"Logic sometimes makes monsters. For half a century we have seen a mass of bizarre functions which appear to be forced to resemble as little as possible honest functions which serve some purpose. More of continuity, or less of continuity, more derivatives, and so forth. Indeed, from the point of view of logic, these strange functions are the most general; on the other hand those which one meets without searching for them, and which follow simple laws appear as a particular case which does not amount to more than a small corner. In former times when one invented a new function it was for a practical purpose; today one invents them purposely to show up defects in the reasoning of our fathers and one will deduce from them only that. If logic were the sole guide of the teacher, it would be necessary to begin with the most general functions, that is to say with the most bizarre. It is the beginner that would have to be set grappling with this teratologic museum." (Henri Poincaré, 1899)
"The orchard of science is a vast globe-encircling monster, without a map, and known to no one man; indeed, to no group of men fewer than the whole international mass of creative scientists. Within it, each observer clings to his own well-known and well-loved clump of trees. If he looks beyond, it is usually with a guilty sigh." (Isaac Asimov, "View from a Height", 1975)
"What were the needs that led me to single out a few of these monsters, calling them fractals, to add some of their close or distant kin, and then to build a geometric language around them? The original need happens to have been purely utilitarian. That links exist between usefulness and beauty is, of course, well known. What we call the beauty of a flower attracts the insects that will gather and spread its pollen. Thus the beauty of a flower is useful - even indispensable - to the survival of its species. Similarly, it was the attractiveness of the fractal images that first brought them to the attention of many colleagues and then of a wide world." (Benoît B Mandelbrot, "Fractals and an Art for the Sake of Science", Leonardo [Supplemental Issue], 1989)
"The term Moonshine [...] has a variety of meanings. It can refer to foolish or naive ideas, but also to the illicit distillation of spirits [...] It gave an impression of dabbling in mysterious matters that might be better left alone, but also had the useful connotation of something shining in reflected light. The true source of light is probably yet to be found, but there were further strange connections to come later [...] The Monster's connections with number theory - the Moonshine connections - had suggested it was a more beautiful and important group of symmetries than first realized. [...] The Moonshine connections between the Monster and number theory have now been placed within a larger theory, but we have yet to grasp the significance of these deep mathematical links with fundamental physics. We have found the Monster, but it remains an enigma. Understanding its full nature is likely to shed light on the very fabric of the universe." (Mark Ronan, "Symmetry and the Monster: One of the greatest quests of mathematics", 2006)
"The Moonshine mystery itself is still unresolved, despite Borcherd's proof! [...] there are facts about the Monster and Moonshine that we don't understand. [...] The method leading to its discovery, brilliant though it was, gave no clue to the Monster's remarkable properties." (Mark Ronan, "Symmetry and the Monster: One of the greatest quests of mathematics", 2006)
"To the average layperson, mathematics is a mass of abstruse formulae and bizarre technical terms (e.g., perverse sheaves, the monster group, barreled spaces, inaccessible cardinals), usually discussed by academics in white coats in front of a blackboard covered with peculiar symbols. The distinction between mathematics and physics is blurred and that between pure and applied mathematics is unknown. But to the professional, these are three different worlds, different sets of colleagues, with different goals, different standards, and different customs." (David Mumford, ["The Best Writing of Mathematics: 2012"] 2012)
"Infinity is a Loch Ness Monster, capturing the imagination with its awe-inspiring size but elusive nature. Infinity is a dream, a vast fantasy world of endless time and space. Infinity is a dark forest with unexpected creatures, tangled thickets and sudden rays of light breaking through. Infinity is a loop that springs open to reveal an endless spiral." (Eugenia Cheng, "Beyond Infinity: An Expedition to the Outer Limits of Mathematics", 2017)
"The rigid electron is in my view a monster in relation to Maxwell's equations, whose innermost harmony is the principle of relativity." (Hermann Minkowski)
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