Talk:Leonhard Euler

Expressions That May Lead to Confusion

Section 2.1 Mathematical notation, line 3: He also introduced ... the letter e for the base of the natural logarithm (now also known as Euler's number)

Section 2.5 ... describing numerous applications of ... Euler numbers

It is hard to distinguish between Euler's number and Euler number. Although there are seperate pages devoted to the two concepts, this may still lead to confusion for beginners and those who use English as a foreign language. Shouldn't there be "see also" links behind both expressions?

-- User:Dale Zhong 14:59, 7 July 2007 (GMT+0800)

Nonsensical statement about function notation

The article says (3rd paragraph of opening section):

   first employing the term f(x) to describe a function's y-axis,

That statement does not use standard terminology. A better way to say it is:

  first employing the notation f(x) for the value of the function f evaluated at x,

I could not make this change because the article is locked. — Preceding unsigned comment added by 2604:CB00:12A8:8300:1071:1719:1465:F5E5 (talk) 19:48, 1 May 2022 (UTC)

I agree. I copyedited that paragraph. I also don't see a good reason for boldfacing the mathematical notation in it. —David Eppstein (talk) 20:03, 1 May 2022 (UTC)

A Commons file used on this page or its Wikidata item has been nominated for deletion

The following Wikimedia Commons file used on this page or its Wikidata item has been nominated for deletion:

• Euler GDR stamp.jpg

Participate in the deletion discussion at the nomination page. —Community Tech bot (talk) 11:41, 22 February 2023 (UTC)

Featured picture scheduled for POTD

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Leonhard Euler (15 April 1707 – 18 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in many other branches of mathematics such as analytic number theory, complex analysis, and infinitesimal calculus. He introduced much of modern mathematical terminology and notation, including the notion of a mathematical function. He is also known for his work in mechanics, fluid dynamics, optics, astronomy and music theory. He is seen here in a painting by Jakob Emanuel Handmann (16 August 1718 in Basel – 3 November 1781 in Bern), a Swiss painter who specialized in portrait painting.

Painting credit: Jakob Emanuel Handmann; restored by Bammesk

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Square root of -1 in lead

The third paragraph of the lead states: "Euler is credited for popularizing ... the letter i to express the imaginary unit sqrt(-1)"

Would this not be more accurately re-worded to something along the lines of "popularizing ... the letter i, the imaginary unit whose square is -1"? Ediniast (talk) 06:44, 19 March 2023 (UTC)

He popularized THE USE OF the letter i for this mathematical purpose. Saying that "he popularized the letter i" without including the "to denote" part that our lead currently includes makes no sense because it was already a popular letter in the orthography of many languages. And saying "the letter i, the imaginary unit..." also makes no sense: a letter is a notation for a mathematical value, not the value itself. And it is the notation that we are crediting him for popularizing, not its value. —David Eppstein (talk) 06:49, 19 March 2023 (UTC)

I wasn't entirely clear, I apologize I meant "Euler is credited for popularizing ... the letter i, the imaginary unit whose square is -1" and got lazy writing it out, my comment was more on the nature of i being defined as a number whose square is negative one, rather than i being equal to negative one. Ediniast (talk) 06:55, 19 March 2023 (UTC)

"The imaginary unit ${\sqrt {-1}}$" is a correct description of $i$. It is an imaginary unit, and among the two imaginary units is the one identified by the principal branch of the complex square root function, the branch denoted by the square root notation. "The imaginary unit whose square is -1" is an ambiguous and inaccurate description of $i$. There are two imaginary units whose square is –1, so the use of the definite article is not justified. —David Eppstein (talk) 07:25, 19 March 2023 (UTC)