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7
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How was Riemann's essay on the foundations of geometry misjudged by Russell?
Jost's recent book on Riemann's famous 1854 essay claims in the introduction that Bertrand Russell misjudged Riemann's work. However, Jost does not elaborate. The index at the end of the book does not even contain an entry for Russell. What is…
Mikhail Katz
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7
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Who was the first scientist to suggest that objects can keep moving without applied force?
In the old days Aristotels argued that object needs a force to keep going in 'space'. Some philosophers, Philoponus and Buridanus (?), later argued that there was a need for some kind of 'impetus'. Did that still imply some kind of active force? Who…
Marijn
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7
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How could the people of the past be sure that $a \times b = b \times a$?
Let me quote from Terence Tao "Analysis 1":
Historically, the realization that numbers could
be treated axiomatically is very recent, not much more than a
hundred years old.
Then, how could the people who lived before the axiomatization of real…
user4633
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7
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2 answers
When was the convention for the indefinite integral $\int\frac{1}{x}dx$ changed?
In Europe, in the 20th century, $\int\frac{1}{x}dx$ equalled $\ln{x}+C$. (I have references from Poland for 1930-1947 and the UK for the 1960s and 1970s).
Now, if one mentions $\int\frac{1}{x}dx=\ln{x}+C$ in Mathematics Stack Exchange, one is…
Martin Kochanski
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7
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Who discovered L'Hôpital's rule?
Who discovered the rule of L'Hôpital?
In the Wikipedia article, it is mentioned that it was not l'Hôpital who proved the rule but that it might have been Johann Bernoulli.
I even heard something about l'Hôpital paid Bernoulli for the privilege to…
user3154270
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7
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3 answers
When did mathematicians first use the contrapositive form to prove a conditional statement?
I am reading parts of Euclid’s Elements and I am surprised, rightly or wrongly, to see that Euclid did not recognize that a conditional is logically equivalent to its contrapositive form. Indeed, one often sees one proposition immediately followed…
nwr
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7
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1 answer
Did Dedekind prove this lemma about posets (or an equivalent)?
Here's an easy lemma:
Any poset $(S, \preceq)$ is order-isomorphic to a subset of the powerset $\mathcal{P}(S)$ ordered by set-inclusion.
I seem to recall having seen this attributed to Dedekind.
Am I right that Dedekind proves this little result?…
Peter Smith
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7
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5 answers
Were matrix theory and functional analysis well-known to physicists before the invention of matrix mechanics?
Were matrix theory and analysis well-known to physicists circa 1920-1925? Did physicists make extended use of this theory in that period? The question is related to the discussion in How did Heisenberg come up with matrix mechanics? thread on…
Frobenius
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7
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What's a good resource for some of mathematics greatest controversies and debates?
We often think of mathematics as being clean-cut, with questions being settled with theorems, and not much room for disagreement. This isn't true though of course.
Going back to ancient history, we hear the story of how Pythagoras murdered the man…
Christopher King
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7
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Diagrams in early Mathematical Paper Publication
I am reading through the Dover publication of Gauss' work on curves and curved surfaces called "General Investigations of Curved Surfaces". This Dover publication presents two major papers authored by Gauss in 1827 and 1825 (the 1825 paper was…
K7PEH
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7
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2 answers
How did Albert Einstein predict the existence of gravitational waves?
From Darkest matter: gravitational waves 2016-06-19 | Espresso
But black-hole pairs orbiting one another emit something else: gravitational waves. These ripples spread outward like sound waves, ever so slightly stretching and squashing spacetime…
Curious
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7
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When and where was Electricity used for the first time?
There are references of Greeks discovering static electricity around 600 BC. Mediterranean's were also thought of having the understanding of rubbing amber rods to attract light objects like feather.
My question is when was it first used…
Amit Tyagi
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7
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When was conical refraction predicted and observed?
I was reading James Ladyman's Understanding Philosophy of Science, and came across the following consequence of Fresnel's theory of light:
The phenomenon is known as conical refraction and has now been observed many times. However, Fresnel knew…
Colin McFaul
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Is the symbol $e$ for the base of natural logarithm honoring Euler?
According to Internet (actually, Wikipedia and Wolfram MathWorld), I have two information: It was Euler who first introduced the symbol $e$ (before people used $b$); the symbol is to honor Euler.
I find this very strange. My theory is that $e$…
Hao Chen
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7
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What is rationale or history for using the symbol $\partial{U}$ to represent surface boundary?
There are many examples where the notation of $\partial{U}$ is used to represent the surface boundary of some volume $U$. For example, the following representation of the Divergence Theorem:
$$
\int_U{\nabla \cdot \mathbf{F}}\,dV =…
K7PEH
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