Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [math-history]

Use this tag for questions concerning history of mathematics, historical primacies of results, and evolution of terminology, symbols, and notations. Consider if History of Science and Mathematics Stack Exchange is a better place to ask your question.

The tag is intended to be used for questions concerning the history of mathematics, historical primacies of results, and evolution of specific terminologies, symbols and notations. Please keep in mind that, for pure historical purposes, it may well be a better to ask your question on the dedicated History of Science and Mathematics site instead.

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What are some examples of notation that really improved mathematics?

I've always felt that the concise, suggestive nature of the written language of mathematics is one of the reasons it can be so powerful. Off the top of my head I can think of a few notational conventions that simplify problem statements and ideas,…
Patrick
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Why did mathematicians take Russell's paradox seriously?

Though I've understood the logic behind's Russell's paradox for long enough, I have to admit I've never really understood why mathematicians and mathematical historians thought it so important. Most of them mark its formulation as an epochal moment…
Uticensis
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Motivation of irrationality measure

I have a question about the irrationality of $e$: In proving the irrationality of $e$, one can prove the irrationality of $e^{-1}$ by using the series $$e^x = 1+x+\frac{x^2}{2!} + \cdots + \frac{x^n}{n!}+ \cdots$$ So the series for $e^{-1}$ is…
Damien
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Are half of all numbers odd?

Plato puts the following words in Socrates' mouth in the Phaedo dialogue: I mean, for instance, the number three, and there are many other examples. Take the case of three; do you not think it may always be called by its own name and also be called…
Jon Ericson
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Past open problems with sudden and easy-to-understand solutions

What are some examples of mathematical facts that had once been open problems for a significant amount of time and thought hard or unsolvable by contemporary methods, but were then unexpectedly solved thanks to some out-of-the-box flash of genius,…
Damian Reding
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What did Alan Turing mean when he said he didn't fully understand dy/dx?

Alan Turing's notebook has recently been sold at an auction house in London. In it he says this: Written out: The Leibniz notation $\frac{\mathrm{d}y}{\mathrm{d}x}$ I find extremely difficult to understand in spite of it having been the one I …
Matta
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Why, historically, do we multiply matrices as we do?

Multiplication of matrices — taking the dot product of the $i$th row of the first matrix and the $j$th column of the second to yield the $ij$th entry of the product — is not a very intuitive operation: if you were to ask someone how to mutliply two…
msh210
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What is the smallest unknown natural number?

There are several unknown numbers in mathematics, such as optimal constants in some inequalities. Often it is enough to some estimates for these numbers from above and below, but finding the exact values is also interesting. There are situations…
Joonas Ilmavirta
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Do mathematicians, in the end, always agree?

I've been trying to study some different sciences in my life, ranging from biology to mathematics, and if I try to explain to people why I like mathematics above the others, I think the most important reason for me is that mathematicians, in the…
Kasper
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Is zero odd or even?

Some books say that even numbers start from $2$ but if you consider the number line concept, I think zero($0$) should be even because it is in between $-1$ and $+1$ (i.e in between two odd numbers). What is the real answer?
mvar2011
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Mathematicians ahead of their time?

It is said that in every field there’s that person who was years ahead of their time. For instance, Paul Morphy (born 1837) is said to have retired from chess because he found no one to match his technique that very much resembled modern chess…
hb20007
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What are some examples of mathematics that had unintended useful applications much later?

I would like to know some examples of interesting (to the layman or young student), easy-to-describe examples of mathematics that has had profound unanticipated useful applications in the real world. For my own purposes, the longer the gap between…
Eric Tressler
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How did Hermite calculate $e^{\pi\sqrt{163}}$ in 1859?

Pretend you are in 1859. What is a fast, efficient, and accurate way to numerically evaluate constants like that to, say, 20 decimal places, using ONLY pen and paper?
Tito Piezas III
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What concept does an open set axiomatise?

In the context of metric (and in general first-countable) topologies, it's reasonably clear what a closed set is: a set $F$ is closed if and only if every convergent sequence of points in $F$ converges to a point also in $F$. This naturally…
Zhen Lin
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Example of a very simple math statement in old literature which is (verbatim) a pain to understand

As you know, before symbolic notations were introduced and adopted by the mathematical community, even simple statements were written in a very complicated manner because the writer had (nearly) only words to describe an equation or a result. What…
Cauchy
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