Number theory
While the word "algorithm" goes back only to certain readers of al-Khwārizmī, careful descriptions of methods of solution are older than proofs: such methods (that is, algorithms) are as old as any recognisable mathematics—ancient Egyptian, Babylonian, Vedic, Chinese—whereas proofs appeared only with the Greeks of the classical period.
An interesting early case is that of what we now call the Euclidean algorithm. In its basic form (namely, as an algorithm for computing the greatest common divisor) it appears as Proposition 2 of Book VII in "Elements", together with a proof of correctness. However, in the form that is often used in number theory (namely, as an algorithm for finding integer solutions to an equation formula_78,
or, what is the same, for finding the quantities whose existence is assured by the Chinese remainder theorem) it first appears in the works of Āryabhaṭa (5th–6th century CE) as an algorithm called
"kuṭṭaka" ("pulveriser"), without a proof of correctness.
Etymology of chemistry
There are two main views on the derivation of the word, which agree in holding that it has an Arabic descent, the prefix "al" being the Arabic article. But according to one, the second part of the word comes from the Greek "χημεία", pouring, infusion, used in connexion with the study of the juices of plants, and thence extended to chemical manipulations in general; this derivation accounts for the old-fashioned spellings "chymist" and "chymistry". The other view traces it to "khem" or "khame", hieroglyph "khmi", which denotes black earth as opposed to barren sand, and occurs in Plutarch as "χημεία"; on this derivation alchemy is explained as meaning the "Egyptian art". The first occurrence of the word is said to be in a treatise of Julius Firmicus, an astrological writer of the 4th century, but the prefix al there must be the addition of a later copyist. In English, Piers Plowman (1362) contains the phrase "experimentis of alconomye", with variants "alkenemye" and " alknamye". The prefix "al" began to be dropped about the middle of the 16th century (further details of which are given below).