Academics From The United States

"[BitCoin]'s the greatest scam of modern times. ... the poor, the average mom-and-pop, the truck driver and the barber, who put their life savings into this, are going to lose their money, and be told to keep holding on, trust us, the value will go up. And they're gonna go bankrupt. They're gonna lose their life savings. ... This is what happened with the dot-com boom, the grandma and grandpa lost their life savings. History is repeating itself. ... We have these scamsters, basically, hyping the heck out of it, while all it's being used for is illegal money laundering. ... It's simply gonna implode before you know it. And regular people who trust you are gonna lose their shirts. ... Would you put your life savings into digital currency? You lose a password and you've lost everything. ... They know it's gonna crash and burn. ... it crashes and it goes to zero, and people lose their life savings. Don't do it. Get out of it, rather than losing everything you have. Yes, the price might increase, but more likely than not it's gonna be zero before you know it."

"Apple is repeating the mistakes it made in China. It is relying on its brand recognition to build a market and failing to understand the needs of its customers. By marketing inferior products, it may also be insulting Indian consumers."

"The numbers make it clear that the future of [Apple] is no longer in its consumer products. The fix? Apple should release a version of iOS for non-Apple devices. This suggestion will seem like heresy to the brand's loyalists, but it may be necessary for the success of the company. ... Without expanding its operating system, the future looks bleak for Apple."

"The last big thing [Apple] did was nine years ago with the iPhone. And since then they made it bigger with the iPad; they made it smaller with the Watch. All they keep doing is playing with the size. ... [Apple] needs an Elon Musk or a Zuckerberg running it. ... [iPhone] is a ten-year-old device. They've done everything they can with it. And Samsung, and even BlackBerry, have similar or even better ratings than the iPhone does. That's the biggest slap in the face you could possibly have: BlackBerry almost ranking the same as an iPhone? Time to move on."

"Steve Jobs was a true visionary who refused to listen to customers — believing that he knew better than they did about what they needed. He ruled with an iron fist and did not tolerate dissent of any type. ... Apple may have peaked. ... its last major innovation — the iPhone — was released in June 2007."

"By picking this particular fight [with the FBI], Apple is doing the technology industry a big disservice. ... Apple will very likely lose this case in the courts and suffer a public relations disaster."

"With the technology advances that are presently on the horizon, not only low-skilled jobs are at risk; so are the jobs of knowledge workers. Too much is happening too fast. It will shake up entire industries and eliminate professions. Some new jobs will surely be created, but they will be few. And we won’t be able to retrain the people who lose their jobs, because, as I said to Andreessen, you can train an Andreessen to drive a cab, but you can’t retrain a laid-off cab driver to become an Andreessen. The jobs that will be created will require very specialized skills and higher levels of education — which most people don’t have."

"Enter to grow in wisdom. / Depart to serve better thy country and thy kind."

"You can ask the question about these ancient topics, such as s and ... and ask, are these good problems... I'd like to give a small amount of evidence... that they are... [S]tudying them helped us develop all of elementary number theory and from elementary number theory we developed the rest of number theory, and also you can argue that from elementary number theory came algebra.."

"Maybe so, but something is going on with the primes."

"Eliot revolutionized the Harvard curriculum, transforming a moribund academic system for training clergy into a modern research institution at the forefront of American and international scholarship."

"A university teaches. What does it teach? It must obviously teach all the languages in which the great literatures which have been preserved were written — Hebrew, Arabic, Sanskrit, Greek, Latin, French, Italian, German, Scandinavian, and English."

"The West never came close to proletarian revolution. The Left likes to believe that it did. They like to argue that 'Franklin Roosevelt saved capitalism from itself'. This is another way of saying that John Maynard Keynes saved capitalism from itself. Both arguments are incorrect. Roosevelt and Keynes met only once. Roosevelt correctly assessed Keynes as a mathematician, not an economist. This was true. Keynes got his degree in mathematics, not economics. Roosevelt was the source of what we call Keynesianism, 1933-36, not Keynes, whose General Theory appeared in 1936. But scholars like to believe that academic arguments shape the world. They don't. They conform what has already begun to take root in the thinking and practices of the general public. When men decided that "thou shalt not steal" means "thou shalt not steal, except by majority vote," the Keynesian worldview was born. This view is dominant today. Marxism is dead. So is . To win this battle, we must persuade men that "" means this: it is immoral to steal, with or without majority vote. This has nothing to do with the mode of production."

"The long-term goal of Christians in politics should be to gain exclusive control over the franchise. Those who refuse to submit publicly to the eternal sanctions of God by submitting to His Church's public marks of the covenant–baptism and holy communion–must be denied citizenship, just as they were in ancient Israel."

"Every one knows that the fine phrase "God geometrizes" is attributed to Plato, but few know where this famous passage is found, or the exact words in which it was first expressed. Those who, like the author, have spent hours and even days in the search of the exact statements, or the exact references, of similar famous passages, will not question the timeliness and usefulness of a book whose distinct purpose it is to bring together into a single volume exact quotations, with their exact references, bearing on one of the most time-honored, and even today the most active and most fruitful of all the sciences, the queen-mother of all the sciences, that is, mathematics."

"Literametrics' may become to philology, what 'Biometrics' has already become to the biological sciences."

"Within mathematics itself, Voevodsky's proposal, if adopted, will create a new paradigm. In his “fairy tale” and some of his other papers, Langlands made deft use of categories and even 2-categories, but number theory is only superficially categorical, and so is the Langlands program. In the event that Univalent Foundations could shed light on a guiding problem in number theory — the Riemann hypothesis or the Birch Swinnerton-Dyer conjecture, which is not so far removed from Voevodsky's motives — then we could easily see Grothendieck's program absorbing the Langlands program within Voevodsky's new paradigm."

"Moreover, according to Alexander, the “troubled mathematical martyr,” exemplified not only by Galois but also by Abel, János Bolyai, Riemann, Cantor, Gödel, Turing, John Nash, Grothendieck, Perelman, and even, in a certain sense, Cauchy, remains to this day the dominant image of the “ideal mathematician,” long after the romantic paradigm was exhausted in the arts."

"Just as Weil's conjectures were about counting solutions to equations in a situation where the number of solutions is known to be finite, the BSD conjecture concerns the simplest class of polynomial equations—elliptic curves—for which there is no simple way to decide whether the number of solutions is finite or infinite."

"Langlands' life has been by no means as extravagant as Grothendieck's, but his romanticism is evident to anyone who reads his prose; the audacity of his program, one of the most elaborate syntheses of conjectures and theorems ever undertaken, has few equivalents in any field of scholarship."

"Langlands and Grothendieck are both (at least) Giants by any measure, and both were consciously successors of Galois."

"It is commonly agreed that Keynes came up with the idea that public works are the best way to help the economy during a recession. As a result, Keynesian economists seem to have developed a blind faith in the government in general, and in the system of public works in particular. I do not share the same faith in the government. I do not share the same faith in public works.And this may help explain why."

"The last chapter modeled technological progress as an increase in the number of types of products, N. In this chapter, we allow for improvements in the quality or productivity of each type. This approach has come to be known as the Schumpeterian approach to endogenous growth. We can think of increases in N as basic innovations that amount to dramatically new kinds of goods or methods of production. In contrast, increases in the quality of the existing products involve a continuing series of improvements and refinements of goods and techniques."

"Part of the downfall came early and on theoretical grounds, with the realization that real-world information lags for aggregate variables like the price level and money supply were much too short to rationalize the persistent multiyear deviations from equilibrium that seemed to characterize business cycles in most industrialized countries. The second dubious assumption, continuous market clearing, was viewed more critically once it was recognized that it was not an inextricable concomitant of rational expectations, especially when Stanley Fischer (1977) and Edmund Phelps and John Taylor (1977) showed that rational expectations could be embedded in a model containing real-world institutional features like multiperiod wage and price contracts to generate nonmarket-clearing behavior. Once Fischer and Phelps-Taylor had shown that rational expectations by itself was a necessary but not a sufficient condition to validate new-classical policy conclusions, the race was on to develop the new-Keynesian theory based on rational expectations and one or another institutional impediment to continuous market clearing."

"I still think Keynesian economics is extremely important, and if anybody didn’t think so, this crisis should have made them rethink."

"Currency competition and free banking might increase the efficiency of the financial system, and bring some small triangle welfare gains. But the key question is whether their adoption would improve macroeconomic performance. Even though Salin argues (p. 281) that ‘the best system is that which produces the least inflation’, fluctuations in output are also expensive. Hayek states that the adoption of his proposal would end recessions. There is absolutely no reason to believe that. Nineteenth century history is evidence that free banking and currency issue, in the wrong legal and regulatory framework, can produce rather than reduce instability. The proponents of free banking and currency issue in this volume do not go much beyond a general belief in competition in justifying their views; they have certainly not explored the necessary legal and regulatory environment in any detail."

"As is well known, when one endeavors to pass from one-dimensional birational geometry to the higher dimensions, the difficulties multiply enormously. Many results do not extend at all, or if they do, they are apt to assume a far more complicated aspect or else to demand most difficult proofs."

"It will be remembered that the positions on a Riemann surface are treated by Hensel, Landsberg, and Jung as arithmetical divisors. At bottom the associated symbolical operations are in no sense different from those that occur in connection with the Noether-Brill theory of groups of points, elements being merely multiplied instead of added."

"I would read Lefschetz's book on analysis situs and algebraic geometry - the book about which Hodge used to say that all the important statements were true and all the others false."

"Lefschetz made a brief trip to Rome, and I asked Severi what he thought of Lefschetz's work. È bravo,' Severi told me, meaning more or less 'he is talented.' The word bravo,' as far as I can tell, has no equivalent in other languages. 'He is no Poincaré,' Severi added. Poincaré was an eagle, un'aquila—and at this, he raised his hand high. Lefschetz was a sparrow, un passero,' and he lowered his hand halfway. But Lefschetz was talented, è bravo però, è bravo."

"Solomon Lefschetz had a reputation for “kibitzing” during the lectures of colleagues; at perhaps the first public talk on computing that von Neumann ever gave, von Neumann said, halfway in, “Well, so far so good” — and Lefschetz added, “and so trivial.” (The students passed down an impious faculty song about their elders; the verse for Lefschetz ended, “When he’s at last beneath the sod, he’ll then begin to heckle God.”)"

"It is quite obvious that he was strongly influenced by the similar problems in algebraic geometry, and in particular by the theory of correspondences, studied since the middle of the nineteenth century by Chasles and the school of “enumerative geometry” (de Jonquières, Zeuthen, Schubert), then by Hurwitz in the theory of Riemann surfaces, and which had been thoroughly investigated by Severi in the first years of the twentieth century; this influence explains the rather unusual frame within which Lefschetz developed his theory."

"In its early phase (Abel, Riemann, Weierstrass), algebraic geometry was just a chapter in analytic function theory. ... A new current appeared however (1870) under the powerful influence of Max Noether who really put "geometry" and more "birational geometry" into algebraic geometry. In the classical mémoire of Brill-Noether (Math. Ann., 1874), the foundations of "geometry on an algebraic curve" were laid down centered upon the study of linear series cut out by linear systems of curves upon a fixed curve ƒ{x, y) = 0. This produced birational invariance (for example of the genus p) by essentially algebraic methods."

"It was my lot to plant the harpoon of algebraic topology into the body of the whale of algebraic geometry."

"The numerical relations existing between ordinary or so-called Plückerian singularities of a plane curve were determined as early as 1834 by P, but the inverse question has been left almost untouched. It may be stated thus: To show the existence of a curve having assigned Plückerian characters; and is equivalent to the determination of the maximum of cusps κM that a curve of order m and genus p may have. V ... has solved the question for rational curves."

"In the development of the theory of algebraic functions of one variable the introduction by Riemann of the surfaces that bear his name has played a well-known part. Owing to the partial failure of space intuition with the increase in dimensionality, the introduction of similar ideas into the field of algebraic functions of several variables has been of necessity slow. It was first done by Emile Picard, whose work along this line will remain a classic. A little later came the capital writings of Poincaré in which he laid down the foundations of Analysis Situs, thus providing the needed tools to obviate the failure of space intuition."

"Students of the human mind have long noted its ability to mimic internally the positive notions and transformations of objects in the external world. In the middle of the eighteenth century, the British empiricist David Hume wrote that to "join incongruous shapes and appearances costs the imagination no more trouble than to conceive the most natural and familiar objects" and that "this creative power of the mind amounts to no more than the faculty of compounding, transposing, augmenting, or diminishing the materials afforded us by the senses and experience.""

"Finke et al. (1992) proposed a cognitive model of creative thinking called geneplore, a name that emphasizes the importance of generative and exploratory phases of the creative process. In the generative phase, one uses processes such as retrieval, analogical transfer, or mental transformation to construct representations of ideas that may take various forms such as visual patterns, verbal combinations, or mental models. These initial ideas, referred to as preinventive forms, ideally have properties such as novelty, meaningfulness, and emergent qualities. Exploratory processes can then be used to develop the initially generated ideas for specific purposes."

"Restricting the ways in which creative cognition are interpreted encourages creative exploration and discovery and further reduces the likelihood that a person will fall back on conventional lines of thought."

"The image discoveries which then ’emerge’ resemble the way perceptual discoveries can follow the active exploration and manipulation of physical objects."

"Perceptual interpretive processes are applied to mental images in much the same way that they are applied to actual physical objects. In this sense, imagined objects can be "interpreted" much like physical objects."

"Surrogate percept, allowing people to detect some pattern or property in a remembered scene that they did not encode explicitly when they saw the scene initially."

"R. N. Shepard [1978] has argued that a number of highly original and significant creations of the human mind have been produced by a mode of thinking which was essentially nonverbal, involving internal representations which could best be described as images of a largely spatial, and often visual character. Shepard provides an impressive list of creative scholars whose most outstanding achievements have been the result of highly visual thinking: Einstein, James Clerk Maxwell, Michael Faraday, Hermann von Helmholtz, Francis Galton, and Friedrich A. Kekule are on the list as is the mathematician ."

"We generalize from one situation to another not because we cannot tell the difference between the two situations but because we judge that they are likely to belong to a set of situations having the same consequence."

"I suggest that the psychophysical function that maps physical parameter space into a species' psychological space has been shaped over evolutionary history so that consequential regions for that species, although variously shaped, are not consistently elongated or flattened in particular directions."

"A psychological space is established for any set of stimuli by determining metric distances between the stimuli such that the probability that a response learned to any stimulus will generalize to any other is an invariant monotonic function of the distance between them. To a good approximation, this probability of generalization (i) decays exponentially with this distance, and (ii) does so in accordance with one of two metrics, depending on the relation between the dimensions along which the stimuli vary. These empirical regularities are mathematically derivable from universal principles of natural kinds and probabilistic geometry that may, through evolutionary internalization, tend to govern the behaviors of all sentient organisms."

"Most studies employing three-dimensional objects as stimuli have used simultaneous presentation whereas most studies employing two-dimensional objects have used comparison of a single visual stimulus with a memory presentation. We suspect that it is this procedural difference rather than the difference in dimensionality that is the principal determiner of rate of mental rotation."

"Nor do such theories provide a ready account for the equivalence of the slopes of the reaction-time functions for the picture-plane and depth pairs. For, in order to explain the dependence of reaction time on angular difference, we must suppose that the features that are being compared are the features of the two-dimensional drawings, which differ more and more with angular departure, and not the features of the three-dimensional objects, which are the same regardless of orientation."

"The subject detects the presence and interrelationships of the basic components of one of the two-dimensional drawings - particularly, the variously oriented straight lines, the several types of vertices by which they are connected and, presumably, something of the structural relationships among these components within the two-dimensional pattern. Then, on the basis of some higher-level processing of these extracted features and their interrelationships, an internal representation, code, or verbal description is generated for each picture separately that captures the intrinsic structure of the three-dimensional object in a form that is independent of the particular orientation in which that object happens to be displayed."

"The universality, invariance, and elegance of principles governing the universe may be reflected in principles of the minds that have evolved in that universe - provided that the mental principles are formulated with respect to the abstract spaces appropriate for the representation of biologically significant objects and their properties. (1) Positions and motions of objects conserve their shapes in the geometrically fullest and simplest way when represented as points and connecting geodesic paths in the six-dimensional manifold jointly determined by the Euclidean group of three· dimensional space and the symmetry group of each object. (2) Colors of objects attain constancy when represented as points in a three-dimensional vector space in which each variation in natural illumination is cancelled by application of its inverse from the three-dimensional linear group of terrestrial transformations of the invariant solar source. (3) Kinds of objects support optimal generalization and categorization when represented, in an evolutionarily shaped space of possible objects, as connected regions with associated weights determined by Bayesian revision of maximum entropy priors"