Algebraic and Mathematical Symbolism
Specious Logistic: This type of [non-traditional] Arithmetic is frequently used…; it is a sibling of [traditional] Arithmetic…
The distinction between them goes no further than that signified by their names: in [traditional] Arithmetic, the quantities of measurable things are expressed and reckoned by characters or figures peculiar to the art, by numerals, as in measurement generally;
in the former [non-traditional Arithmetic], however, the quantities themselves are indicated and in every way handled through written signs—the letters of the alphabet, that is—‘speciously’. Hence it has received the name Specious.
— Thomas Harriot (1631 posthumously), influential English mathematician, astronomer, a founding father of symbolic algebra
Indeed the operations of symbolical arithmetick (or the modern Algebra) seem to me to afford men one of the clearest exercises of reason that I ever yet met…the whole method and progress of that appearing at once upon the paper, when the operation is finished, and affording the analyst a lasting, and, as it were, visible ratiocination [train of thought].
— Robert Boyle (ca. 1671), Anglo-Irish chemist, a founding father of modern chemistry, co-founder of the Royal Society
This science is called by the word Stel-konst [the art of place] because that means, for the unknown place x, y, z, the last three or more letters of the alphabet; and for the known, the letters a,b,c,d and so forth.
— Pieter Venema (1730), Dutch mathematician-educator, author of the Dutch text “Arithmetica of Cyffer-Konst…” (the first known textbook printed in America having a portion devoted to algebra)
Algebra, in the modern sense of the word, is the art of computing by symbols, that is, generally speaking, by letters of the alphabet; which, for the simplicity and distinctness both of their sounds and characters, are much more commodious for this purpose than any other symbols or marks whatever.
— Nicholas Saunderson (1740 posthumously), English mathematician, 4th Lucasian Professor of Mathematics, developed for himself a type of tactile/Braille-like arithmetic on a specially made abacus (or calculating table) called ‘palpable arithmetic’
The principal object of Algebra, as well as of all the other branches of Mathematics, is to determine the value of quantities that were before unknown; and this is obtained by considering attentively the conditions given, which are always expressed in known numbers.
For this reason, Algebra has been defined, The science which teaches how to determine unknown quantities by means of those that are known.
— Leonard Euler (ca. 1765), influential Swiss mathematician, author, researcher/administrator (St. Peterburg’s Academy, Berlin Academy)
Computation is performed either by numbers, as in…arithmetic, or by species, as is usual in algebra. Both these rest on the same foundations, and aim at the same end; arithmetic, definitely and particularly; algebra, indefinitely and universally…
The principal advantage of algebra consists in this, that whereas in arithmetic questions are only solved by proceeding from quantities given to quantities sought; algebra tends in a retrograde order, from quantities sought, as if they were given, to quantities given as if they were sought,
in order that we may by some means or other come to a conclusion, from which the quantity sought may be discovered; and thus the most difficult problems are solved, whose solution would be sought in vain from only common arithmetic.
— Richard Francis Purdon (1822), Irish mathematician, author
Many people think that it is impossible to make Algebra about anything except number. This is a complete mistake. We make an Algebra whenever we arrange facts that we know round a centre which is a statement of what it is that we want to know and do not know; and then proceed to deal logically with all the statements…
— Mary Everest Boole (1909), English mathematician, teacher, author, editor, popularizer of mathematics
An ounce of algebra is worth a ton of verbal argument.
— J. B. S. Haldane (1892 – 1964), British evolutionary biologist, geneticist, popularizer of science
Algebra has contributed the machinery for expressing in a universal code, the cosmic relationships which have become the alphabet of science and industry. The formulas …are the cumulative result of age-long investigation and effort. Hence they represent a treasure house of information,—an armory of priceless value.
— William Betz (1930), German-American mathematician, educator, textbook author
My [algebraic] methods are really methods of working and thinking; this is why they have crept in everywhere anonymously.
— Amalie Emmy Noether (1931), influential German mathematician, professor of mathematics (University of Göttingen, Bryn Mawr College)
Symbolic algebra…is an analytical problem solving method for arithmetical and geometrical problems consisting of systematic manipulation of a symbolic representation of the problem.
— Albrecht Heeffer (2007), contemporary electrical engineer, mathematician-historian, educator, author