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18
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Why isn't Feynman's path integral taught more widely and earlier in today's academic physics curricula?
Anyone who has studied Feynman's path integral will know that it makes quantum mechanics more like classical mechanics. A student who has learned about the Lagrangian will easily understand the concept of quantum mechanics through the path integral…
Ooker
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Did Archimedes use epicycles in his planetarium?
Archimedes constructed a planetarium where as described by Cicero "he had thought out a way to represent accurately by a single device for turning the globe those various and divergent movements with their different rates of speed. And when Gallus…
Conifold
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What did Kurt Gödel mean by nonstandard analysis being "the analysis of the future"?
I found this:
There are good reasons to believe that nonstandard analysis, in some version or other, will be the analysis of the future.
What exactly did Kurt Gödel mean?
copper
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How was the Möbius strip discovered?
Britannica is terse:"Möbius discovered this surface in 1858. The German mathematician Johann Benedict Listing had discovered it a few months earlier, but he did not publish his discovery until 1861". Möbius never published the discovery, it was…
Conifold
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18
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Considered a breakthrough at its time – almost forgotten nowadays
In the comments on this question on Physics about the usefulness of expensive experiments such as the CERN, the following short discussion happened:
Has there ever been a major basic science result that did not lead to practical applications within…
Wrzlprmft
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Did Guinness Book of Records screw up on the "longest-standing maths problem (ever)"?
Did they screw this up? It says that Fermat's Last Theorem was the longest open problem - with only 365 years. See Guinness Book of Records. However, there are Greek problems that were longer open:
Squaring the circle, proposed before 428 BCE…
wythagoras
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Why don't we learn Buridan's laws of motion?
My question is why has Jean Buridan faded into obscurity while Newton is venerated as a God by scientists? Here is a description of Buridan's impetus theory:
The concept of inertia was alien to the physics of Aristotle.
Aristotle, and his…
Neil Meyer
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18
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Was 18th century algebra more symbolic/formal than the modern conception?
I've found Lagrange's Sur la résolution des équations algébriques to be a very confusing and difficult read, and I think I'm starting to see why: it seems that Lagrange thinks of algebra in a much more formal/symbolic way than I'm used to. Whereas I…
Jack M
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Examples of Kuhn loss?
A Kuhn loss is:
a success, empirical or theoretical, of a prior theory – or paradigm as Kuhn would have preferred – that does not carry over to the theory or paradigm that replaced it. [Midwinter and Janssen, see below.]
Kuhn introduced the…
Michael Weiss
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Who calculated for the first time the volume (and surface area) of the sphere exactly?
As we know, even Archimedes did soon some experimental calculations.
My question were, who calculated first time the exact formulas ($V=\frac{4\pi}{3}r^3$, $A=4\pi r^2$)?
As I know, these formulas require the higher understanding of differential…
peterh
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Secrecy in Mathematics
I've been told that Pythagoreans kept as a secret the incommensurability of certain quantities like the diagonal of the square. Are there other mathematical discoveries whose authors didn't want the public to learn or know about?
Leandro Caniglia
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Is the story about Fermat's writing on a margin true?
Is there any evidence that Fermat wrote on the margin of a book "I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain." Everyone repeats this, but is there an image of the note? And did…
Wynne
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Who discovered smooth non-analytic functions of a real variable?
Some functions of a real variable are infinitely smooth (have derivatives of all orders) but are not analytic (at some points $a$, the Taylor series at $a$ does not represent the function at any interval around $a$). All sources, such as Wikipedia…
user145
17
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Is the prime notation for derivatives $f'$ due to Euler?
Cajori, the website on Earliest Uses of Symbols of Calculus and many other sources claim that Lagrange introduced the notation $f'(x)$ for the derivative of $f(x)$ with respect to $x$. But I see Euler using it 1748 in Sur la vibration des cordes p.…
Michael Bächtold
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How did the publication feat of Einstein's four 1905 Annus Mirabilis papers get through peer review?
Einstein's early career is well-known for the lack of success he had applying for assistant lecturer positions with universities; he could not get a position, and he ended up working in a Bern patent office, in large part because his academic record…
DBS
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