Mathematical Operations Quotes

The dot was introduced as a symbol for multiplication by Leibniz. On July 29, 1698, he wrote in a letter to Johann Bernoulli: "I do not like X as a symbol for multiplication, as it is easily confounded with x.

Seeing there is nothing that is so troublesome to mathematical practice, nor that doth more molest and hinder calculators, than the multiplications, divisions, square and cubical extractions of great numbers.... I began therefore to consider in my mind by what certain and ready art I might remove those hindrances.

The Analytical Engine is an embodying of the science of operations, constructed with peculiar reference to abstract number as the subject of those operations.

The science of operations, as derived from mathematics more especially, is a science of itself, and has its own abstract truth and value.

"She can't do Subtraction." said the White Queen. "Can you do Division? Divide a loaf by a knife-what's the answer to that?" "I suppose-" Alice was beginning, but the Red Queen answered for her. "Bread-and-butter, of course."

The Analytical Engine has no pretensions whatever to originate anything. It can do whatever we know how to order it to perform.

... mathematics is the science of skillful operations with concepts and rules invented just for this purpose.

In the old physics, three times two equals six and two times three equals 6 are reversible propositions. Not in quantum physics. Three times two and two times three are two different matters, distinct and separate propositions.

In abstract mathematics, of course operations alter those particular relations which are involved in the considerations of number and space, and the results of operations are those peculiar results which correspond to the nature of the subjects of operation.

I write rhymes with addition and algebra, mental geometry.

A lot of people... use a calculator!

The Analytical Engine, on the contrary, can either add, subtract, multiply or divide with equal facility; and performs each of these four operations in a direct manner, without the aid of any of the other three.

But the science of operations, as derived from mathematics more especially, is a science of itself, and has its own abstract truth and value; just as logic has its own peculiar truth and value, independently of the subjects to which we may apply its reasonings and processes.

Mathematics is the queen of science, and arithmetic the queen of mathematics.

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.

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.

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.

With four? Doing a little... Addition? Multiplication?

It were much to be desired, that when mathematical processes pass through the human brain instead of through the medium of inanimate mechanism, it were equally a necessity of things that the reasonings connected with operations should hold the same just place as a clear and well-defined branch of the subject of analysis, a fundamental but yet independent ingredient in the science, which they must do in studying the engine.

...the science of calculation also is indispensable as far as the extraction of the square and cube roots: Algebra as far as the quadratic equation and the use of logarithms are often of value in ordinary cases: but all beyond these is but a luxury; a delicious luxury indeed; but not be in indulged in by one who is to have a profession to follow for his subsistence.

"She can't do sums a bit!" the Queens said together, with great emphasis. "Can you do sums?" Alice said, turning suddenly on the White Queen, for she didn't like being found fault with so much. The Queen gasped and shut her eyes. "I can do Addition, if you give me time-but I can do Subtraction, under any circumstances!"

The Theory of Groups is a branch of mathematics in which one does something to something and then compares the result with the result obtained from doing the same thing to something else, or something else to the same thing.

The introduction of numbers as coordinates by reference to the particular division scheme of the open one-dimensional continuum is an act of violence whose only practical vindication is the special calculatory manageability of the ordinary number continuum with its four basic operations.

32 grams raw, chop it in half, get 16. Double it times three, we got 48. Which mean a whole lot of cream. Divide the profit by four. Subtract it by eight. We back to 16.

In studying the action of the Analytical Engine, we find that the peculiar and independent nature of the considerations which in all mathematical analysis belong to operations, as distinguished from the objects operated upon and from the results of the operations performed upon those objects, is very strikingly defined and separated.