useful instrument for the human mind; it presents an inexhaustible wealth of remarkable laws obtained by the introduction of the four fundamental operations of arithmetic.”

Richard Dedekind (1831–1916) German mathematician

p, 125
Stetigkeit und irrationale Zahlen (1872)

“The Fourier expansion of an elliptic modular form has been fruitfully utilized in various arithmetical problems as well as in the study of the analytic properties of the form itself. The same can be said also for the Hilbert and Siegel modular forms.”

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Goro Shimura 2

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