Introductio in analysin infinitorumL. Euler
Introductio in analysin infinitorum
by L. Euler · first published 1748
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…prolific was he that the journal of the St. Petersburg Academy was still publishing the backlog of his papers a full 48 years after his death." – Euler: The Master Of Us All p.s. Last year I read his Introductio in analysin infinitorum (1748), "one of the most influential mathematics books of all time", which made the function concept basic in mathematics. Polynomials, trig functions, exponential functions, the logarithm function, etc…
on “Paul Erdős (2000)” ↗Leonhard Euler: Born: 1707 completes masters in philosophy: 1723 lost vision in right eye: 1735 Solved 7 bridges problem: 1736 publish Introductio in analysin infinitorum, volume 1: 1748 [2] Euler-Bernoulli Beam Theory: 1750 Euler's Formula (geometry): 1750 [1] publish Institutiones calculi differentialis: 1755 [2] near total blindness: 1766 publish Theoria motuum…
on “Can't solve a quintic? Galois Theory in 1500 words” ↗…ignoring the problem of the fact that many other functions have precisely the same zeros. But Euler was not, in fact, always so glib in presenting this argument! For example, in Volume 1, Chapter 9 of his Introductio in Analysin Infinitorum (translation by Ian Bruce available at http://www.17centurymaths.com/contents/introductiontoanalysi...), we see that Euler argues for the product formula by noting (what would in modern notation be) that…
on “An Elementary Proof of Wallis’ Product Formula for Pi (2005)” ↗I recently learned: > It has been claimed that Euler's identity appears in his monumental work of mathematical analysis published in 1748, Introductio in analysin infinitorum. However, it is questionable whether this particular concept can be attributed to Euler himself, as he may never have expressed it. https://en.m.wikipedia.org/wiki/Euler's_identity But it is still cool.…
on “The exponential function is a miracle” ↗…said it would "create forgetfulness in the learners' souls, because they will not use their memories" (274e-275b) 2. Leonard Euler criticized the use of logarithm tables in calculating: in his 1748 "Introductio in analysin infinitorum" he insisted on deriving logarithms from first principles 3. William Thomson (Lord Kelvin) initially dismissed mechanical calculators, stating in an 1878 lecture at Glasgow University that they would…
on “Metacognitive laziness: Effects of generative AI on learning motivation” ↗