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History and philosophy of mathematics, biographies of mathematicians, mathematics education, recreational mathematics, communication of mathematics.
3
votes
Whence “uniform distribution”?
Mr John Pond, Esq. in the Philosophical transactions of the Royal Society of London, 1806, part II, p431: "this quantity was very uniformly distributed though the intermediate arc".
Rev. Baden Powell …
11
votes
Accepted
True origin of the term "Spline"
The Oxford English Dictionary doesn't necessarily give the earliest uses of a word. But spline with the meaning "A long, narrow, and relatively thin piece or strip of wood, metal, etc.; a slat." is q …
28
votes
How come mathematicians published in Annals of Eugenics?
One should note that in the pre-WWII period eugenics was not the dirty word that it became later. Actually it was a popular notion across the world, including in countries like the United States. The …
3
votes
What are some early examples of creation of lists / catalogues of (particularly) combinatori...
A lot of people counted Latin squares, going back to Euler (1782) and Cayley and Frolov (independently, 1890). Many of those who tried got the wrong answer. A summary is in this paper:
B. D. McKay, …
2
votes
What are some early examples of creation of lists / catalogues of (particularly) combinatori...
Jan de Vries compiled a list of cubic graphs up to 10 vertices in the 19th century. His papers (in Dutch and French) are:
J. de Vries. Over vlakke configuraties waarin elk punt met twee lijnen incid …
9
votes
History of "without loss of generality"
"But in dealing with given quantics, we may without loss of generality consider the covariant as a function of the like form with the quantic,..." — Arthur Cayley, An Introductory Memoir upon Quantics …
1
vote
Who invented the expression "pairwise different" and what is its advantage over "different"
When something is defined as a binary relation, "pairwise" is strictly-speaking required in order to apply it to a set larger than two. That's one advantage. Another is that in normal English "differ …
7
votes
Accepted
Integrating powers without much calculus
Here is a very simple proof for nonnegative integer $p$.
By elementary combinatorial reasoning, we have
$$ \sum_{j=0}^{n-1} \binom{j}{p} = \binom{n}{p+1}, $$
which is the same as
$$ \sum_{j=0}^{n-1} …
43
votes
3
answers
2k
views
History of the four-colour problem
It is stated in many places that the first published reference to the four-colour problem (aka the four-color problem) was an anonymous article in The Athenæum of April 14, 1860, attributed to de Morg …
33
votes
Titles composed entirely of math symbols
$R(4,5)=25$
B. D. McKay and S. P. Radziszowski, J. Graph Theory, 19 (1995) 309-322.
The title is also the main theorem. $R(4,5)$ is a classical Ramsey number (the one most recently determined exact …
23
votes
Mathematical habits of thought and action which would be of use to non-mathematicians
This is a sort of anti-answer. When the Unabomber Manifesto was published by the NYT, someone in sci.math (or sci.math.research) recognised the reasoning as being like that of a mathematician. I don' …