Group: philosophy of mathematics
Topic: history of computers
Topic: history of programming
Topic: history of science
Topic: what is a number
 
Subtopic: theory vs. practice
Quote: physicists do Babylonian mathematics because different formulations of the same law give different clues for related laws [»feynR_1965]
 Subtopic: nature as theory
Quote: da Vincia bird is an instrument working according to mathematical law; man can reproduce all of its movements [»daviL_1505]
 Quote: construct a Universal Character by assigning symbols for simple notions and compose these symbols for everything else; like logic and mathematics [»sparK7_1972]
 Subtopic: mathematical physics
Quote: Galileo depended on the Euclidean theory of proportion for the application of mathematics to physics
 Subtopic: algorithm
Quote: most engineering and scientific problems consist of initiate, perform, communicate result with optional repetition until acceptable [»perlAJ4_1957]
 Quote: Pingala (before 200 B.C.) gives an algorithm for computing the total number of arrangements of two things in n places
 Quote: ancient Babylonian algorithms from 18001600 B.C.; "This is the procedure"; no branching [»knutDE7_1972]
 Quote: first description of an algorithm for computing the cuberoot [»dattB_1935]
 Quote: Aryabhata (499) gave a solution for quadratic equations. Here is a sample problem [»dattB_1935]
 Quote: AlKhowarizmi's examples repeatedly occur in mathematical literature [»alkhMM_825, OK]
 Subtopic: number
Quote: Babylonian astronomers used a sign for zero; about 311 BCE [»ifraG_2000]
 Quote: positional notation independently discovered by Babylonians, Chinese, Mayan, and Indians [»ifraG_2000]
 Quote: in India, the knowledge of fractions can be traced to very early times [»dattB_1935]
 Quote: example of an Indian number using zero; sixth century [»ifraG_2000]
 Quote: Sanskrit possessed names for all powers of ten up to 10^8, and by 300 CE, 10^17; used the names to mark position [»ifraG_2000]
 Quote: In 628, Brahmagupta defined zero as the subtraction of a number by itself and listed its properties; a number multiplied by zero becomes zero [»ifraG_2000]
 Subtopic: arithmetic
Quote: early representation of division with remainder; tablet from 2650 BCE [»ifraG_2000]
 QuoteRef: dattB_1935 ;;History of Hindu Mathematics: a source book, part 1, numeral notation and arithmetic
 QuoteRef: leon_1202 ;;Liber abaci
 Quote: Leonardo wrote a voluminous compendium of Arabic arithmetic and mercantile practice; includes the Fibonacci series [»leon_1202]
 Quote: AlKhowarizmi introduction to calculation by completion and reduction; useful in inheritance, lawsuits, trade, digging canals, etc. [»alkhMM_825, OK]
 Quote: description of early, Indian instruction in arithmetic: memorized problems and solutions; calculated by writing in dust spread on a board [»dattB_1935]
 Quote: all arithmetical operations resolve to increase and decrease, i.e., addition and subtraction [»dattB_1935]
 Quote: the Hindus admired the Rule of Three for its simple and universal solution of proportion problems [»dattB_1935]
 Subtopic: algebra
Quote: the product of 10x and 10+x is 100x^2 [»alkhMM_825, OK]
 Quote: example of solving a quadratic equation [»alkhMM_825, OK]
 Quote: solving a proportional equation with one unknown [»alkhMM_825, OK]
 Quote: another example of solving a quadratic equation [»alkhMM_825, OK]
 Quote: the roots of a quadratic equation depend on b^24ac
 Quote: algebraic ideas appeared independently in Egypt, Babylon, China, Greece, and India [»alkhMM_825, OK]
 Quote: the oldest mathematical text book contains first degree equations; Egyptian papyrus from about 1700 B.C. [»alkhMM_825, OK]
 Quote: Viete introduced "analytics" and the use of letters in the theory of equations; e.g., x^2+ax+b=0 [»vietF_1591]
 QuoteRef: vietF_1591 ;;In artem analyticem isagoge
 Quote: mathematical analysis uses the art and rules of logic to obtain equations of species (e.g., 'x') instead of numbers [»vietF_1591]
 Quote: rules of arithmetic for calculation by species or forms of things, as, for instance, the letters of the alphabet [»vietF_1591]
 Subtopic: grammar
Quote: Panini's mathematical grammar described the language as spoken, concisely defined by enumerations and rules; transmitted orally; transform from syntactic relationship to phonemic realization [»misrVN_1966]
 Quote: Panini stood at the culmination point of a rich grammatical tradition; 7th4th century B.C.; replaced the old systems [»misrVN_1966]
 Subtopic: logic
Quote: Peirce's system of existential graphs visually displayed an assertion and its logical structure [»lehmF12_1988]
 Quote: Begriffschrift introduced truthfunctional propositional calculus, functions instead of subject/predicate, quantification, derivational forms, and a definition of sequence [»fregG_1879]
 QuoteRef: fregG_1879 ;;Begriffschrift, a formula language, modeled upon that of arithmetic, for pure thought
 Subtopic: calculus
Quote: Leibniz developed differential and integral calculus [»struDJ_1967]
 Quote: Babbage introduced Cambridge to Leibniz's calculus in preference to Newton's calculus
 Quote: Leibniz's infinitesimal calculus was independent of what differentials actually are; avoids metaphysical disputes [»kramS2_1996]
 Subtopic: number theory
Quote: Peano's axioms for number concern 0, unique successors, and induction [»russB_1919, OK]
 Subtopic: vector equations
Quote: Maxwell developed his theory in cartesian coordinates and promoted the use of quaternion or vector equations
 Subtopic: large numbers
Quote: India used immense numbers from ancient times; for example, the Hindus used 18 denominations and in the Lalitavistara, tallaksana is 10^53 [»dattB_1935]
 Quote: some of the numbers named by Archimedes exceed the grains of sand that would fill the universe [»arch_287]
 Subtopic: zero
Quote: example of an Indian number using zero; sixth century [»ifraG_2000]
 Quote: Babylonian astronomers used a sign for zero; about 311 BCE [»ifraG_2000]
 Quote: the Hindus define zero as the result of aa [»dattB_1935]
 Quote: the earliest known use of the zero symbol is by Pingala (before 200 B.C.) [»dattB_1935]
 Quote: In 628, Brahmagupta defined zero as the subtraction of a number by itself and listed its properties; a number multiplied by zero becomes zero [»ifraG_2000]
 Quote: Bhaskara II (1150): in a/0 there is no alteration, as no change takes place in the infinite and immutable God [»dattB_1935]
 Subtopic: notation
Quote: any number can be written with the nine digits from India and zero from Arabic [»leon_1202]
 Quote: mathematical notation had a long and painful evolution [»falkAD8_1978]
 Quote: development of math notation: variable names, functions, symbol lists, numeric rep, vectors/etc. as entities, quantity vs. representation [»falkAD8_1978, OK]
 Quote: India has a placevalue system of word numerals; 1 is anything markedly unique, e.g., the moon, the earth; 0 is denoted by words meaning void, sky, complete; still used today [»dattB_1935]

Related Topics
Group: philosophy of mathematics (11 topics, 330 quotes)
Topic: history of computers (66 items)
Topic: history of programming (91 items)
Topic: history of science (52 items)
Topic: what is a number (55 items)
