Today all school maths subjects are taught separately as: Arithmetic, Geometry, Trigonometry and Algebra, influenced by Euler in 1727.
Since 18th century Maths has evolved rapidly with the biggest revolution of Modern (Abstract) Maths in 19th century from the French prodigy Galois in Group Theory.The 20th and 21st centuries Maths continues to expand from Galois Abstract Maths to a chaotic state where no single mathematician can claim to know all aspects of Maths like Newton, Euler, Gauss…did.
It is time to re-look at Euler’s outdated Maths pedagogy of 4 distinct disciplines… Can these 4 subjects be taught as ONE combined ‘Math’ (americans spell as singular) subject ?
Euler was invited by Peter I of Russia in 1727 to work in the
Petersburg Academy of Sciences. He introduced the fundamental math
disciplines in school math education:
1. Arithmetic
2. Geometry
3. Trigonometry
4. Algebra
these 4 are taught as separate and specific subjects, versus 19 duplicated disciplines in Europe.
Euler influenced not only in Russia schools, but in schools worldwide today.
Source: Russian Mathematics Education
Vol 1: History and world significance
Vol 2: Programs and practices
(Publisher: World Scientific)
Mathtuition88 
Felix Klein, the great german math educator of 20th CE, also the Father of Gottingen University, which built to be the World’s center of Math before WW2, had proposed to unify Math teaching based on the Foundation of
“Functions”.Why ? Function is intuitive because it has graphical view, it links Geometry, Trigo and Algebra, and Algebra studies Number Theory based on Arithmetic. An ideal ‘connector’ for these 4 subjects.
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After WW2, a group of French students codename “Bourbaki” from the Ecole Normale Supérieure, re-wrote all the Math textbooks based on Cantor’s Set Theory – the Birth of Axiomatic Abstract Math, or “New Math”, influence France till today and the USA until 1970s.
This New Math is criticized for being too abstract at the expense of classical Math. However today’s University Math has the ‘Bourbakian’ influence.
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Ironically while Ruler was the culprit of dividing
Math into 4 distinct subjects, he later
showed to the world these 4 are connected by his most wonderful formula in history:
e^ i (pi) = -1
Right hand side -1 is Arithmetic.
Left hand side: e is Trigo,
i is Algebra
pi is geometry (circle).
That is in Summary:
Trigo ^ Algebra x Geometry = Arithmetic
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Euler was the culprit …
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