New discoveries in the history of Euler’s equation
Abstract
Abstract. Much has been written about the history of Euler’s formula and Euler’s equation, but there are
many blank spots left in it. The equality ln(cosx + isinx) = xi was first obtained in verbal form forty-two
years before it appeared in Euler’s work. Was this verbal formula correct? Euler’s equation or Euler’s
identity eiπ = −1 was never written down by Euler himself. Rewritten in the form eiπ + 1 = 0, it connects the
five most important numbers in mathematics, but this formula is not in Euler’s works.Today this identity
attracts wide attention from physicists, philosophers and popularizers of science; it is given an almost
mystical meaning. Who received it for the first time? We will look at all these mathematical events in order.
many blank spots left in it. The equality ln(cosx + isinx) = xi was first obtained in verbal form forty-two
years before it appeared in Euler’s work. Was this verbal formula correct? Euler’s equation or Euler’s
identity eiπ = −1 was never written down by Euler himself. Rewritten in the form eiπ + 1 = 0, it connects the
five most important numbers in mathematics, but this formula is not in Euler’s works.Today this identity
attracts wide attention from physicists, philosophers and popularizers of science; it is given an almost
mystical meaning. Who received it for the first time? We will look at all these mathematical events in order.
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