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How much did the ancient Greeks know of non-Euclidian geometry?

They knew the Earth was a sphere, and Eratosthenes even computed the radius. Menelaus and possibly Hipparchus knew that the angles inside a triangle add to more than $\pi$ on a sphere. Did they have ...
thedude's user avatar
  • 101
3 votes
0 answers
34 views

Sparse matrix ("matrice creuse") etymology in French

I am looking for the etymology of matrice creuse. According to wikipedia, it seems James Joseph Sylvester used the term "matrix" in 1850, and Harry Markowitz used the term "sparse ...
Fnifni's user avatar
  • 131
3 votes
1 answer
45 views

When was Kelvin's vitalism rejected in physics?

In 1851, in one of the most famous publications in the history of thermodynamics, On the Dynamical Theory of Heat, with numerical remits deduced from Mr JOULE'S equivalent of a Thermal Unit. etc., ...
hyportnex's user avatar
  • 337
12 votes
3 answers
4k views

Did Alan Turing know the German language?

In the film "The Imitation Game" Alan Turing, while being interviewed at Bletchley Park, confesses that he doesn't speak German, which almost makes him fail the interview. I think I read ...
bereal's user avatar
  • 223
0 votes
1 answer
46 views

Earth's and Sun's rotation in the Ptolemaic world

In Ptolemy's geocentric model the Sun travels through the ecliptic and around the Earth once every 24 hours and the Earth does not rotate about its axis. What is Ptolemy referring to when he talks ...
Adrien Hingert's user avatar
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0 answers
42 views

How likely is it that a first-century man could have survived having a piece of wood embedded in his body in a way that could not be removed? [closed]

In the New Testament of the Bible, the apostle Paul wrote, And lest I should be exalted above measure through the abundance of the revelations, there was given to me a thorn in the flesh, the ...
Someone's user avatar
  • 101
4 votes
2 answers
669 views

When and why was the concept of "having a least upper bound" dubbed "completeness", as in Axiom of Completeness?

The Axiom of Completeness states that any non-empty set with an upper bound has a least upper bound. When and why was this concept of least upper bound dubbed "completeness"? It's true, of ...
SRobertJames's user avatar
1 vote
0 answers
31 views

Understanding Ptolemy's Almagest

This is an extract from page 138 of Ptolemy's Almagest (Toomer): [Hipparchus] made a very accurate observation of the autumnal equinox, and says that he calculated that it occurred at midnight, third-...
Adrien Hingert's user avatar
1 vote
0 answers
49 views

What does Dedekind mean by "laws characteristic for the concepts"?

I’m slightly confused by what Dedekind means by “characteristic for the concepts they designate” in the quote below: "But [. . . ] these extensions of definitions no longer allow scope for ...
Jerry's user avatar
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0 answers
46 views

What are the wrong assumptions made in Anagaxoras' model in his calculation of Earth-Sun distance?

The greek mathematician Anaxagoras made an inacurrate evaluation of the distance between the Sun and the Earth. I've been thinking about his work and would like to know what exactly was wrong about ...
niobium's user avatar
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0 answers
27 views

Notation for Propositional values in Church's "Simple Theory of Types"

In Alanzo Church's "A Formulation of the Simple Theory of Types" (The Journal of Symbolic Logic 5 no.2 (1940) 56--68, DOI:10.2307/2266170), he adopts the ...
Alex Nelson's user avatar
0 votes
1 answer
59 views

Was it understood in the first century AD that some diseases are sexually transmitted?

Did physicians in the first century AD understand that some diseases are sexually transmitted? Would a typical well-educated person who was not a physician have likely known this?
Someone's user avatar
  • 101
0 votes
0 answers
44 views

Is complete materialism essential for scientific progress? [closed]

A common argument against any hint of non materialism in science, be it idealism, supernaturalism, substance dualism, etc. is that complete materialism is essential for making scientific progress. I ...
yters's user avatar
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1 vote
1 answer
57 views

What's the history of the use of crude oil for transportation before the Industrial Revolution?

What's the history of the use of crude oil for transportation before the Industrial Revolution? Wiktionary says the Latin word petroleum, from petra (“rock”) + oleum (“oil”), is medieval Latin, so ...
Geremia's user avatar
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0 votes
1 answer
67 views

Data that motivated early discussions about the mean and about error distributions

The way in which scientists should deal with errors in observations of natural phenomena was a subject of much debate over a period of about 150 years between around 1720 and 1870. The history is well ...
CrimsonDark's user avatar
1 vote
0 answers
67 views

Archimedes on hornangles?

Did Archimedes ever discuss hornangles? A hornangle (also known as angle of contingence, etc.) is the "crevice" between the circle and its tangent line at a point (from the modern viewpoint, ...
Mikhail Katz's user avatar
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1 vote
0 answers
65 views

Did the principle of permanence have an influence on mathematicians like Dedekind and Cauchy?

Around the time when mathematics was becoming formal, the notion of detaching from attaching "contextual interpretation" to symbols in algebra, up to the point of avoiding inconsistency (...
Demon's user avatar
  • 31
0 votes
0 answers
63 views

How did the Ancient Greek gears look like (identify this)

I've noticed these gear-like Ancient Greek items in a local museum annotated along the lines of "decorative clothing pins". These don't look like much decorative to me (too symmetric for ...
alamar's user avatar
  • 101
4 votes
1 answer
347 views

What were Auguste Comte's contributions to mathematics (if any)?

Auguste Comte is often described (e.g., on Wikipedia) as a “mathematician” besides being a philosopher of science. I am aware that he taught mathematics (he was at various times a répétiteur and/or ...
Gro-Tsen's user avatar
  • 399
17 votes
1 answer
1k views

Did Ronald Fisher ever say anything on varying the threshold of significance level?

There has been a growing chorus against the conventional NHST (Null Hypothesis Significance Testing). One thing is the blind usage of a monolithic significance level $5\%.$ In a recent thread at CV, ...
User1865345's user avatar
0 votes
0 answers
62 views

A brief history of Geometry [closed]

I'm looking for a relatively quick summary (about a page or between 1 and 2 pages) of the origins of Geometry in the ancient world and its main applications then, plus a few key breakthroughs that ...
Nate's user avatar
  • 1
0 votes
0 answers
44 views

Where is Fock on Klein-Gordon equation?

I was researching a bit about the history of the famous Klein-Gordon equation and I found out that Fock also independently discovered it in the same year as Klein and Gordon, 1926. However, ...
Jimeens's user avatar
  • 101
2 votes
0 answers
45 views

When was the parity of a permutation first understood?

In combinatorics, it is well understood that a permutation has a parity or sign: each permutation is either odd or even (sometimes described as negative and positive, respectively). Composing two ...
richard's user avatar
  • 121
2 votes
0 answers
93 views

I would like to read about Euler's view on negative numbers

So, I've been over fixated on negative numbers lately. I'm coming to the conclusion that, mathematics is usually progressed if it is "useful". The more "useful" a mathematical ...
Demon's user avatar
  • 31
14 votes
9 answers
4k views

Works of scientists, philosophers and mathematicians that (re)surfaced after a long time

Sometimes, for one reason or the other, the works of scholars get lost. In some cases, they're lost forever. This happened to many books during the fire of the library of Alexandria, for instance. ...
Max Muller's user avatar
0 votes
1 answer
97 views

Why and how did the study of complex numbers progress despite the denial of negative numbers?

I am going over some history of the complex numbers, and two things baffle me (and they are not mathematics). From Cardano's time to around the 18th century, negative numbers were not accepted by all ...
James's user avatar
  • 1
1 vote
0 answers
65 views

What paper or papers about molecules did Heisenberg "like", and what has Heisenberg published or otherwise commented about it?

In the 2023 film Oppenheimer based on the 2005 biography American Prometheus by Kai Bird and Martin J. Sherwin, there seems to be two references to work by Oppenheimer on molecules: RABI: I caught ...
uhoh's user avatar
  • 2,163
1 vote
0 answers
101 views

Relationship between electromagnetic and topological invariant

I read 17 equations that changed the world by Ian Stewart. This book provides information about the correlation between electromagnetic force and topological invariant. The idea of a topological ...
user1274233's user avatar
2 votes
0 answers
85 views

Origin of "Sierpinski space"?

Nowadays the unique 2 point, nondiscrete, nontrivial topological space goes by the name of the Sierpinski space. How did that space come to be named after Sierpinski? The comments to this MathOverflow ...
Lee Mosher's user avatar
-1 votes
0 answers
52 views

When was it the negative numbers were accepted as “negatives” instead of “subtractions” in European Mathematics?

After Cordano and Bombelli had ways of dealing with “subtractions” and “imaginary” numbers. John wallis published a book where he examined “negatives” motivated by physical and scientific applications ...
Fraser's user avatar
  • 19
1 vote
3 answers
108 views

How were complex analysis methods, like the Joukowsky transform, used in early aircraft design?

The Joukowsky transform is a conformal mapping of a disk to an airfoil shape. The wiki page says that "it was historically used to understand some principles of airfoil design". That's kind ...
Daniel Shapero's user avatar
1 vote
1 answer
79 views

Black body radiation before Hertz's observation?

From the timeline of Maxwell's prediction 1865 and Hertz's observation in 1887 that gave an understanding of the light wave as EM wave, How did the Black body radiation study understand the emitted ...
Kanokpon Arm's user avatar
0 votes
0 answers
111 views

How did negative numbers “force themselves” onto Cardano, and was it analogous to how imaginary numbers were forced upon him?

I was reading “A brief history of numbers” by Corry, but I came across a part that confused me. Cardano accepted the law of signs for “subtractions” proposed by an older group of Italian ...
Fraser's user avatar
  • 19
2 votes
1 answer
161 views

Did Rafael Bombelli write any commentary about his rules for arithmetic involving negative numbers?

Rafael Bombelli was the first European mathematician to write about the laws of arithmetic for negative numbers. On Wikipedia I read that he wrote: “Minus 5 times minus 6 makes plus 30”. I also read ...
Fraser's user avatar
  • 19
1 vote
2 answers
205 views

Motivation and history of singular homology

Among the many cohomology theory's branches I asked about last time, I was curious about $d^2=0$ because I know that it is the formula that is the basis of all cohomology. So this time, I would like ...
user1274233's user avatar
1 vote
0 answers
76 views

Why is the Feynman propagator named after Feynman?

In his book Surely You're Joking, Mr. Feynman!, Feynman himself says that he did not know how to compute contour integrals. To give a direct quote, he says: One thing I never did learn was contour ...
CBBAM's user avatar
  • 111
3 votes
1 answer
130 views

History of cohomology theory

I saw this post. And I already posted it on Math stack exchange, but since someone recommended this site, I'm refining it and posting it again. And I understand that the mathematical object called ...
user1274233's user avatar
3 votes
0 answers
87 views

Width of zodiac

Why is conventional width of zodiac set to 16 degrees (8 degrees at both sides of ecliptic), see for example this Taurus plate from Bayer's Uranometria? I assume that the planet which defines the ...
Leos Ondra's user avatar
1 vote
0 answers
66 views

How exactly did Auguste Bravais come up with the regression line?

I am new to statistics and linear regression and I came across the face that auguste bravais discovered regression line but didn't realize it. Auguste Bravais (1811-1863), professor of astronomy and ...
Alexander's user avatar
  • 123
0 votes
0 answers
44 views

History on ancient thoughts regarding bones and blood

I heard a story about how ancient people believed that fathers contributed to the white things in a child (bones), while mothers contributed the red matter (blood). However, I found no reference ...
phk's user avatar
  • 101
4 votes
2 answers
441 views

Who was the inventor of the 18-electron rule?

According to Wikipedia, the first person who proposed 18-electron rule was American chemist Irving Langmuir, but the rule is widely known by the name Sidgwick's rule. I cannot find any information ...
Seiji's user avatar
  • 43
3 votes
1 answer
111 views

Mathematization of natural sciences

When was a mathematical formula (instead of just words) used for the 1st time in natural sciences to describe a natural phenomenon?
Sedat Olcer's user avatar
4 votes
1 answer
140 views

What is the history of vector bundles and their characteristic classes?

The theory of vector bundles (and their characteristic classes) appears to have been standardized in the 20th century by all of the familiar names. Considering its substantial importance throughout ...
user19642's user avatar
2 votes
1 answer
145 views

Height function following Borel

Borel introduces the notion of hauteur (French for 'height') in a note titled Sur l'approximation les uns par les autres des nombres formant un ensemble dénombrable in the Comptes Rendus journal in ...
Sam Sanders's user avatar
1 vote
1 answer
103 views

David Hilbert's paper: Substitution of the group of cyclotomic field

A question about a notation in David Hilberts's "Ein neuer Beweis des Kroneckerschen Fundamentalsatzes über Abelsche Zahlkörper" (here a german online available source, not sure if there ...
user267839's user avatar
2 votes
0 answers
108 views

What were Cantor’s “real numbers of higher type”?

In the preamble to “Essays on the Theory of Numbers”, Dedekind makes passing reference to a theory (expounded in Cantor’s “Ueber die Ausdenung eines Satzes aus der Theorie der trigonometrischen Reihen”...
James Propp's user avatar
0 votes
1 answer
135 views

Would they have known you can't go faster than light in 1790 [duplicate]

I came across this short: https://www.youtube.com/shorts/LjBaPxutpQo where Brian Cox says the idea of black holes dates back to 1790. It stemmed according to it from escape velocity and that you could ...
Rohit Pandey's user avatar
0 votes
0 answers
101 views

A brief history of "delocalization" of electrons

I have been studying the concepts of "resonance" and "mesomerism" recently and a common principle of these concepts is the "delocalization" (of electrons, molecular ...
Bhavya Jain's user avatar
0 votes
0 answers
88 views

History of Bernoulli numbers

I have been trying to understand what is the meaning of Bernoulli numbers, but to my mind it has been obscured behind complicated formulas without much explaination. I presume finding the history ...
Gustamons's user avatar
3 votes
1 answer
345 views

Ancient drawing board in mathematics

According to Van Der Waerden's "Science Awakening", it was common for Ancient Greek mathematicians to use a board filled with sand to draw their figures, ie : But the ancients made their ...
Slereah's user avatar
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