Questions tagged [euler]

Question 1

I've been reading Gautschi's brief biographical review of Euler in which he quotes Euler's autobiography (as provided in Fellmann's biography of Euler) a passage about Euler's study with Johann ...

Question 2

(posted & answered, then closed in MSE) I've been interested in the Basel problem and its famous solution $$ \sum_{n=1}^{\infty}{\frac{1}{n^2}} = \frac{\pi^2}{6}. $$ Recently I saw this video ...

Question 3

If $n$ is a positive integer then there is a monic irreducible polynomial $f(x)$ such that if $p$ is an odd prime not dividing $n$ nor the discriminant of $f$ then $$ p=x^2+ny^2\iff \left(\frac{-n}{p}\...

Question 4

So, I've been over fixated on negative numbers lately. I'm coming to the conclusion that, mathematics is usually progressed if it is "useful". The more "useful" a mathematical ...

Question 5

In DOI: 10.4236/ahs.2020.94019 235 Advances in Historical Studies, p.234 D’Alembert and the Wave Equation: Its Disputes and Controversies, or https://www.scirp.org/pdf/ahs_2020112716312281.pdf p.6 of ...

Question 6

In a previous question on this website: What was Euler's first language?, Alexandre Eremenko wrote the following about Leonard Euler: There is little doubt that he also learnt French in his ...

Question 7

In §4 of the Stanford Encyclopedia of Philosophy article on continuity and infinitesimals, the author (John L. Bell) mentions that: ... Johann Bernoulli (1667–1748) [in a] letter of his to Leibniz ...

Question 8

Can someone please provide an early reference to the use of the continued fraction expansion of $\frac{1+\sqrt D}2$ to solve the Diophantine equation $x^2 - D y^2 = 4$ for a positive integer $D$ ...

Question 9

Euler is usually credited with denoting this number with the letter $\mathrm e$. But It seems unlikely that Euler chose the letter because it is the initial of his own name, as occasionally been ...

Question 10

I am interested in reading Euler's works. The Euler Archive contains some translated works but not all of them. I am just checking here to see if anyone know a complete translation of all of Euler's ...

Question 11

In this answer and the comments Joel David Hamkins talks about a conflict between Cantor-Hume principle and Euclid's principle. He writes: This principle [Cantor-Hume] is often defended as a ...

Question 12

Euler was a non-confrontational and deeply religious person. He was kind and could get on well with anyone. He worked under any circumstances and in any environment: “A baby on his lap, a cat on his ...

Question 13

A famous technique in the modification of integrands is the set of “euler substitutions” that provide substitutions for the structure $$\sqrt{ax^2 +bx+c}$$ That is a fairly common occurence in ...

Question 14

There is a famous legend inspired by Euler's arguments with secular philosophers over religion, which is set during Euler's second stint at the St. Petersburg Academy. The French philosopher Denis ...

Question 15

I am reading Proofs and Confirmations by David Bressoud. On page $150$ is a long excerpt by Richard Askey, from "How can mathematicians and mathematical historians help each other?" There is ...

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Questions tagged [euler]

Do we know what books Euler read/worked through while studying with Johann Bernoulli at the University of Basel?

Did Euler guess the Basel problem’s solution to be $\frac{\pi^2}{6}$?

Was Euler aware of the general form of the characterization of primes of the form $p=x^2+ny^2$ for arbitrary $n>0$?

I would like to read about Euler's view on negative numbers

Need a reference for Euler's velocity initial condition for the wave equation

Did Euler know Ancient Greek?

Did any mathematicians of the time (the 17th Century) try out an intermediary between Bernoulli's and Nieuwentijdt’s infinitesimals?

17th or 18th century use of the continued fraction expansion of $(1 + \sqrt D)/2$ to solve the diophantine equation $x^2 - D y^2 = 4$

Who first called $\mathrm e$ "Euler's number"?

Have all of Euler's works been translated?

When and why Cantor-Hume principle was universally adopted in set theory instead of Euclid's principle?

Euler: “A baby on his lap, a cat on his back — that’s how he wrote his immortal works” (origin?)

In which work did Euler invent the Euler Substitutions for a quadratic composed into a radical?

Leonhard Euler's Mathematical Proof of God [closed]

Euler's "comfortable" series

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