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When was string theory first heralded as a theory of everything?
Today, string theory is considered one of the leading candidates - perhaps the leading candidate - for a theory of everything. I'm guessing it wasn't always that way, but I haven't figured out just when this hope was kindled in the hearts of string…
HDE 226868
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Was Paul Cohen a student or assistant of Gödel?
In The Man Who Loved Only Numbers, a biography about Paul Erdős, by Paul Hoffman, the author claims that Paul Cohen was "Gödel's former assistant" (p 225). However, I can't find any other sources corroborating the claim, and while I don't know much…
Kevin Long
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Who was (were) the first mathematician(s) who did not doubt the empty set?
Today there is no doubt that the empty set for the whole of mathematics is as reasonable and useful as zero for arithmetic. This however was not always the case, and surprisingly even Zermelo, who based his infinite set on the empty set, was unsure.…
Franz Kurz
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When did people realize that the eye was a lens?
All in the title:
When did scientists realize that our eye functions like a lens/magnifying glass?
EigenDavid
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Who was the first to use the "does not exist" sign ∄?
Who was the first to use the "does not exist" sign ∄? I'm aware that Giuseppe Peano originated serifed ∃ and, moreover that Whitehead and Russell repurposed Peano's serifed ∃; I'm also aware that Gerhard Gentzen introduced the ∃ sans serif (and used…
אהרן רובין
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How was the sum of squares formula discovered by Archimedes?
AFAIK, Archimedes is credited with discovering the following formula for computing the sum of squares:
$$1^2 + 2^2 + 3^2 + \cdots + n^2 = \frac{n(n+1)(2n+1)}{6}$$
This seems to have come up in his quest for finding the area of a parabolic segment. I…
PhD
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Are there any canonical books on history of science?
I was looking for some fundamental books on history of science. I picked Thomas Kuhn book "The Structure of Scientific Revolutions" but it's not exactly about history of science - it's more on methodology and philosophy of science. Can you recommend…
Sergey
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What did Fermat do as a lawyer?
Fermat is easily one of the best known mathematicians of all time. We all know about Fermat's Last Theorem, Fermat's Little Theorem, his quadrature rule, his invention of probability theory, etc. Every introduction of Fermat, however, mentions that…
Joel
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When did the name “Boltzmann constant” prevail, and how?
This question is prompted by (comments at) another one. There, I was surprised to find that despite traditional claims to the contrary, Boltzmann himself did once write his formula $S=k\log W$:
$\hspace{11em}$
That’s in his book (1898, §61, p. 172),…
Francois Ziegler
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Could scientists of Newton's time have explored the limits of his laws of motion?
As noted on this Wikipedia page Newton's laws of motion and of gravity were "verified by experiment and observation for over 200 years" and found to be a "good approximation for macroscopic objects under everyday conditions". Now, of course, we know…
TripeHound
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Has Chinese Remainder Theorem ever been used by Chinese military?
The Chinese Remainder Theorem says, in rough terms, that if you know the remainders of an integer $n$ modulo $m_1,m_2,\dots,m_r$, you also know $n$ modulo $\mathrm{lcm}(m_1,m_2,\dots,m_r)$.
In the mathematical folklore, I've often heard it…
Jakub Konieczny
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(Co)Homology: From topology to the rest of mathematics?
I can appreciate how (co)homology arose in the context of topology/geometry. Trying to get a handle on the handles of spaces leads one to this idea. It's not obvious, but I can see how this would lead you to homology.
But how does one…
User0112358
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Whence “homomorphism”, “homomorphic”?
The kernel question leads to another : Today, homomorphism (resp. isomorphism) means what Jordan (1870) had called isomorphism (resp. holoedric isomorphism). How did the switch happen?
“Homomorphic” appears e.g. in de Séguier (1904, pp.…
Francois Ziegler
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How did Eratosthenes knew the exact time of the day?
Eratosthenes measured the radius of the Earth with an incredibly accuracy.
To do it, you need to measure the length of the shadows from 2 different cities at the same time of the day. Then knowing the distance between the cities and a little bit of…
Elerium115
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Are there well-known mathematicians who shared Arnold's view about mathematics as natural science?
V. I. Arnold asserted that mathematics is a natural science:
Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap.
V.I. Arnold: "On teaching…
Franz Kurz
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