“Number theory is useful, since one can graduate with it.”

— Edmund Landau

Die Zahlentheorie ist nützlich, weil man mit ihr promovieren kann.
Foreword to Vorlesungen über Zahlentheorie (Lectures on Number Theory) (1927).

Original

Die Zahlentheorie ist nützlich, weil man mit ihr promovieren kann.

Edmund Landau, Vorlesungen über Zahlentheorie, Aus der elementaren Zahlentheorie, Nachdruck, AMS Chelsea Publisching, Providence, Rhode Island, 2004, S. 21, von Landau allerdings ausdrücklich Paul Gordan zugeschrieben
Fälschlich zugeschrieben

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Edmund Landau 7

German Jewish mathematician 1877–1938

Carl Pomerance (1944) American mathematician

"Paul Erdős and the Rise of Statistical Thinking in Elementary Number Theory" https://www.youtube.com/watch?v=5cU0g9dI1S8&t=9m40s (July, 2013) Erdős Centennial Conference, Budapest.

“By interlinking causes, by searching always for unity in the face of superficial diversity, modern scientific explanations prize depth above breadth. A deep and narrow theory can, and often does, graduate to become a deep and broad one. A broad and shallow theory never does.”

John D. Barrow (1952–2020) British scientist

Source: New Theories of Everything (2007), Ch. 1, p. 7

“P. Bernays has pointed out on several occasions that, since the consistency of a system cannot be proved using means of proof weaker than those of the system itself, it is necessary to go beyond the framework of what is, in Hilbert’s sense, finitary mathematics if one wants to prove the consistency of classical mathematics, or even that of classical number theory. Consequently, since finitary mathematics is defined as the mathematics in which evidence rests on what is intuitive, certain abstract notions are required for the proof of the consistency of number theory…. In the absence of a precise notion of what it means to be evident, either in the intuitive or in the abstract realm, we have no strict proof of Bernays’ assertion; practically speaking, however, there can be no doubt that it is correct…”

Paul Bernays (1888–1977) Swiss mathematician

Kurt Gödel (1958, CW II, p. 241) as cited in: Feferman, Solomon. " Lieber Herr Bernays!, Lieber Herr Gödel! Gödel on finitism, constructivity and Hilbert's program* http://math.stanford.edu/~feferman/papers/bernays.pdf." dialectica 62.2 (2008): 179-203.

“Imaginary numbers are not imaginary and the theory of complex numbers is no more complex than the theory of real numbers. Complex numbers are as intuitive for an electronics engineer as -100 is for the average person with an overdrawn bank account.”

Mordechai Ben-Ari (1948) Israeli computer scientist

Source: Just a Theory: Exploring the Nature of Science (2005), Chapter 3, “Words Scientists Don’t Use: At Least Not the Way You Do” (p. 56)

“Since others have explained my theory, I can no longer understand it myself.”

Albert Einstein (1879–1955) German-born physicist and founder of the theory of relativity

Source: Attributed in posthumous publications, Einstein and the Poet (1983), p. 13

“Laws never become theories! The theory of gravity includes a number of Newtonian laws. There is not one law of gravity; there are several laws included within the theory. The same goes for Relativity and even for evolution for that matter.”

Aron Ra (1962) Aron Ra is an atheist activist and the host of the Ra-Men Podcast

Patheos, Orwellian Legislative Duplicity on HB 1485 http://www.patheos.com/blogs/reasonadvocates/2017/05/05/orwellian-legislative-duplicity-hb-1485/ (May 5, 2017)

“Secularization theory is a term that was used in the fifties and sixties by a number of social scientists and historians. Basically, it had a very simple proposition. It could be stated in one sentence. Modernity inevitably produces a decline of religion.”

Peter L. Berger (1929–2017) Austrian-born American sociologist

Peter L. Berger, Gregor Thuswaldner. " A Conversation with Peter L. Berger "How My Views Have Changed http://thecresset.org/2014/Lent/Thuswaldner_L14.html," at thecresset.org, Lent 2014, Vol LXXVII, No. 3, pp 16-21

“Since you are advising high school students and undergrads, I suggest that you mention to them that they can start being independent researchers before they graduate from college. For example I came up with my b-money idea (a precursor to Bitcoin) as an undergrad, and was also already thinking about some of the questions that would eventually lead to [updateless decision theory].”

Wei Dai Cryptocurrency pioneer and computer scientist

In a discussion thread https://www.lesswrong.com/posts/x2fkoZMuMNhBashH4/academia-as-a-career-option-its-social-value-and#AZCrzTMa4yvywgahE on LessWrong, March 2014

“The process of theory construction in organizational studies is portrayed as imagination disciplined by evolutionary processes analogous to artificial selection. The quality of theory produced is predicted to vary as a function of the accuracy and detail present in the problem statement that triggers theory building, the number of and independence among the conjectures that attempt to solve the problem, and the number and diversity of selection criteria used to test the conjectures.”

Karl E. Weick (1936) Organisational psychologist

Source: 1980s-1990s, "Theory construction as disciplined imagination," 1989, p. 516

“Topology and number theory are my faves.”

Janna Levin (1967) American theoretical cosmologist

Barnard Physics Mechanics PHYS BC2001 (Autumn 2010)

“Number theory is useful, since one can graduate with it.”

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Edmund Landau 7

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