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3 votes
1 answer
613 views

What did Gauss think about infinite?

Did Gauss think that the size of infinite was incomparable? Or did he leave some opinions about infinity or infinitesimals? Did he have any letters or unpublished research materials that can tell us ...
3 votes
1 answer
89 views

Why is Einstein summation named after Einstein?

Why is Einstein summation of tensors (summation of repeated indices) named after Einstein? "Einstein rule" in the Encyclopedia of Mathematics only says: This rule was proposed by A. ...
21 votes
5 answers
3k views

I want to know the tricks to search for and find old academic journals for free

In the research of scientific and mathematical history, efficient skills in searching for and accessing old academic journals (preferably for free) are essential. However, even when using platforms ...
21 votes
4 answers
2k views

Books on the history of linear algebra

I'm quite desperate to understand the historical motivation and origin of all of the "geometrical" concepts of linear algebra, namely: The concept of thinking of elements of $\mathbb R^n$ or some ...
5 votes
1 answer
286 views

Non-standard model of arithmetic and Gödel's theorem

I've read Skolem's paper on his non-standard models of the arithmetic ("Über die Nicht-charakterisierbarkeit der Zahlenreihe mittels endlich oder abzählbar unendlich vieler Aussagen mit ...
0 votes
5 answers
440 views

Looking for math history but keep finding the same old stuff

I've browsed many math history books, but I've never read too deep into any single one. I always find myself reading the about the same facts and same people over and over -- the set of topics doesn't ...
0 votes
0 answers
82 views

Source of Galileo quote on curves

In George Simmons' Calculus Gems there is an interesting quote, supposedly from Galileo, pertaining to whether one can compare curved and straight lines (in length, for instance): Who is so blind as ...
16 votes
1 answer
2k views

Who was Nicolò Paganini that discovered the amicable pair 1184, 1210?

Nicolò Paganini (not the violinist) was a 16 yo Italian schoolboy when he discovered that 1184 and 1210 form a pair of amicable numbers. It is in fact, the 2nd smallest such pair, and it did escape ...
3 votes
1 answer
639 views

Where did Lagrange prove the Four Squares Theorem?

I am trying to confirm the initial publication of Lagrange's Four Squares Theorem. Most of my sources give that it was proved by him in $1770$. However, the generally very good Penguin Dictionary of ...
3 votes
5 answers
2k views

What was the main language in science/mathematics before 1850

I know that English is the most popular language to write scientific/mathematical papers after World War 2. I also know that in the second half of 19th century and first half of 20th century, German ...
2 votes
1 answer
176 views

What is the origin (and perhaps original) of this quote by André Weil

I found this quote by André Weil in a few places online: As every mathematician knows, nothing is more fruitful than these obscure analogies, these indistinct reflections of one theory into another, ...
2 votes
1 answer
119 views

I'm searching for the original paper from 1924 where Max Born first proposed the term "quantum mechanics."

I'm searching for historical documents pertaining to quantum mechanics because I aim to write a popular essay on the topic for a web magazine. Specifically, I'm seeking free access to Max Born's paper ...
6 votes
2 answers
6k views

An English copy of One Hundred Authors Against Einstein?

I've been trying to find the famous article, "One hundred authors against Einstein" (100 Autoren gegen Einstein), of various objections to special relativity, which is quite often referenced, but ...
13 votes
4 answers
915 views

What resources are available for lives of recent mathematicians besides E.T. Bell's Men of Mathematics?

I am about halfway through reading E.T. Bell's Men of Mathematics, and I absolutely love it. I'm a mathematician, and I enjoy learning about the lives behind the names that I know and use so often. (I ...
2 votes
0 answers
95 views

Looking for a letter written by Gauss in which he remarks that he has worked very hard on mathematics

In my memory, I once read a letter that Gauss wrote to a friend or acquaintance in which he remarks something along the following lines---if people worked on mathematics as much as I did, they would ...
13 votes
10 answers
5k views

Who are the youngest mathematicians that published an original research article in a peer-reviewed journal?

There is a lot of interesting information about young mathematicians, but I cannot find any information about the youngest mathematician that published an original research article in a peer-reviewed ...
2 votes
0 answers
43 views

About the acceptance of Newton's light experiment

I originally posted this question in History Stack Exchange, but I was recommended to post it here instead. My question starts with the following statement from a book I'm reading "Moreover, ...
8 votes
2 answers
986 views

What were the obstacles that made the discovery of calculus very late?

I wonder What were the obstacles that made the discovery of calculus very late ? Why the discovery of calculus took so long? I know that some of the ideas and techniques of calculus appeared in ...
0 votes
0 answers
54 views

Correct citation of “The method of successive approximation for functional equations” by L. Kantorovich, Leningrad, 1939?

The citation we get from http://projecteuclid.org/journals/acta-mathematica/volume-71/issue-none/The-method-of-successive-approximation-for-functional-equations/10.1007/BF02547750.full says ...
1 vote
1 answer
74 views

Which people are considered to be the founders of Projective Geometry?

What were the fundamental principles and ideas of projective geometry that made people consider it groundbreaking and separates it from the rest of the geometry? I would love to learn about a good ...
3 votes
4 answers
151 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?
0 votes
0 answers
82 views

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 ...
1 vote
0 answers
81 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 ...
2 votes
2 answers
437 views

Poincaré quote regarding instability

Poincaré wrote (English translation of the French) in 1903: ``A very small cause that escapes our notice determines a considerable effect that we cannot fail to see, and then we say that the effect ...
3 votes
1 answer
104 views

Is reference cited by Rene Descartes available?

In 1634 Descartes wrote to Mersenne : let me tell you about an experiment that was published not long ago in Leurechon’s Mathematical Games. It involves a large cannon placed on flat ground, pointing ...
2 votes
0 answers
62 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 ...
4 votes
1 answer
256 views

Source of a Quote by M. Stone on Poincaré and Bourbaki

The quote in question is the following: For Bourbaki, Poincaré was the devil incarnate. For students of chaos and fractals, Poincaré is of course God on Earth. The common reference for this quote ...
0 votes
3 answers
123 views

Has Alphonse Pyramus de Candolle's "Géographie botanique raisonnée" ever been translated into German or English?

Alphones Pyramus de Candolle (1806-1893), the son of Augustin-Pyrame de Candolle (1778-1841), has been an important figure (as was his father) in the development of plant geography. The younger ...
10 votes
3 answers
1k views

How did Eratosthenes know the distance between Aswan and Alexandria?

In his well-known measurement of the Earth, and according to Cleomedes, Eratosthenes estimated in 5000 stades the distance between Aswan and Alexandria. Modern accounts state that he calculated the ...
2 votes
1 answer
174 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 ...
10 votes
1 answer
471 views

Was the phlogiston theory ahead of its time?

I've always "known" that the phlogiston theory was naive and unsupported by the facts, which is why it was toppled pretty much instantaneously by Lavoisier's discovery of the role of oxygen. However, ...
2 votes
1 answer
151 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 ...
6 votes
5 answers
7k views

Why was the development of mathematics very slow between Ancient Greece and Descartes?

I asked this question on MSE here In my studies of mathematics (I am not very good at mathematics, I only studied real analysis, some linear algebra, geometry and calculus ), I noticed that ...
0 votes
0 answers
76 views

What is Laguerre's definition of the angle via the cross ratio?

I recently read an article which said Cayley showed that affine geometry could be developed from projective geometry after he learnt of Laguerre's definition of the angle using the cross ratio. This ...
1 vote
4 answers
216 views

Is there a concise but detailed history of electricity?

I have recently become fascinated by the history of electricity. I have researched and come up with the following observations: Static electricity was discovered in early times, by phenomena such as ...
14 votes
2 answers
1k views

Early history of the phase concept in the physical sciences

One of the first distinctions encountered in science education is that substances can assume different states of matter: for example, water can be found as a liquid, as a solid (ice), or as a gas (...
0 votes
1 answer
95 views

The history of motivations [closed]

Most histories, that I've encountered, of mathematics about the 18th century and onward focus on a chronology of publications, results, definitions, and similar "pure" interests. However, I ...
0 votes
0 answers
105 views

Seeking References on the History of Scientific Dissemination

recently read a book on the history of science by academic Tatiana Roque. In it, she discusses how, during the Enlightenment, scientific dissemination was a fundamental assumption. Roque writes that ...
2 votes
1 answer
4k views

Where did Galileo say "All truths are easy to understand once they are discovered. The point is to discover them."?

I've heard it claimed Galileo said or wrote: All truths are easy to understand once they are discovered. The point is to discover them. Where did he say this?
8 votes
1 answer
1k views

DeMorgan's commentary on Euclid's Elements

Augustus DeMorgan wrote comments on Euclid's Elements, which capture many of the most important points. Heath quotes them extensively. I cannot find any source for the original: Where can I see ...
10 votes
4 answers
13k views

Who was the first to say "Shut up and calculate!"?

The best thing I could find on the internet was this apparently forgotten article from 2004: N. David Mermin, Could Feynman have said this?, Physics Today 57 (5), 2004.
9 votes
2 answers
5k views

The history and motivation of eigenvectors

I want to understand more about the history of eigenvectors. Was the discovery of eigenvectors inspired from an application to achieve a result in a historical context, was there a phenomenon which ...
1 vote
0 answers
107 views

A collection of the fragments of Eudemus of Rhodes?

I am looking for a complete collection of fragments of Eudemus of Rhodes. He is considered to be the first historian of science. His fragments have given us a glimpse of how Greek mathematics ...
1 vote
0 answers
83 views

Whence Whitehead's essence?

In the article Quine’s New Foundations of The Stanford Encyclopedia of Philosophy (Summer 2019 Edition), Thomas Forster writes: In [1944] Hailperin gave the first of a number of finite ...
1 vote
1 answer
183 views

Was "potency set" used for power set?

Cross posted at Math Overflow For historical reasons, the English term "power set" in set theory is a translation of the German "Potenzmenge", which is still in use in German ...
4 votes
2 answers
465 views

Reference request: What were the problems of accepting zero, negative numbers, and complex numbers? And how were they solved?

I asked this question on MSE and comments suggested I should ask it here I am currently reading Baby Rudin as my second analysis book (after Introduction to Real Analysis by Robert G. Bartle and ...
0 votes
0 answers
49 views

Reference request: What were the problems of accepting zero, negative numbers, and complex numbers? And how were they solved? [duplicate]

I didn't know that can happen and since I already asked the question here I don't know what to do with this question should I delete it ? I am currently reading Baby Rudin as my second analysis book (...
9 votes
1 answer
3k views

Did Newton say: "If I have ever made any valuable discoveries, it has been due more to patient attention, than to any other talent"?

I came across the above quote, and found it quite interesting. However, I struggled to find an actual source. Did Newton truly say this?
2 votes
0 answers
92 views

Who evaluated the surface of the Torricelli solid/Gabriel's horn

The Torricelli solid/Gabriel's Horn is defined as the rotation-invariant solid delimited by a hyperbola. It appears in De solido hyperbolico acuto where Torricelli proves that it has a finite volume, ...
3 votes
1 answer
310 views

Question about Leibniz's "characteristic numbers" and propositional logic

The Wikipedia article on Gottfried Wilhelm Leibniz mentions, in the chapter on symbolic thought, that: Leibniz saw that the uniqueness of prime factorization suggests a central role for prime numbers ...

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