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Which mathematical concepts do not have any obvious origin outside mathematics?

Some mathematical concepts, such as that of number and that of geometrical figure, presumably originate from pre-existing notions already used by at least some non-mathematicians. Others seem to have ...
Speakpigeon's user avatar
1 vote
0 answers
94 views

Origin of Einstein quote "Quantum mechanics: Real Black Magic Calculus"

The description of the 1993 English translation of The Quantum Dice, by Ponomarev and Kurchatov, as well as one of the quotes for chapter 2 of Quantum Computation and Quantum Information, by Nielsen ...
elutionary's user avatar
2 votes
1 answer
91 views

What was the first human gene sequenced/annotated?

The Human Genome Project was famously declared complete in 2003, and to date there are 6000 genes discovered/annotated. What was the first one discovered and annotated?
imrobert's user avatar
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2 votes
0 answers
39 views

Why are the terms electrophile/nucleophile used? Are they not identical to Lewis acids/bases?

My understanding is that the above pairs of terms are identical in definition, indicating acceptors/donors of an electron pair. So, why are both used?
imrobert's user avatar
  • 195
1 vote
1 answer
135 views

F = ma -- How was did we come to understand that this compact form expressed what Newton said in words?

My understanding is, Newton in the 17th century did not use this formula but rather said, in words basically that if you apply a force it will cause a mass to accelerate in the direction of that force....
releseabe's user avatar
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6 votes
1 answer
1k views

How come there is no portrait of Legendre?

Besides the famous cartoon, of course, there seems to be no portrait of Legendre. Legendre is well regarded nowadays and he was also quite influential at his time, for example, Jacobi and Abel praised ...
Croqueta's user avatar
0 votes
0 answers
56 views

References for converting old units to new units

I am currently looking for references on books that deal with the conversion of old units to new units. I am particularly interested in books that actually have tables of conversion because I need to ...
Lucas Nardi's user avatar
2 votes
0 answers
74 views

Who did introduce homomorphism concept for the first time?

I read that: "The term "homomorphism" appeared as early as 1892, when it was attributed to the German mathematician Felix Klein (1849–1925). Homomorphisms of vector spaces are also ...
Iman Mosleh's user avatar
0 votes
0 answers
38 views

Why did Kronecker say "the integers are the work of God, the rest is the work of man"? [duplicate]

To me, it seems no number is the work of God, they are all concepts of the mind. However, it seems negative numbers are more artificial than the rest of the numbers out there. So why did he describe ...
Demon's user avatar
  • 63
3 votes
1 answer
74 views

When did they start requiring holotypes for species description?

I know they weren't required in the early 1800s but obviously they are now so just wondering when this started being required and/or who coined holotype. Internet research yielded no good answers.
imrobert's user avatar
  • 195
3 votes
1 answer
183 views

How did Gauss determine the number of primes?

In Brian Conrey's article on Riemann's hypothesis, one reads in the very beginning: On Christmas Eve 1849 Gauss wrote a letter to his former student Encke in which he described his thoughts about the ...
Hans-Peter Stricker's user avatar
1 vote
0 answers
174 views

How did Azumaya come up with the Nakayama lemma?

Thanks to Conifold and Chris Leary's comments, I learned that the Nakayama lemma was not first created by a mathematician named Nakayama, but that mathematicians named Azumaya and Krull first created ...
user1274233's user avatar
2 votes
0 answers
63 views

Reference to a comment by Arthur C. Clarke

In one of his non-fiction works, probably "Mysterious World" or "World of Strange Powers", Arthur C. Clarke tells an anecdote about an astronomers' expedition to Africa (if I ...
Igor F.'s user avatar
  • 21
18 votes
1 answer
2k views

Emmy Noether's announcement in 1932 ICM

I read a book "a history of abstract algebra"- chapter 6 by Israel Kleiner. And in this book, it is said that Emmy Noether gave a presentation at the ICM congress held in Zurich in 1932, ...
user1274233's user avatar
2 votes
0 answers
54 views

Did Democritus predict atoms using sharp phase transitions

In the Wikipedia page for the Ising Model it is written without citations: One of Democritus' arguments in support of atomism was that atoms naturally explain the sharp phase boundaries observed in ...
Diana's user avatar
  • 21
0 votes
1 answer
62 views

Is there a resource about integer constructions and motivations?

I have an assignment about the foundations of mathematics. I am trying to compile a list where I get common construction of integers and a small writing about the constructor and their explanation. ...
Fraser James's user avatar
0 votes
0 answers
41 views

References on the history of electromagnetism

I am looking for complete and trustable references on the history of electromagnetism. Does anyone have some good recommendations?
Léo Vacher's user avatar
13 votes
5 answers
5k views

Great battles in the history of mathematics

Could someone list me the most important battles between mathematicians which happened in history, especially such that strong emotions played role in that time? Perhaps the most known one is the ...
Widawensen's user avatar
1 vote
0 answers
47 views

Did Dedekind's construction of the integers and rational numbers become standard in mathematics textbooks?

I am referring to the construction using pairs of natural numbers in 1858. Since we use pretty much the same construction today in some analysis courses (Analysis 1, Terence Tao), except without the ...
Demon's user avatar
  • 63
1 vote
0 answers
30 views

History of Kronecker's Divisorentheorie

I saw André Weil's Weil divisor. So I became curious about the history of the divisor. However, when I searched the history of divisor, I found that Leopold Kronecker announced the beginning of the ...
pokssin's user avatar
  • 309
2 votes
1 answer
350 views

Isn't Descartes' account of refraction wrong?

In his account of refraction, which can be found for example here, Descartes compares it with the motion of a tennis ball. He says that going into a denser medium must reduce the total speed, while ...
thedude's user avatar
  • 121
3 votes
4 answers
153 views

Translated articles of Fatou and Julia

Is there any English translation of the 1918-1920 Memoirs of Fatou and Julia on the iteration of rational functions?
Prelude's user avatar
  • 201
0 votes
1 answer
52 views

The Sun's direction of rotation in the geocentric model [closed]

In what direction does the Sun rotate in the geocentric model? It seems to me that this should rotate in a clockwise direction around Earth (as seen from the north pole), but all the illustrations I'...
Adrien Hingert's user avatar
1 vote
1 answer
176 views

When were negative numbers fully accepted into mathematics?

Dedekind gave a construction and explanation of integers and rational in 1858. This was as ordered pairs of natural numbers. I'm not sure if this was the standard view of these objects after this ...
Demon's user avatar
  • 63
3 votes
0 answers
66 views

What can I read to learn the history of multivariable calculus?

People have been doing calculus of several variables since well before the concepts of vectors, matrices, and linear algebra were formalized. Where can I learn about the development of multivariable ...
Dominic Stewart-Guido's user avatar
2 votes
0 answers
38 views

History of Observational "Nowruz" (Iranian New Year)

The Iranian New Year unlike most other cultural celebrations of our planet completing a trip around the sun is exact and observational, I am curious exactly when the observational nature of the ...
Bertrand Einstein IV's user avatar
0 votes
0 answers
32 views

Did Heinrich Weber have a structural approach to mathematics similar to Dedekind?

So I was reading a History of Mathematics by Katz, and noticed that the first definition of a field came from Weber, who had previously done extensive joint work with Dedekind. His definition was used ...
Demon's user avatar
  • 63
1 vote
1 answer
57 views

Did Dedekind's work directly influence the work of Hilbert?

I am wondering if Dedekind's theory about the structure of deductive science influenced the work of Hilbert. Hilbert obviously favored axioms at the beginnings of a deductive science, whereas Dedekind ...
Demon's user avatar
  • 63
2 votes
1 answer
114 views

History of doubly periodic functions

I am curious about the origin and history of the doubly periodic function. I was looking for the Eisenstein series, and the Eisenstein series is one of the representative examples of a doubly ...
user1274233's user avatar
4 votes
3 answers
288 views

Origin of modern definition of a function as a graph

In the past, I came across a very elegant direct definition (below) of a function, which is based on the fundamental concepts of triples, pairs, and sets. However, I find it difficult to search the ...
Kamil Kiełczewski's user avatar
4 votes
1 answer
189 views

Did the earliest inklings of hyperbolic geometry come from medieval Islamic mathematicians?

This question is a follow-up to How much did the ancient Greeks know of non-Euclidean geometry?, where it was claimed in a comment that "the earliest inklings [of hyperbolic geometry] came from ...
Mikhail Katz's user avatar
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0 votes
0 answers
105 views

How much did the ancient Greeks know of non-Euclidean 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
  • 121
4 votes
0 answers
72 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
  • 141
3 votes
1 answer
80 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
  • 347
26 votes
4 answers
9k 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
  • 363
0 votes
1 answer
60 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
4 votes
2 answers
783 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
40 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
77 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
  • 11
0 votes
0 answers
50 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
  • 123
0 votes
0 answers
31 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
84 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
1 vote
1 answer
87 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
  • 5,401
0 votes
1 answer
74 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
71 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
  • 6,331
1 vote
0 answers
75 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
  • 63
0 votes
0 answers
72 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
376 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
19 votes
2 answers
2k 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
49 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

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