"Theorems are fun especially when you are the prover, but then the pleasure fades. What keeps us going are the unsolved problems." (Carl Pomerance, 2000)"
"The existence of the tipping point means it is theoretically possible to completely eradicate a disease. Eradication does not require a perfect vaccine and universal immunization but only the weaker condition that the reproduction rate of the disease fall and remain below one so that new cases arise at a lower rate than old cases are resolved." (John D Sterman, "Business Dynamics: Systems thinking and modeling for a complex world. ", 2000)
"Theorems are fun especially when you are the prover, but then the pleasure fades. What keeps us going are the unsolved problems." (Carl Pomerance, MAA, 2000)
"And although mathematical ideas and thought are constantly evolving, you will also see that the most basic fundamental problems never go away. Many of these problems go back to the ancient Greeks, and maybe even to ancient Sumer, although we may never know for sure. The fundamental philosophical questions like the continuous versus the discrete or the limits of knowledge are never definitively solved. Each generation formulates its own answer, strong personalities briefly impose their views, but the feeling of satisfaction is always temporary, and then the process continues, it continues forever." (Gregory Chaitin, "Meta Math: The Quest for Omega", 2005)
"A model does not always predict all the features of the data. Nature has no privileged tendency to present me with solvable challenges." (Eliezer S Yudkowsky, "A Technical Explanation of Technical Explanation", 2005)
"Solvable Lie algebras are close to both upper triangular matrices and commutative Lie algebras. In contrast to this, semisimple Lie algebras are as far as possible from being commutative. By Levi’s decomposition theorem, any Lie algebra is built out of a solvable and a semisimple one. The nontrivial prototype of a solvable Lie algebra is the Heisenberg algebra. [3](Eberhard Zeidler, "Quantum Field Theory I: Gauge Theory", 2006)
"Knowing a solution is at hand is a huge advantage; it’s like not having a 'none of the above' option. Anyone with reasonable competence and adequate resources can solve a puzzle when it is presented as something to be solved. We can skip the subtle evaluations and move directly to plugging in possible solutions until we hit upon a promising one. Uncertainty is far more challenging." (Garry Kasparov, "How Life Imitates Chess", 2007)
"Social ecology is based on the conviction that nearly all of our present ecological problems originate in deep-seated social problems. It follows, from this view, that these ecological problems cannot be understood, let alone solved, without a careful understanding of our existing society and the irrationalities that dominate it. To make this point more concrete: economic, ethnic, cultural, and gender conflicts, among many others, lie at the core of the most serious ecological dislocations we face today - apart, to be sure, from those that are produced by natural catastrophes." (Murray Bookchin, "Social Ecology and Communalism", 2007)
"When in the sciences or techniques one states that a certain problem is unsolvable, a rigorous demonstration of such unsolvability is required. And when a scientist submits an article to publication, the least that its referees demand is that it be intelligible. Why? Because rational beings long for understanding and because only clear statements are susceptible to be put to examination to verify whether they are true or false. In the Humanities it is the same, or it should be, but it is not always so." (Mario Bunge, "Xenius, Platón y Manolito", La Nación, 2008)
"An algorithm refers to a successive and finite procedure by which it is possible to solve a certain problem. Algorithms are the operational base for most computer programs. They consist of a series of instructions that, thanks to programmers’ prior knowledge about the essential characteristics of a problem that must be solved, allow a step-by-step path to the solution." (Diego Rasskin-Gutman, "Chess Metaphors: Artificial Intelligence and the Human Mind", 2009)
"Chess also offers a modality that includes an exercise of totally free creation - compositions. These artificial positions are created for didactic reasons to illustrate a certain subject or to propose a problem that has to be solved following a series of indications" (Diego Rasskin-Gutman, "Chess Metaphors: Artificial Intelligence and the Human Mind", 2009)
"Chess, as a game of zero sum and total information is, theoretically, a game that can be solved. The problem is the immensity of the search tree: the total number of positions surpasses the number of atoms in our galaxy. When there are few pieces on the board, the search space is greatly reduced, and the problem becomes trivial for computers’ calculation capacity." (Diego Rasskin-Gutman, "Chess Metaphors: Artificial Intelligence and the Human Mind", 2009)
"Mental acuity of any kind comes from solving problems yourself, not from being told how to solve them." (Paul Lockhart,"A Mathematician's Lament", 2009)
"What literally defines social ecology as ‘social’ is its recognition of the often overlooked fact that nearly all our present ecological problems arise from deep-seated social problems. Conversely, present ecological problems cannot be clearly understood, much less resolved, without resolutely dealing with problems within society." (Murray Bookchin, "What is Social Ecology", 2009)
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