# „Pure mathematics is in its way the poetry of logical ideas.“

1930s, Obituary for Emmy Noether (1935)
Contexto: Pure mathematics is, in its way, the poetry of logical ideas. One seeks the most general ideas of operation which will bring together in simple, logical and unified form the largest possible circle of formal relationships. In this effort toward logical beauty spiritual formulas are discovered necessary for the deeper penetration into the laws of nature.

1879 - 1955

### „Pure mathematics is, in its way, the poetry of logical ideas. One seeks the most general ideas of operation which will bring together in simple, logical and unified form the largest possible circle of formal relationships. In this effort toward logical beauty spiritual formulas are discovered necessary for the deeper penetration into the laws of nature.“

—  Albert Einstein German-born physicist and founder of the theory of relativity 1879 - 1955

1930s, Obituary for Emmy Noether (1935)

### „There is a logic of language and a logic of mathematics.“

—  Thomas Merton Priest and author 1915 - 1968

Contexto: There is a logic of language and a logic of mathematics. The former is supple and lifelike, it follows our experience. The latter is abstract and rigid, more ideal. The latter is perfectly necessary, perfectly reliable: the former is only sometimes reliable and hardly ever systematic. But the logic of mathematics achieves necessity at the expense of living truth, it is less real than the other, although more certain. It achieves certainty by a flight from the concrete into abstraction. Doubtless, to an idealist, this would seem to be a more perfect reality. I am not an idealist. The logic of the poet — that is, the logic of language or the experience itself — develops the way a living organism grows: it spreads out towards what it loves, and is heliotropic, like a plant.

### „Gödel's theorem shows conclusively that in pure mathematics reductionism does not work. To decide whether a mathematical statement is true, it is not sufficient to reduce the statement to marks on paper and to study the behavior of the marks. Except in trivial cases, you can decide the truth of a statement only by studying its meaning and its context in the larger world of mathematical ideas.“

—  Freeman Dyson theoretical physicist and mathematician 1923

The Scientist As Rebel (2006)

### „A painter makes patterns with shapes and colours, a poet with words. A painting may embody an ‘idea’, but the idea is usually commonplace and unimportant. In poetry, ideas count for a good deal more; but, […] the importance of ideas in poetry is habitually exaggerated: '… Poetry is not the thing said but a way of saying it.' [In poetry, ] the poverty of the ideas seems hardly to affect the beauty of the verbal pattern.“

—  G. H. Hardy, livro A Mathematician's Apology

A Mathematician's Apology (1941)

### „Common Logic is the Grammar of the higher Speech, that is, of Thought; it examines merely the relations of ideas to one another, the Mechanics of Thought, the pure Physiology of ideas. Now logical ideas stand related to one another, like words without thoughts. Logic occupies itself with the mere dead Body of the Science of Thinking.“

—  Novalis German poet and writer 1772 - 1801

Metaphysics, again, is the Dynamics of Thought; treats of the primary Powers of Thought; occupies itself with the mere Soul of the Science of Thinking. Metaphysical ideas stand related to one another, like thoughts without words. Men often wondered at the stubborn Incompletibility of these two Sciences; each followed its own business by itself; there was a want everywhere, nothing would suit rightly with either. From the very first, attempts were made to unite them, as everything about them indicated relationship; but every attempt failed; the one or the other Science still suffered in these attempts, and lost its essential character. We had to abide by metaphysical Logic, and logical Metaphysic, but neither of them was as it should be.
Pupils at Sais (1799)

### „The arithmetization of mathematics… which began with Weierstrass… had for its object the separation of purely mathematical concepts, such as number and correspondence and aggregate, from intuitional ideas, which mathematics had acquired from long association with geometry and mechanics.These latter, in the opinion of the formalists, are so firmly entrenched in mathematical thought that in spite of the most careful circumspection in the choice of words, the meaning concealed behind these words, may influence our reasoning. For the trouble with human words is that they possess content, whereas the purpose of mathematics is to construct pure thought.“

—  Tobias Dantzig American mathematician 1884 - 1956

p, 125
Number: The Language of Science (1930)

### „Only mathematics and mathematical logic can say as little as the physicist means to say.“

—  Bertrand Russell logician, one of the first analytic philosophers and political activist 1872 - 1970

The Scientific Outlook (1931)
1930s
Contexto: Ordinary language is totally unsuited for expressing what physics really asserts, since the words of everyday life are not sufficiently abstract. Only mathematics and mathematical logic can say as little as the physicist means to say.

### „The word 'definition' has come to have a dangerously reassuring sound, owing no doubt to its frequent occurrence in logical and mathematical writings.“

—  Willard van Orman Quine American philosopher and logician 1908 - 2000

"Two dogmas of Empiricism", p. 26
From a Logical Point of View: Nine Logico-Philosophical Essays (1953)

### „That logic, as a science, is susceptible of very wide applications is admitted; but it is equally certain that its ultimate forms and processes are mathematical.“

—  George Boole English mathematician, philosopher and logician 1815 - 1864

p. 12; Cited in: William Stanley Jevons (1887) The Principles of Science: : A Treatise on Logic and Scientific Method. p. 155
1850s, An Investigation of the Laws of Thought (1854)

### „Pure mathematics is on the whole distinctly more useful than applied. […] For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics.“

—  G. H. Hardy, livro A Mathematician's Apology

A Mathematician's Apology (1941)

### „Pure mathematics is religion.“

—  Novalis, livro Blüthenstaub

Reine Mathematik ist Religion.
Blüthenstaub (1798), Unsequenced

### „Geometry can in no way be viewed… as a branch of mathematics; instead, geometry relates to something already given in nature, namely, space. I… realized that there must be a branch of mathematics which yields in a purely abstract way laws similar to geometry.“

—  Hermann Grassmann German polymath, linguist and mathematician 1809 - 1877

Forward, as quoted by Mario Livio, Is God a Mathematician? (2009)
Ausdehnungslehre (1844)

### „But how can we avoid the use of human language? The… symbol. Only by using a symbolic language not yet usurped by those vague ideas of space, time, continuity which have their origin in intuition and tend to obscure pure reason—only thus may we hope to build mathematics on the solid foundation of logic.“

—  Tobias Dantzig American mathematician 1884 - 1956

p, 125
Number: The Language of Science (1930)

### „The science of pure mathematics, in its modern developments, may claim to be the most original creation of the human spirit.“

—  Alfred North Whitehead English mathematician and philosopher 1861 - 1947

1920s, Science and the Modern World (1925)

### „The rules of logic are to mathematics what those of structure are to architecture.“

—  Bertrand Russell logician, one of the first analytic philosophers and political activist 1872 - 1970

1900s, "The Study of Mathematics" (November 1907)

### „The function of logic in mathematics is critical rather than constructive.“

—  George Frederick James Temple British mathematician 1901 - 1992

100 Years of Mathematics: a Personal Viewpoint (1981)

### „Our family are an alternate stratification of poetry and mathematics.“

—  Ada Lovelace English mathematician, considered the first computer programmer 1815 - 1852

In a letter to Andrew Crosse, as quoted in Eugen Kölbing's Englische Studien, Volume 19 https://archive.org/stream/englischestudien19leipuoft#page/156/mode/1up (1894), Leipzig; O.R. Reisland, "Byron's Daughter", p. 156.

### „Music, when combined with a pleasurable idea, is poetry; music without the idea is simply music; the idea without the music is prose from its very definitiveness.“

—  Edgar Allan Poe American author, poet, editor and literary critic 1809 - 1849

"Letter to Mr. B — ".

### „The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.“

—  John Von Neumann Hungarian-American mathematician and polymath 1903 - 1957

As quoted in Bigeometric Calculus: A System with a Scale-Free Derivative (1983) by Michael Grossman, and in Single Variable Calculus (1994) by James Stewart.

### „A poetry of revolt against moral ideas is a poetry of revolt against life; a poetry of indifference towards moral ideas is a poetry of indifference towards life.“

—  Matthew Arnold English poet and cultural critic who worked as an inspector of schools 1822 - 1888

Wordsworth, originally published as "Preface to the Poems of Wordsworth" in Macmillan's Magazine (July 1879)
Essays in Criticism, second series (1888)
Contexto: If what distinguishes the greatest poets is their powerful and profound application of ideas to life, which surely no good critic will deny, then to prefix to the word ideas here the term moral makes hardly any difference, because human life itself is in so preponderating a degree moral.
It is important, therefore, to hold fast to this: that poetry is at bottom a criticism of life; that the greatness of a poet lies in his powerful and beautiful application of ideas to life — to the question, How to live. Morals are often treated in a narrow and false fashion, they are bound up with systems of thought and belief which have had their day, they are fallen into the hands of pedants and professional dealers, they grow tiresome to some of us. We find attraction, at times, even in a poetry of revolt against them; in a poetry which might take for its motto Omar Khayam's words: "Let us make up in the tavern for the time which we have wasted in the mosque." Or we find attractions in a poetry indifferent to them, in a poetry where the contents may be what they will, but where the form is studied and exquisite. We delude ourselves in either case; and the best cure for our delusion is to let our minds rest upon that great and inexhaustible word life, until we learn to enter into its meaning. A poetry of revolt against moral ideas is a poetry of revolt against life; a poetry of indifference towards moral ideas is a poetry of indifference towards life.