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The Soweto uprising in South Africa was sparked by the insistence of the apartheid regime that Afrikaans – the language of the Boer white minority – had to be used for mathematics, arithmetic and social studies in black schools from 7th grade.
According to the Afrikaans Medium Decree of 1974, Afrikaans had to be used for mathematics, arithmetic and social studies from seventh grade on, and English would be taught in general science and what was called practical subjects: needlework, woodworking, metal work, art, agriculture.
ℒ0 is adequate for the constructive part of the usual elementary mathematics—arithmetic and analysis but not for metamathematics, if this is to include a proof of Gödel's completeness theorem, and not for category theory, if this is to include the Yoneda embedding of a small category into a set-valued functor category.
Al-Fārābī's influence is particularly obvious in the enumeration of the seven parts of grammar, the eight parts of natural science (covering the spectrum of Aristotle's libri naturales), and the seven parts of mathematics: arithmetic, music, geometry, optics, astrology, astronomy, the science of weights, the science of technical devices (ingenia) (see the tables in Bouyges 1923, 65 69).
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The syllabus in mathematics included arithmetic, algebra, trigonometry, plane geometry, coordinate geometry and calculus, both differential and integral.
A number of 19th-century mathematicians found fault with the program of reducing mathematics to arithmetic and set theory as suggested by the work of Cantor and Frege.
Elaine Hope Darlington When I did my O-levels in the 60s in Scotland, I achieved separate passes in both mathematics and arithmetic, exactly as proposed by Jeanne Warren (Letters, 15 March).
In the organizational chart of knowledge at the beginning of the preliminary discourse to the Encyclopédie, Jean Le Rond d'Alembert distinguished between "pure" mathematics (geometry, arithmetic, algebra, calculus) and "mixed" mathematics (mechanics, geometric astronomy, optics, art of conjecturing).
The Greeks divided the field of mathematics into arithmetic (the study of "multitude," or discrete quantity) and geometry (that of "magnitude," or continuous quantity) and considered both to have originated in practical activities.
Translated into an Aristotelian manner of discourse, meaningful interactions between individuals could be transferred to an equally rational closed system of mathematics: an arithmetic for simple transactions, an algebra for solving certain well-delimited puzzles, a calculus to simulate changes, rates and flows, and a geometry for purposes of illustration and model construction.
His textbook, Clavis Mathematicae (The Key to Mathematics) on arithmetic published in 1631 was used by Wallis and Newton amongst others.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com