History of Science and Math Stack Exchange
History of Science and Math Stack Exchange

Most Popular

more tags
1500 questions
8
votes
2 answers

Did Euler ever write $f(x)$, with parentheses?

Euler is often credited with introducing the notation $f(x)$, and people cite the example $f(\frac{x}{a}+c)$, where he had to use parentheses around the function argument. On the other hand, when the argument was a single letter like $x$, I have…
Michael Bächtold
  • 1,775
  • 14
  • 24
8
votes
7 answers

Seeking sources: Catholic church and the development of mathematics

I teach mathematics at a Catholic liberal arts college. This semester, I am teaching Real Analysis and I want students to complete a semester-long research project that extends beyond the course content and into relevant issues of history and…
Brendan W. Sullivan
  • 191
  • 7
8
votes
2 answers

Is Spivak right in what he says about Galileo?

On chapter 9 of M. Spivak's book on calculus there is an exercise in which Spivak asks the reader to prove that Galileo "got his facts wrong". More specifically, Spivak asks one to to show if a body falls a distance $d(t)$ in $t$ second and…
Jamai-Con
  • 271
  • 1
  • 4
8
votes
0 answers

\mathbb versus \mathbf

When was the use of \mathbb popularized as an alternative to \mathbf? Of course there are the subjective preferences of certain authors, but when I read older articles, there appears to be an almost unanimous usage of what we would think of as…
AnotherPerson
  • 309
  • 2
  • 6
8
votes
3 answers

Origin of operators in quantum mechanics

Historically, where did the concept of operators in quantum mechanics come from? How did people first understand that momentum operator should be of the form of $i \hbar \frac{{\rm d}}{{\rm d}x}$? Also how did they find the expression for kinetic…
user157588
  • 205
  • 1
  • 4
8
votes
4 answers

Why did Euclid Avoid Using the 5th Postulate?

In Euclid's elements, some of the theorems (e.g. SAA congruence) can be proven using the parallel postulate, much easier than without it. But it seems that Euclid has intentionally avoided using it, when possible. Am I right? What is the reason…
user2321323
  • 181
  • 2
8
votes
2 answers

What did Farcas Bolyai write to his son?

There are famous quotes about what Farcas Bolyai wrote to his son Janos to persuade him not to study the "theory of parallels " or what is now known as hyperbolic geometry But not all translation of this quote are the same. What was originally…
Willemien
  • 303
  • 1
  • 8
8
votes
1 answer

Paul Erdos' quote "Mathematics is not yet ready for such problems"

It is believed, and often cited, that in relation to the Collatz conjecture Paul Erdos once said "Mathematics is not yet ready for such problems". However, I have not found any credible reference for this. Is it rumor, common misconception or the…
Klangen
  • 265
  • 2
  • 6
8
votes
1 answer

Why is Dirichlet's L-function called "L-function"?

In analytic number theory, the function $$ L(s,\chi_m) = \sum_{n=1}^\infty \frac{\chi_m(n)}{n^s}. $$ is called the Dirichlet L-function and has many important uses in the study of prime numbers. In particular, if $\chi_1$ is the trivial Dirichlet…
Klangen
  • 265
  • 2
  • 6
8
votes
2 answers

Did Gauss know Jacobi's four squares theorem?

In pp. 283–285 of volume 2 of Dickson's “history of the theory of numbers” appear several formulas of striking similarity: some of them are stated by Gauss (p. 283) and some are stated by Jacobi (p. 285); they are actually the same and only the…
user2554
  • 4,409
  • 1
  • 13
  • 21
8
votes
2 answers

Did the ancient Greeks have zero in their number system?

I was taught that the Arabs introduced zero in their Arabic numerals and it was depicted as a decimal point. They got their number system from India in turn in Sanskrit where the zero digit was also used. Roman numerals, however, didn't have a zero…
0tyranny0poverty
  • 183
  • 1
  • 1
  • 4
8
votes
1 answer

Gauss accused of witchcraft: apocryphal?

I recall reading years ago in a linear algebra book that Gauss was accused of witchcraft for his (re)discovery of what we now call the row reduction algorithm for solving linear equations. Has anyone else encountered the same story? Is there…
Paul Siegel
  • 1,031
  • 8
  • 17
8
votes
6 answers

Instances of suppression of scientific ideas

I have started to compile a list of instances of suppression of scientific ideas in history. Up to now I have collected the following points: According to Dioganes Laertius Anaxagoras was imprisoned and then exiled because of impiety. He had…
Franz Kurz
  • 1
  • 1
  • 5
  • 23
8
votes
1 answer

Origin of the latitude 36 of Eratosthenes

How did Eratosthenes come up with the latitude 36 line, also called 36th parallel north, in the Mediterranean world? Rhodes was one of the navel points in his calculations and even today N36.00 goes through the southern part of the Rhodes. So I'd…
MarkokraM
  • 183
  • 3
8
votes
1 answer

Why is the action from the principle of least action traditionally denoted $S$?

In theoretical physics, a Hamiltonian is traditionally denoted by some variant of $H$, a Lagrangian is some variant of $L$, but why is an action always some variant of S (as opposed to, say, $A$)? Does the letter refer to a particular person, place,…
Mark B
1 2 3
…
99 100