Casti (1996), John L, Five Golden Rules: Great Theories of 20th-Century Mathematics - and Why They Matter, John Wiley and Sons 1996 Preface: '[this book] is intended to tell the general reader about mathematics by showcasing five of the finest achievements of the mathematician's art in this [20th] century.' p ix. Treats the Minimax theorem (game theory), the Brouwer Fixed-Point theorem (topology), Morse's theorem (singularity theory), the Halting theorem (theory of computation) and the Simplex method (optimisation theory). 
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von Neumann (2018), John, and Nicholas A. Wheeler (editor), Robert T Beyer (translator), The Mathematical Foundations of Quantum Mechanics, Princeton University Press 2018 ' Quantum mechanics was still in its infancy in 1932 when the young John von Neumann, who would go on to become one of the greatest mathematicians of the twentieth century, published Mathematical Foundations of Quantum Mechanics--a revolutionary book that for the first time provided a rigorous mathematical framework for the new science. Robert Beyer's 1955 English translation, which von Neumann reviewed and approved, is cited more frequently today than ever before. But its many treasures and insights were too often obscured by the limitations of the way the text and equations were set on the page. In this new edition of this classic work, mathematical physicist Nicholas Wheeler has completely reset the book in TeX, making the text and equations far easier to read. He has also corrected a handful of typographic errors, revised some sentences for clarity and readability, provided an index for the first time, and added prefatory remarks drawn from the writings of Léon Van Hove and Freeman Dyson. The result brings new life to an essential work in theoretical physics and mathematics.' 
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Alexis Szejnoga (2013), Persian Perspective on Prima Philosophia: The influence of Avicenns's interpetation of Aristotelian ontology in the De ente et essentia of Saint Thomas Aquinas, Chapter 1: The wider context of the De ente et essentia In this chapter, we will take a look at the context in which the De ente et essentia was written. The first part will focus on historical-philosophical aspects, treating topics like the renewed interest in Aristotelian philosophy, the attention being paid to translations of Arabian works on theology and philosophy, notably of Avicenna and Averroës, and to two philosophicalt reatises, the Fons vitae and the Liber de causis, which were at the time wrongly attributed to Aristotle and an unknown Christian theologian. In addition, we will look at some bibliographical details of the De ente et essentia: an approximation of the period in which it was written, the rationale behind its structure, a summary of its intent and scope, and its reception among medieval and modern philosophy.' back

Allegory of the cave - Wikipedia, Allegory of the cave - Wikipedia, the free encyclopedia, ' Plato's allegory of the cave is an allegory presented by the Greek philosopher Plato in his work Republic (514a–520a, Book VII) to compare "the effect of education (παιδεία) and the lack of it on our nature". It is written as a dialogue between Plato's brother Glaucon and his mentor Socrates and is narrated by the latter. The allegory is presented after the analogy of the Sun (508b–509c) and the analogy of the divided line (509d–511e).' back

Apophatic theology - Wikipedia, Apophatic theology - Wikipedia, the free encyclopedia, 'Apophatic theology (from Greek ἀπόφασις from ἀπόφημι - apophēmi, "to deny")—also known as negative theology or via negativa (Latin for "negative way")—is a theology that attempts to describe God, the Divine Good, by negation, to speak only in terms of what may not be said about the perfect goodness that is God. It stands in contrast with cataphatic theology.' back

Aquinas, Summa I, 15, 1, Are there ideas in God?, ' . . . in other agents (the form of the thing to be made pre-exists) according to intelligible being, as in those that act by the intellect; and thus the likeness of a house pre-exists in the mind of the builder. And this may be called the idea of the house, since the builder intends to build his house like to the form conceived in his mind. As then the world was not made by chance, but by God acting by His intellect, as will appear later, there must exist in the divine mind a form to the likeness of which the world was made. And in this the notion of an idea consists.' back

Aquinas, Summa I, 25, 3, Is God omnipotent?, '. . . God is called omnipotent because He can do all things that are possible absolutely; which is the second way of saying a thing is possible. For a thing is said to be possible or impossible absolutely, according to the relation in which the very terms stand to one another, possible if the predicate is not incompatible with the subject, as that Socrates sits; and absolutely impossible when the predicate is altogether incompatible with the subject, as, for instance, that a man is a donkey.' back

Aquinas, Summa, I, 3, 4, Are essence and existence the same in God?, ' I answer that, God is not only His own essence, as shown in the preceding article, but also His own existence. This may be shown in several ways. First, whatever a thing has besides its essence must be caused either by the constituent principles of that essence (like a property that necessarily accompanies the species — as the faculty of laughing is proper to a man — and is caused by the constituent principles of the species), or by some exterior agent — as heat is caused in water by fire. Therefore, if the existence of a thing differs from its essence, this existence must be caused either by some exterior agent or by its essential principles. Now it is impossible for a thing's existence to be caused by its essential constituent principles, for nothing can be the sufficient cause of its own existence, if its existence is caused. Therefore that thing, whose existence differs from its essence, must have its existence caused by another. But this cannot be true of God; because we call God the first efficient cause. Therefore it is impossible that in God His existence should differ from His essence.' back

Brouwer fixed point theorem - Wikipedia, Brouwer fixed point theorem - Wikipedia, the free encyclopedia, 'Among hundreds of fixed-point theorems] Brouwer's is particularly well known, due in part to its use across numerous fields of mathematics. In its original field, this result is one of the key theorems characterizing the topology of Euclidean spaces, along with the Jordan curve theorem, the hairy ball theorem, the invariance of dimension and the Borsuk–Ulam theorem. This gives it a place among the fundamental theorems of topology.' back

Charles Darwin (1869), The Variation of Animals and Plants under Domestication, ' 'In scientific investigations . . . it is permitted to invent any hypothesis, and if it explains various large and independent classes of facts, it rises to the rank of a well grounded theory.' back

Claude Shannon (1949), Communication in the Presence of Noise, 'A method is developed for representing any communication system geometrically. Messages and the corresponding signals are points in two “function spaces,” and the modulation process is a mapping of one space into the other. Using this representation, a number of results in communication theory are deduced concerning expansion and compression of bandwidth and the threshold effect. Formulas are found for the maximum rate of transmission of binary digits over a system when the signal is perturbed by various types of noise. Some of the properties of “ideal” systems which transmit at this maximum rate are discussed. The equivalent number of binary digits per second for certain information sources is calculated.' [C. E. Shannon , “Communication in the presence of noise,” Proc. IRE, vol. 37, pp. 10–21, Jan. 1949.] back

Complex number - Wikipedia, Complex number - Wikipedia, the free encyclopedia, 'A complex number is a number that can be expressed in the form a + bi, where a. and b are real numbers and is the imaginary unit, which satisfies the equation i² = −1. In this expression, a is the real part and b is the imaginary part of the complex number. Complex numbers extend the concept of the one-dimensional number line to the two-dimensional complex plane (also called Argand plane) by using the horizontal axis for the real part and the vertical axis for the imaginary part.' back

Eigenvalues and eigenvectors - Wikipedia, Eigenvalues and eigenvectors - Wikipedia, the free encyclopedia, ' In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted by λ, is the factor by which the eigenvector is scaled. Geometrically, an eigenvector, corresponding to a real nonzero eigenvalue, points in a direction in which it is stretched by the transformation and the eigenvalue is the factor by which it is stretched. If the eigenvalue is negative, the direction is reversed. Loosely speaking, in a multidimensional vector space, the eigenvector is not rotated.' back

Heraclitus - Wikipedia, Heraclitus - Wikipedia, the free encyclopedia, ' Heraclitus of Ephesus (Greek: Ἡράκλειτος ὁ Ἐφέσιος)Ephesus, Ionia, on the coast of Asia Minor. . . . Heraclitus is famous for his insistence on ever-present change in the universe, as stated in his famous saying, "No man ever steps in the same river twice" (see panta rhei, below). He believed in the unity of opposites, stating that "the path up and down are one and the same", all existing entities being characterized by pairs of contrary properties. His cryptic utterance that "all entities come to be in accordance with this Logos" (literally, "word", "reason", or "account") has been the subject of numerous interpretations.' ' back

Neoplatonism and Christianity - Wikipedia, Neoplatonism and Christianity - Wikipedia, the free encyclopedia, 'Neoplatonism was a major influence on Christian theology throughout Late Antiquity and the Middle Ages in the West due to St. Augustine of Hippo, who was influenced by the early Neoplatonists Plotinus and Porphyry, and the works of the Christian writer Dionysius the Pseudo-Areopagite, who was influenced by later Neoplatonists, such as Proclus and Damascius.' back

Parmenides - Wikipedia, Parmenides - Wikipedia, the free encyclopedia, 'Parmenides of Elea (early 5th century BC) was an ancient Greek philosopher born in Elea, a Greek city on the southern coast of Italy. He was the founder of the Eleatic school of philosophy, his only known work is a poem which has survived only in fragmentary form. In it, Parmenides describes two views of reality. In the Way of Truth, he explained how reality is one; change is impossible; and existence is timeless, uniform, and unchanging. In the Way of Opinion, he explained the world of appearances, which is false and deceitful. These thoughts strongly influenced Plato, and through him, the whole of western philosophy.' back

Plato - Wikipedia, Plato - Wikipedia, the free encyclopedia, ' Plato (c. 427 – 348 BC) was an ancient Greek philosopher of the Classical period who is considered a top thinker in Philosophy. Plato founded the Academy, a philosophical school in Athens where Plato taught the doctrines that would later become known as Platonism. The philosopher was an innovator of the written dialogue and dialectic forms in philosophy. He was a system-builder. He also raised problems for what became all the major areas of both theoretical philosophy and practical philosophy.' back

Rolf Landauer (1991), Information is physicaL, Abstract Information is inevitably tied to a physical representation and therefore to restrictions and possibilities related to the laws of physics and the parts available in the universe. Quantum mechanical superpositions of information bearing states can be used, and the real utility of that needs to be understood. Quantum parallelism in computation is one possibility and will be assessed pessimistically. The energy dissipation requirements of computation, of measurement and of the communications link are discussed. The insights gained from the analysis of computation has caused a reappraisal of the perceived wisdom in the other two fields. A concluding section speculates about the nature of the laws of physics, which are algorithms for the handling of information, and must be executable in our real physical universe.' back

Theory of Forms - Wikipedia, Theory of Forms - Wikipedia, the free encyclopedia, ' Plato's theory of Forms or theory of Ideas asserts that non-material abstract (but substantial) forms (or ideas), and not the material world of change known to us through sensation, possess the highest and most fundamental kind of reality. When used in this sense, the word form or idea is often capitalized. Plato speaks of these entities only through the characters (primarily Socrates) of his dialogues who sometimes suggest that these Forms are the only true objects of study that can provide us with genuine knowledge; thus even apart from the very controversial status of the theory, Plato's own views are much in doubt. Plato spoke of Forms in formulating a possible solution to the problem of universals.' back

Thomas Aquinas, De Ente et Essentia, Latin text of one of Thomas Aquinas early works.
Textum a L. Baur Monasterii Westfalorum 1933 editum emendatum a J. Koch ac translatum in taenias magneticas a Roberto Busa SJ. denuo recognovit Enrique Alarcón atque instruxit<
[69871] De ente et essentia, pr.
Quia parvus error in principio magnus est in fine, secundum philosophum in I caeli et mundi, ens autem et essentia sunt quae primo intellectu concipiuntur, ut dicit Avicenna in principio suae metaphysicae, ideo ne ex eorum ignorantia errare contingat, ad horum difficultatem aperiendam dicendum est quid nomine essentiae et entis significetur et quomodo in diversis inveniatur et quomodo se habeat ad intentiones logicas, scilicet genus, speciem et differentiam. Quia vero ex compositis simplicium cognitionem accipere debemus et ex posterioribus in priora devenire, ut, a facilioribus incipientes, convenientior fiat disciplina, ideo ex significatione entis ad significationem essentiae procedendum est. back

Unmoved mover - Wikipedia, Unmoved mover - Wikipedia, the free encyclopedia, ' The unmoved mover (Ancient Greek: ὃ οὐ κινούμενον κινεῖ, lit. 'that which moves without being moved' or prime mover (Latin: primum movens) is a concept advanced by Aristotle as a primary cause (or first uncaused cause) or "mover" of all the motion in the universe. As is implicit in the name, the unmoved mover moves other things, but is not itself moved by any prior action. In Book 12 (Greek: Λ) of his Metaphysics, Aristotle describes the unmoved mover as being perfectly beautiful, indivisible, and contemplating only the perfect contemplation: self-contemplation. He equates this concept also with the active intellect. This Aristotelian concept had its roots in cosmological speculations of the earliest Greek pre-Socratic philosophers and became highly influential and widely drawn upon in medieval philosophy and theology. St. Thomas Aquinas, for example, elaborated on the unmoved mover in the Quinque viae. ' back