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What results did C. F. Gauss add to Euler’s dioptrics?
I’m a fan of C. F. Gauss but I have to be objective — I don’t understand why the classical theory of lenses is called “Gaussian optics”. I think so since it seems that almost all the results of Gauss’s treatise from 1840 were already known — the…
user2554
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When did error propagation become prominent in physics?
I think is well known that greek scientists and even founding fathers of modern science did not use error propagation in their calculations. Today, instead, is unacceptable to work out any prediction of a physical theory without giving an estimate…
Rho Phi
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5
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Where did Borel stress that $\mathbb{Q}$ being effectively enumerable by $\mathbb{N}$ is not about its size?
In the book 'Practical Foundations of Mathematics' (Paul Taylor), available online, one reads:
As Emile Borel stressed in 1908, the important observation about $\mathbb{Q}$ [that there is a bijection from $\mathbb{Q}$ to $\mathbb{N}$] is that there…
weakmoons
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"Tension" between Electromagnetism and Newton's laws
When talking about the inconsistencies in physics that led up to Einstein's discovery of relativity today's professors always say that Maxwell's discovery of the constant speed of light $c$ created a huge contradiction in physics. (namely: was…
alex
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Was an expanding universe proposed before Edwin Hubble's observations?
General relativity (1915), as I've heard it explained, describes a universe that is either shrinking or expanding. By adding a cosmological constant it can describe a universe in eternal steady state, which was favored at the time.
Were there…
LocalFluff
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History of the Fundamental Theorem of Calculus
The Fundamental Theorem of Calculus links the concepts of differentiation and integration together.
How did mathematicians of the past see the link between these two concepts? Integration is used to compute areas while differentiation is used to…
Kyoma
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Did English ever use a third (1/60 of a second) for measuring time?
An hour has been divided in sixty minutes since medieval times. During the 16th and 17th century, clocks measuring a second subdivision emerged. Today we still use the sexagesimal system for dividing hours into minutes and seconds, but below that…
gerrit
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How important was the prediction of Neptune in 1846 for the Oxford evolution debate?
The short story is that based on Kepler's and Newton's physics, in 1846 Le Verrier mathematically predicted the existence and current location of Neptune within a single angular degree, and it was observed at first attempt. It not only demonstrated…
LocalFluff
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Beware the Ides of March!
Apropos of the murder of Gaius Julius Caesar, the late V. I. Arnold told the following amusing story in pages 89-90 of his "Yesterday and Long Ago":
CAESAR AND GAULS: THE DEFENSE OF ROME FROM THE GERMANS
Long ago, Caesar gave a vivid description of…
José Hdz. Stgo.
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Evaluating the Mehrtens hypothesis concerning Felix Klein
Historian H. Mehrtens hypothesized an opposition between moderns and countermoderns in early 20th century mathematics, with the former led by Hilbert and the latter by Klein.
Hilbert's lecture at the ICM in Paris in 1900 presented 10 of the famous…
Mikhail Katz
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What was Liouville's contribution to Liouville's theorem?
Liouville's theorem asserts that the volume of phase space is incompressible. This was first shown by Gibbs 1903 but his name is mostly forgotten. The Wikipedia article says
It is referred to as the Liouville equation because its derivation for
…
Diracology
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When William Herschel discovered Uranus, who else at the time had a comparable telescope?
William Herschel built a big telescope and observed Uranus in 1781. I'm trying to figure out who else had a comparable telescope at the time, who could verify these observations?
Apparently Johan Bode could but I could not find much data about his…
DrZ214
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When was the mechanism behind seasons on Earth discovered
When was the mechanism behind seasons on Earth discovered?
I'm talking about the angle between the Earth's rotational axis and its orbital axis. I read on Wikipedia here that
Earth's obliquity may have been reasonably accurately measured as early…
Antoine
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Were ratios of incommensurable magnitudes interpreted as irrational numbers prior to Fibonacci?
I have read that a lost book by Fibonacci (a commentary on Book X of Euclid's Elements) gives a numerical treatment of incommensurable magnitudes.
Given that Fibonacci grew up in North Africa and travelled extensively throughout the Middle East…
nwr
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Who was the first person to describe turbulence in mathematical terms?
Here I found that:
Sixty years later, Russian mathematician Andrey Kolmogorov furthered
our mathematical understanding of turbulence when he proposed that
energy in a turbulent fluid at length $R$ varies in proportion to the
five-thirds power of…
Paula
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