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42 votes

Why are quaternions more popular than tessarines despite being non-commutative?

Commutativity is over-rated: in fact, it holds back bicomplex numbers: It prevents your number system characterising non-commuting operations, e.g. rotations in $3$-dimensional space, Hamilton's ...
J.G.'s user avatar
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39 votes
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What makes the right angle special enough to be distinguished in the French metric system?

"When a straight line standing on a straight line makes the adjacent angles equal to one another, each of the equal angles is right" is one of the opening definitions of Euclid's Elements. ...
Conifold's user avatar
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35 votes
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Story of a student who solves an open problem

That's John von Neumann, about whom George Pólya wrote: There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain theorem, and I ...
José Carlos Santos's user avatar
34 votes
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Secrecy in Mathematics

In antiquity Archimedes kept his method of mechanical theorems about areas and volumes secret because, under Plato's influence, using lowly mechanics in glorious geometry was frowned upon at the time. ...
Conifold's user avatar
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33 votes
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Is the story about Fermat's writing on a margin true?

Yes, it is true. Fermat's own copy was used in the publication of Diophantus by Fermat's son Samuel, and he included Fermat's notes. The original with Fermat's handwriting is lost. https://www.joh.cam....
Alexandre Eremenko's user avatar
33 votes
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Has physics ever given a physical significance to a mathematically abstract idea?

Physics cannot help giving physical significance to things. But, yes, the first item on your list should have been Lie Groups. Developed as a mathematical "sudoku" game generalizing ...
Cosmas Zachos's user avatar
33 votes

Historical example of research papers being misinterpreted due to poor wording and creating controversy?

Giovanni Schiaparelli ... He wrote in 1877 about his telescopic observations of Mars. He described some features using the Italian word canali. English translation would be channels. But the term ...
Gerald Edgar's user avatar
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30 votes

Why are $X$ and $Y$ commonly used as mathematical placeholders?

See Earliest uses of mathematical symbols, which quotes F. Cajori, A History of Mathematical Notations, 2 volumes (1928-29) The use of z, y, x ... to represent unknowns is due to René Descartes, ...
Gerald Edgar's user avatar
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29 votes
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Did president Garfield make any contributions to Mathematics?

No. The library of Congress has a well-organized website of Garfield's papers, and he did not publish anything on mathematics other than that one note on the Pythagorean theorem in April 1, 1876 issue ...
Conifold's user avatar
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28 votes
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Is there any example of a long-standing mathematical conjecture whose resolution did not require advanced knowledge?

Sylvester's line problem (1893) was to prove that there exists no finite configuration of points in real projective plane such that every line through two points actually contains at least 3 points, ...
Alexandre Eremenko's user avatar
28 votes
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How did Isaac Newton write the integral symbol?

Newton used both vertical bars ($\overset{|}{x}$) and rectangles ($\boxed{x}$) to denote integrals in his Quadratura curvarum published in 1704. Here, the bar notation is used on the bottom of page 9 ...
Scene's user avatar
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27 votes
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Which mathematician traveled to and moved in with each collaborator?

The man is Paul Erdős. As pointed out by the OP in the comments, his "nomadic" lifestyle is briefly mentioned in the Brown Numbers - Numberphile video, 3.05-3.30. It is also concisely ...
Conifold's user avatar
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27 votes

Why are quaternions more popular than tessarines despite being non-commutative?

Your description "total uselessness of quaternions" in a comment above is poorly chosen, and reflects more on your interests than on the real state of knowledge of mathematics. The Hamilton ...
KCd's user avatar
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27 votes

Are there any mathematical objects that got renamed over time?

Newton referred to his concept of a derivative as a "fluxion". He called time-varying functions "fluents". Generally speaking, it is common for important mathematical concepts and ...
Adam Brown's user avatar
24 votes
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Where were mathematical/science works posted before the arxiv website?

Before 1991 - nowhere, there were no platforms to "post" preprints on. Some were distributed by mail, and even collected and catalogued by large libraries. US National Institutes of Health ...
Conifold's user avatar
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23 votes

Who discovered the covering homomorphism between SU(2) and SO(3)?

Hamilton and Klein, Klein was more explicit about it. Hamilton in Lectures on Quaternions (1853) realized that his representation of rotations of rigid bodies by the unit quaternions was not $1$-$1$, ...
Conifold's user avatar
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22 votes

Why are étale morphisms called "étale"?

From Milne's site: There are two different words in French, "étaler", which means spread out or displayed and is used in "éspace étalé", and "étale", which is rare ...
anon's user avatar
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22 votes
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When were vectors invented?

This question was actually discussed on this site several times, for example here: When was the vector notation in physics and other sciences first introduced? It indeed looks strange to modern people ...
Alexandre Eremenko's user avatar
22 votes
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What is the origin of the negation ( ¬ ) operator from logic?

If vague resemblance is enough, then "$¬$" resembles "$-$", which denotes negation in arithmetic. Lambert in Sechs Versuche einer Zeichenkunst in der Vernunftlehre (1782) and Boole ...
Conifold's user avatar
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21 votes

Where were mathematical/science works posted before the arxiv website?

I remember those days. (I am in mathematics.) When I completed a paper, I would mail (not email) photocopies (called "preprints") to researchers I knew that I hoped would be interested in ...
Gerald Edgar's user avatar
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21 votes

Has physics ever given a physical significance to a mathematically abstract idea?

fractal The so-called Cantor set was described by Georg Cantor, 1884 (or H. J. S. Smith, 1875?) Sets with "fractional" dimension were described by Felix Hausdorff, 1918 Investigated ...
Gerald Edgar's user avatar
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20 votes

What is the etymology behind sine, cosine, tangent, etc.?

Victor Katz is not a linguist and a lot of what he says in the quoted extract is wrong: for example that “Arabic is written without vowels” and that the word in question is spelt “jb”. In fact it is ...
fdb's user avatar
  • 3,485
20 votes

How was Fourier analysis important to the development of set theory?

It was Fourier series rather than Fourier transform. Considering that the sets where Fourier series converge can be very intricate it is not that surprising that they led Cantor to develop set theory ...
Conifold's user avatar
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20 votes
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Why was the development of mathematics very slow between Ancient Greece and Descartes?

Making my comment into an answer: Was there a gap of knowledge or slow-down of progress in math as a whole between Ancient Greeks and the 17th century? The answer is probably no. Islamic Medieval ...
Mauricio's user avatar
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19 votes

Why do many names of technical and scientific subjects end with "ics"?

It is not random. These names are of Greek origin, and -ic or -ics are Anglicizations of the Greek suffix -ikos, which meant "pertaining to". In other languages it can be rendered as -ika or -ica, ...
Conifold's user avatar
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18 votes
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Did the ancient Greeks have zero in their number system?

During the classical and early Hellenistic period (until 200 BC) Greeks did not use any positional system, they had their own which was decimal but not positional. The units from 1 to 9 are assigned ...
Conifold's user avatar
  • 77.7k
18 votes

Who discovered the covering homomorphism between SU(2) and SO(3)?

Before Hamilton (1847) one should cite Euler (1771), Gauss (1819), Rodrigues (1840), and Cayley (1845). Detailed references in e.g. Pujol, J., Hamilton, Rodrigues, Gauss, quaternions, and rotations: ...
Consigliere ZARF's user avatar
18 votes

Has physics ever given a physical significance to a mathematically abstract idea?

The following quote is from C. N. Yang, delivered at a 1979 symposium dedicated to the geometer Chern: "When I met Chern, I told him that I finally understood the beauty of the theory of fibre ...
Mark Yasuda's user avatar
  • 1,548
18 votes

Markov chains origins and how is Christianity involved

I'm not an expert on history or theology, but it seems that the motivation behind Nekrasov's claim is related to the Russian Orthodox's Church's doctrine of free will. If this is the only context ...
angryavian's user avatar

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