Mathematical Symbols Quotes & Sayings

In presenting a mathematical argument the great thing is to give the educated reader the chance to catch on at once to the momentary point and take details for granted: two trivialities omitted can add up to an impasse). The unpractised writer, even after the dawn of a conscience, gives him no such chance; before he can spot the point he has to tease his way through a maze of symbols of which not the tiniest suffix can be skipped. — John Edensor Littlewood

Men cannot be treated as units in operations of political arithmetic because they behave like the symbols for zero and the infinite , which dislocate all mathematical operations. — Arthur Koestler

We humans have a wide range of abilities that help us perceive and analyze mathematical content. We perceive abstract notions not just through seeing but also by hearing, by feeling, by our sense of body motion and position. Our geometric and spatial skills are highly trainable, just as in other high-performance activities. In mathematics we can use the modules of our minds in flexible ways - even metaphorically. A whole-mind approach to mathematical thinking is vastly more effective than the common approach that manipulates only symbols. — William Thurston

Nothing can be more fatal to progress than a too confident reliance on mathematical symbols; for the student is only too apt to take the easier course, and consider the formula not the fact as the physical reality. — Lord Kelvin

Consider a cognitive scientist concerned with the empirical study of the mind, especially the cognitive unconscious, and ultimately committed to understanding the mind in terms of the brain and its neural structure. To such a scientist of the mind, Anglo-American approaches to the philosophy of mind and language of the sort discussed above seem odd indeed. The brain uses neurons, not languagelike symbols. Neural computation works by real-time spreading activation, which is neither akin to prooflike deductions in a mathematical
logic, nor like disembodied algorithms in classical artificial intelligence, nor like derivations in a transformational grammar. — George Lakoff

Many persons who are not conversant with mathematical studies imagine that because the business of [Babbage's Analytical Engine] is to give its results in numerical notation, the nature of its processes must consequently be arithmetical and numerical, rather than algebraical and analytical. This is an error. The engine can arrange and combine its numerical quantities exactly as if they were letters or any other general symbols; and in fact it might bring out its results in algebraical notation, were provisions made accordingly. — Ada Lovelace

If a lunatic scribbles a jumble of mathematical symbols it does not follow that the writing means anything merely because to the inexpert eye it is indistinguishable from higher mathematics. — Eric Temple Bell

The chief difficulty of modern theoretical physics resides not in the fact that it expresses itself almost exclusively in mathematical symbols, but in the psychological difficulty of supposing that complete nonsense can be seriously promulgated and transmitted by persons who have sufficient intelligence of some kind to perform operations in differential and integral calculus ... — Celia Green

The practical man demands an appearance of reality at least. Always dealing in the concrete, he regards mathematical terms not as symbols or thought but as images of reality. A system acceptable to the mathematician because of its inner consistency may appear to the practical man to be full of contradictions because of the incomplete manner in which it represents reality. — Tobias Dantzig

Too large a proportion of recent "mathematical" economics are mere concoctions, as imprecise as the initial assumptions they rest on, which allow the author to lose sight of the complexities and interdependencies of the real world in a maze of pretentious and unhelpful symbols. — John Maynard Keynes

In enabling mechanism to combine together general symbols in successions of unlimited variety and extent, a uniting link is established between the operations of matter and the abstract mental processes of the most abstract branch of mathematical science. — Ada Lovelace

In this book, you will encounter various interesting geometries that have been thought to hold the keys to the universe. Galileo Galilei (1564-1642) suggested that "Nature's great book is written in mathematical symbols." Johannes Kepler (1571-1630) modeled the solar system with Platonic solids such as the dodecahedron. In the 1960s, physicist Eugene Wigner (1902-1995) was impressed with the "unreasonable effectiveness of mathematics in the natural sciences." Large Lie groups, like E8-which is discussed in the entry "The Quest for Lie Group E8 (2007)"- may someday help us create a unified theory of physics. in 2007, Swedish American cosmologist Max Tegmark published both scientific and popular articles on the mathematical universe hypothesis, which states that our physical reality is a mathematical structure-in other words, our universe in not just described by mathematics-it is mathematics. — Clifford A. Pickover

In order to translate a sentence from English into French two things are necessary. First, we must understand thoroughly the English sentence. Second, we must be familiar with the forms of expression peculiar to the French language. The situation is very similar when we attempt to express in mathematical symbols a condition proposed in words. First, we must understand thoroughly the condition. Second, we must be familiar with the forms of mathematical expression. — George Polya

That man is a reality, mankind an abstraction; that men cannot be treated as units in operations of political arithmetic because they behave like the symbols for zero and the infinite, which dislocate all mathematical operations; that the end justifies the means only within very narrow limits; that ethics is not a function of social utility, and charity not a petty bourgeois sentiment but the gravitational force which keeps civilization in its orbit. — Arthur Koestler

No doubt there are some who, when confronted with a line of mathematical symbols, however simply presented, can only see the face of a stern parent or teacher who tried to force into them a non-comprehending parrot-like apparent competence
a duty and a duty alone
and no hint of magic or beauty of the subject might be allowed to come through. — Roger Penrose

As soon as a thought or word becomes a tool, one can dispense with actually 'thinking' it, that is, with going through the logical acts involved in verbal formulation of it. As has been pointed out, often and correctly, the advantage of mathematics the model of all neo-positivistic thinking lies in just this 'intellectual economy.' Complicated logical operations are carried out without actual performance of the intellectual acts upon which the mathematical and logical symbols are based ... Reason ... becomes a fetish, a magic entity that is accepted rather than intellectually experienced. — Max Horkheimer

If you'd like to see how to apply these ideas directly to memorizing formulas, try out the SkillsToolbox website for a list of easy-to-remember visuals for mathematical symbols.7 — Barbara Oakley

Time is said to have only one dimension, and space to have three dimensions ... The mathematical quaternion partakes of both these elements; in technical language it may be said to be 'time plus space', or 'space plus time': and in this sense it has, or at least involves a reference to, four dimensions. And how the One of Time, of Space the Three, Might in the Chain of Symbols girdled be. — William Rowan Hamilton

What distinguishes a mathematical model from, say, a poem, a song, a portrait or any other kind of "model," is that the mathematical model is an image or picture of reality painted with logical symbols instead of with words, sounds or watercolors. — John L. Casti

Economists who speak the English tongue are strangely intimidated by mathematical symbols. — Al Nichol

There is nothing that can be said by mathematical symbols and relations which cannot also be said by words. The converse, however, is false. Much that can be and is said by words cannot successfully be put into equations, because it is nonsense. — Clifford Truesdell

Philosophy [nature] is written in that great book which ever is before our eyes
I mean the universe
but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. The book is written in mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth. — Galileo Galilei

What governs what we choose to notice? The first (which we shall have to qualify later) is whatever seems advantageous or disadvantageous for our survival, our social status, and the security of our egos. The second, again working simultaneously with the first, is the pattern and the logic of all the notation symbols which we have learned from others, from our society and our culture. It is hard indeed to notice anything for which the languages available to us (whether verbal, mathematical, or musical) have no description. This is why we borrow words from foreign languages. — Alan W. Watts

The history of art cannot be properly understood without some reference to the history of science. In both we are studying the symbols by which man affirms his mental scheme, and these symbols, be they pictorial or mathematical, a fable or formula, will reflect the same changes. — Kenneth Clark

One main reason why the separate nature of the science of operations has been little felt, and in general little dwelt on, is the shifting meaning of many of the symbols used in mathematical notation. First, the symbols of operation are frequently also the symbols of the results of operations. — Ada Lovelace