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I became interested in Euler because of his theories in Harmonics and music. Only later did I understand he is a Mathematician.In my book "Ragachikitsa " (Readworthy Publications 2008) I have mentioned some of Euler's mathematical concepts related to harmonics. The book Titled "Euler- The master of us all Vol 22 by William Duham ,published by the Mathematical Association of America, therefore roused my interest. The Title is obviously influenced by Laplace' famous Quote with which the Volume starts : Read Euler,Read Euler, He is the master of us all.Mathematics,Arts and Architecture re Intangible and they exist in the stones, in poems,music and other creations and in the human imagination or that of the creator.Though existing in imagination, they are real too when created .All creations have its own masters.Euler had been a prolific writer.From 1911 onwards a stupendous volume of 73 were published in his name. (The work of 60 years of his life).
It is not the number of books or the thickness of the Volumes alone but the content of the Books also which makes a creator a real creator. Euler's works span in several such important fields of Mathematics starting from Number Theories.The author says it was Euler who first introduced the expression
1+1/3+1/5+1/&…..+ …=0.66215 +1/2 in(α)3
Or 1-x0/0= in x14 for x>0''
Left and right side are infinite .0.66215 on right in first equation is absurdly superfluous , it seems but in the second equation it is perfectly secure.
Euler was not a commander like Washington, a Revolutionary like Robspierre, or explorer of oceans like Captain Cook but an intellectual adventurer which perfectly suits my tastes.In his childhood he had mastered languages, had a superb memory , had oratory,poetry, and a list of prime numbers were in his evergreen memory and did mental calculations without any paper or pen.In him Bernoulli found a good disciple and a mathematical genius and the Saturday classes they had together were great influence in the life of both.In the university he talked on Temperence,history of Law,and took Master's degree in Philosophy and was preparing to learn Theology since his family wanted him to be a priest.When the junior Bernoulli took the position of Chair of Mathematics he invited Euler to join the Physiology/Medicine chair (Though Euler had no learning in that field).And he joined.As a faculty in Medicine he learned Physiology.But was more interested in Physics.He wrote on cartography ,acoustics,musical harmony and many more.Such a prolific writer , is a rarity.
Mathematics:- The Basel problem to determine the exact value of infinite series was a challenge for Mathematicians.The finite geometric series :- 1+1/4+1/9+1/16+1/25+…..+1/k2+…..This number is somewhere in the vicinity of 8/5.The answer evaded Mathematicians from 1644 (when it was first introduced to Western world) till 1735 when Euler came up with solution.The series sums to π2/6.The fraction 8/5 and its integers come in Indus valley Mathematics as I had poited out elsewhere earlier. Euler dealt with the Classical Number Theory,Analytical Number Theory and Theory of Partitions and his book Mechanica deals with Motion within the framework of Calculus ,and was alandmark in the history of Physics. In the middle phase of his Professional career he shifted from St Petersburg Uty to Berlin University because of the political turmoils in Russia at that time.His two major books on Functions and on Calculus came in this period. At that time he was asked to give lessons to a German Princess Anhalt Dessau . The lectures and lessons he gave her came out as a massive volume :- Letters of Euler on different subjects in Natural philosophy addressed to a German princess . This becme an international hit instantly.At this time he discovered the famous Euler's identity dealing with sin and cos theta ( which was an ancient discovery of Indians several millennia before him).
It is sad that with all these Euler was called a Pumpkin ( aBrilliant pumpkin) byFrederick