Best Integers Quotes | Short & Famous Sayings

“Integers 1 to 10 walk into a bar, and are soon appalled at the bartender's math when he asks them for their order.”

Author:Rajesh`

“All results of the profoundest mathematical investigation must ultimately be expressible in the simple form of properties of the integers.”

Form Simple Results Mathematics Property Mathematical Investigation Integers

Author:Leopold Kronecker

“God made the integers, man made the rest.”

Men Made Integers

Author:Leopold Kronecker

“The gods and their tranquil abodes appear, which no winds disturb, nor clouds bedew with showers, nor does the white snow, hardened by frost, annoy them; the heaven, always pure, is without clouds, and smiles with pleasant light diffused.”

Doe Light Heaven White Wind Pure Clouds Snow Pleasant Annoying Showers Frost Tranquil Hardened Abode Integers

Author:Lucretius

“All of mathematics can be deduced from the sole notion of an integer; here we have a fact universally acknowledged today.”

Facts Today Numbers Mathematics Notion Sole Integers

Author:Emile Borel

“The page of my notebook was filled with many messy integrals, but all of a sudden I saw emerge a formula for counting. I had begun to calculate a quantity on the assumption that the result was a real number, but found instead that, in certain units, all the possible answers would be integers. This meant that areas and volumes cannot take any value, but come in multiples of fixed units.”

Real Would Be Certain Values Found Answers Results Numbers Saws Pages Areas Mathematics Filled Fixed Assumption Formulas Quantity Volume Units Counting Messy Notebook Integers

Book:Three Roads To Quantum Gravity

Source: Three Roads To Quantum Gravity

“Numbers are the product of counting. Quantities are the product of measurement. This means that numbers can conceivably be accurate because there is a discontinuity between each integer and the next. Between two and three there is a jump. In the case of quantity, there is no such jump; and because jump is missing in the world of quantity, it is impossible for any quantity to be exact. You can have exactly three tomatoes. You can never have exactly three gallons of water. Always quantity is approximate.”

World Mean Two Three Next Water Numbers Cases Impossible Missing Products Quantity Accurate Counting Measurement Tomatoes Gallons Discontinuity Integers

Author:Gregory Bateson

“The development of mathematics towards greater precision has led, as is well known, to the formalization of large tracts of it, so that one can prove any theorem using nothing but a few mechanical rules.”

Wells Known Greater Development Prove Mathematics Well Known Precision Theorems Integers

Book:Kurt Gödel: Collected Works: Volume I: Publications 1929-1936

Source: Kurt Gödel: Collected Works: Volume I: Publications 1929-1936

“By itself, an ordinary snapshot is no less banal than the petite madeleine in Proust's In Search of Lost Time... but as goad to memory, it is often the first integer in a sequence of recollections that has the power to deny time for the sake of love.”

Firsts Lost Memories Ordinary Sake Deny Sequence Recollection Snapshots Proust Lost Time Petite Madeleines Integers

Author:Michael Lesy

“Numbers are the product of counting. Quantities are the product of measurement. This means that numbers can conceivably be accurate because there is a discontinuity between each integer and the next.”

Mean Next Numbers Products Quantity Accurate Counting Measurement Discontinuity Integers

Author:Gregory Bateson

“Is a woman a thinking unit at all, or a fraction always wanting its integer?”

Thinking Units Fractions Integers

Book:Jude the Obscure: Works of Hardy

Source: Jude the Obscure: Works of Hardy

“Increasing pressure on students to subject themselves to ever more tests, whittling themselves down to rows and rows of tight black integers upon a transcript, all ready to goose-step straight into a computer.”

Black Steps Subjects Students Ready Computer Tests Pressure Geese Integers Whittling

Book:Heart, You Bully, You Punk

Source: Heart, You Bully, You Punk

“Integers are the fountainhead of all mathematics.”

Mathematics Fountainhead Integers

Author:Hermann Minkowski

“The development of mathematics toward greater precision has led, as is well known, to the formalization of large tracts of it, so that one can prove any theorem using nothing but a few mechanical rules... One might therefore conjecture that these axioms and rules of inference are sufficient to decide any mathematical question that can at all be formally expressed in these systems. It will be shown below that this is not the case, that on the contrary there are in the two systems mentioned relatively simple problems in the theory of integers that cannot be decided on the basis of the axioms.”

“In this communication I wish first to show in the simplest case of the hydrogen atom (nonrelativistic and undistorted) that the usual rates for quantization can be replaced by another requirement, in which mention of "whole numbers" no longer occurs. Instead the integers occur in the same natural way as the integers specifying the number of nodes in a vibrating string. The new conception can be generalized, and I believe it touches the deepest meaning of the quantum rules.”

“If we can dispel the delusion that learning about computers should be an activity of fiddling with array indexes and worrying whether X is an integer or a real number, we can begin to focus on programming as a source of ideas.”

Ifs Should Ideas Real Numbers Worry Focus Source Activity Computer Programming Delusion Integers

Author:Hal Abelson

“The Good Lord made all the integers; the rest is man's doing.”

Men Made Lord Mathematics Math Math Education Good Math Integers

Author:Leopold Kronecker

“My problem is that I have been persecuted by an integer.”

Has Beens Problem Persecuted Integers

Author:George Armitage Miller

“The trouble with integers is that we have examined only the very small ones. Maybe all the exciting stuff happens at really big numbers, ones we can't even begin to think about in any very definite way. Our brains have evolved to get us out of the rain, find where the berries are, and keep us from getting killed. Our brains did not evolve to help us grasp really large numbers or to look at things in a hundred thousand dimensions.”

“I read in the proof sheets of Hardy on Ramanujan: "As someone said, each of the positive integers was one of his personal friends." My reaction was, "I wonder who said that; I wish I had." In the next proof-sheets I read (what now stands), "It was Littlewood who said..."”

Said Next Wish Friendship Wonder Mathematics Math Proof Reactions Mathematical Sheets Hardy Mathematical Proof Integers Ramanujan

Book:Littlewood's Miscellany

Source: Littlewood's Miscellany

“The series of integers is obviously an invention of the human mind, a self-created tool which simplifies the ordering of certain sensory experiences.”

Mind Humans Self Certain Education Tools Series Invention Human Mind Simplify Sensory Integers

Book:Ideas and Opinions

Source: Ideas and Opinions

“I have tried, with little success, to get some of my friends to understand my amazement that the abstraction of integers for counting is both possible and useful. Is it not remarkable that 6 sheep plus 7 sheep makes 13 sheep; that 6 stones plus 7 stones make 13 stones? Is it not a miracle that the universe is so constructed that such a simple abstraction as a number is possible? To me this is one of the strongest examples of the unreasonable effectiveness of mathematics. Indeed, I find it both strange and unexplainable.”

“Arithmetic starts with the integers and proceeds by successively enlarging the number system by rational and negative numbers, irrational numbers, etc... But the next quite logical step after the reals, namely the introduction of infinitesimals, has simply been omitted. I think, in coming centuries it will be considered a great oddity in the history of mathematics that the first exact theory of infinitesimals was developed 300 years after the invention of the differential calculus.”

Integers Quotes

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Integers Quotes