“Since the 1950s, the key equation of quantum gravity has been called the Wheeler-DeWitt equation. Bryce DeWitt and John Wheeler wrote it down, but in all the time since then, no one had been able to solve it. We found we could solve it exactly, and in fact we found an infinite number of exact solutions.”

—  Lee Smolin

Describing work with Ted Jacobson
"Loop Quantum Gravity," The New Humanists: Science at the Edge (2003)

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Lee Smolin 52
American cosmologist 1955

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“Elegance requires that the number of defining equations be small. Five is better than ten, and one is better than five. On this score, one might facetiously say that String Theory is the ultimate epitome of elegance. With all the years that String Theory has been studied, no one has found even a single defining equation! The number at present count is zero. We know neither what the fundamental equations of the theory are nor even if it has any.”

Leonard Susskind book The Cosmic Landscape

[The Cosmic Landscape: String Theory and the Illusion of Intelligent Design, 2008, Little, Brown, https://books.google.com/books?id=RIW9E1sOyxUC&q=epitome#v=snippet&q=epitome&f=false]

“When an equation…clearly leads to two negative or imaginary roots, [Diophantus] retraces his steps and shows by how by altering the equation, he can get a new one that has rational roots. …Diophantus is a pure algebraist; and since algebra in his time did not recognize irrational, negative, and complex numbers, he rejected equations with such solutions.”

Morris Kline (1908–1992) American mathematician

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“It is better to have been, then not to have been, then to have been nothing at all." What truly is logic? Who decides reason? "It is only in the mysterious equations of love that any logic or reason can be found."-JOHN NASH JR.”

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“all the standard equations of mathematical physics can be separated and solved in Kerr geometry.”

Subrahmanyan Chandrasekhar (1910–1995) physicist

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“We have a given problem to solve. If we undertake the solution, there is, of course, always danger that we may not solve it aright; but to refuse to undertake the solution simply renders it certain that we cannot possibly solve it aright.”

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“In the beginning of 1917, two solutions of the field equations for a homogeneous isotropic universe had been found, which I… call the solutions "A" and "B."… at that time only static solutions were looked for. It was thought that the universe must be a stable structure… In one of these solutions (B) the average density was zero, it was empty; the other one (A) had a finite density…. In B, to get the real universe, we should have to put in a few galactic systems, in A we should have to condense the evenly distributed matter into galactic systems. The universe A… has an average density, but no expansion. It is therefore called the static universe. B, on the other hand… expands, and it could only parade in the garb of a static universe because there is nothing in it to show the expansion. B is therefore called the empty universe. Thus we had two approximations : the static universe with matter and without expansion, and the empty one without matter and with expansion. The actual universe… has both matter and expansion… In 1917… the actual value of the density was still entirely unknown, and the expansion had not yet been discovered.”

Willem de Sitter (1872–1934) Dutch cosmologist

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“Cellular automata are now being used to model varied physical phenomena normally modelled by wave equations, fluid dynamics, Ising models, etc. We hypothesize that there will be found a single cellular automaton rule that models all of microscopic physics; and models it exactly. We call this field DM, for digital mechanics.”

Edward Fredkin (1934) American physicist and computer scientist, a pioneer of digital physics

[An informational process based on reversible universal cellular automata, Physica D: Nonlinear Phenomena, 45, 1–3, September 1990, 254–270, https://www.sciencedirect.com/science/article/pii/016727899090186S, 10.1016/0167-2789(90)90186-S]

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“It may be in some measure due to the defects of notation in his time that Diophantos will have in his solutions no numbers whatever except rational numbers, in [the non-numbers of] which, in addition to surds and imaginary quantities, he includes negative quantities. …Such equations then as lead to surd, imaginary, or negative roots he regards as useless for his purpose: the solution is in these cases ὰδοπος, impossible. So we find him describing the equation 4=4x+20 as ᾰτοπος because it would give x=-4. Diophantos makes it throughout his object to obtain solutions in rational numbers, and we find him frequently giving, as a preliminary, conditions which must be satisfied, which are the conditions of a result rational in Diophantos' sense. In the great majority of cases when Diophantos arrives in the course of a solution at an equation which would give an irrational result he retraces his steps and finds out how his equation has arisen, and how he may by altering the previous work substitute for it another which shall give a rational result. This gives rise, in general, to a subsidiary problem the solution of which ensures a rational result for the problem itself. Though, however, Diophantos has no notation for a surd, and does not admit surd results, it is scarcely true to say that he makes no use of quadratic equations which lead to such results. Thus, for example, in v. 33 he solves such an equation so far as to be able to see to what integers the solution would approximate most nearly.”

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“If a problem has no solution, it may not be a problem, but a fact, not to be solved, but to be coped with over time.”

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As quoted by Donald Rumsfeld in "Sharon's Victory" (link is to a preview, but the quote is in the first few visible lines) https://www.wsj.com/articles/SB981508176687515426, Wall Street Journal (7 February 2001)

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