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Which mathematical concepts do not have any obvious origin outside mathematics?

Some mathematical concepts, such as that of number and that of geometrical figure, presumably originate from pre-existing notions already used by at least some non-mathematicians. Others seem to have ...
Speakpigeon's user avatar
4 votes
3 answers

Origin of modern definition of a function as a graph

In the past, I came across a very elegant direct definition (below) of a function, which is based on the fundamental concepts of triples, pairs, and sets. However, I find it difficult to search the ...
Kamil Kiełczewski's user avatar
2 votes
0 answers

The habit of definition

G. H. Hardy wrote (apropos of the task of assigning values to divergent series): It is plain that the first step towards such an interpretation must be some definition, or definitions, of the 'sum' ...
James Propp's user avatar
2 votes
0 answers

Peano's question about how to define a definition

In Wikipedia’s Peano entry I find the following quote: [In] the First International Conference of Philosophy [Peano] presented a paper which posed the question of correctly formed definitions in ...
zeynel's user avatar
  • 307
3 votes
2 answers

What's the difference between Galileo's "impeto" and "momento"?

In Galileo's Two New Sciences, he describes an experiment demonstrating pendulum motion and how the pendulum will rise to the same height from where it started its fall. This discussion can be found ...
Andrew R.'s user avatar
  • 685
2 votes
2 answers

Definition and name change of the oscillation function

I have two related questions: Who first defined the oscillation function (perhaps under a different name)? When did the switch from the phrase "saltus function"(*) to "oscillation ...
Alp Uzman's user avatar
  • 347
1 vote
2 answers

What is the difference between Newton's definitions and axioms?

What is the difference between definition and axiom? For instance, Newton's Definition 1 reads: (Cohen p. 403) Quantity of matter is a measure of matter that arises from its density and volume ...
zeynel's user avatar
  • 307
3 votes
1 answer

Examples of mathematical definitions motivated by engineering problems

I'm interested in the development of mathematical definitions for the sake of engineering, and what makes a particular definition better suited for a problem than another in any particular context. ...
melembroucarlitos's user avatar
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What does P. G. Tait mean by "double points"?

I am reading the following short paper: P. G. Tait. Some elementary properties of closed plane curves. Messenger (2) 6 (1877), 132–133. JFM 09.0393.01 Here, Tait writes The closed curves ...
The Amplitwist's user avatar
4 votes
0 answers

Why did the mathematical community settle on these properties to define a topology?

The following post is long, but I decided to write more rather than less in case it's helpful. I tried to make it clear, quick, and easy to skip to the short version of my question, so the reader can ...
Addem's user avatar
  • 511
0 votes
1 answer

Motivation behind original definition of metre? [duplicate]

The first original definition of the metre, presented by the French Academy of Sciences in 1795 is: The length of the metre is one ten-millionth of the Earth quadrant, the distance from the North ...
Sasha's user avatar
  • 171
2 votes
1 answer

History of the definition of complex derivative

Almost all of modern complex analysis (Cauchy residue theorem, analytic continuation, etc) depend on the definition of a complex derivative. That definition requires the derivative at a point $z_0$ is ...
Penelope's user avatar
  • 415
3 votes
1 answer

When were equivalence classes formalized?

Neither wikipedia or the first few pages of Google are showing me much about the history of the development of equivalence classes. When was this notion first formalized? Footnote: I originally asked ...
Galen's user avatar
  • 309
2 votes
2 answers

What did Euclid mean by a straight line in his time?

The third and fourth definitions in Euclid's Elements say: The ends of a line are points. A straight line is a line which lies evenly with the points on itself. The fourth definition is usually ...
Euclid Looked On Beauty Bare's user avatar
6 votes
1 answer

Definition of ordinal multiplication

The ordinal multiplication $\cdot$ can be defined recursively via ordinal addition $+$ for any ordinal $\alpha$ as follows: $\alpha\cdot 0=0$. $\alpha\cdot (\beta+1)=\alpha\cdot \beta+\alpha$ for any ...
modnar's user avatar
  • 575