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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 Did he have any letters or unpublished research materials that can tell us ...
gaussianbonjuir's user avatar
3 votes
1 answer
90 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. ...
Geremia's user avatar
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21 votes
5 answers
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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 ...
enjin2000's user avatar
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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 ...
kcrisman's user avatar
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16 votes
1 answer
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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 ...
Rodrigo A. Pérez's user avatar
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 ...
Prime Mover's user avatar
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2 votes
1 answer
178 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, ...
Lukas Heger's user avatar
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 ...
enjin2000's user avatar
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2 votes
0 answers
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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 ...
user20971's user avatar
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, ...
madame p's user avatar
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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 ...
AlMa1r's user avatar
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1 vote
1 answer
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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 ...
Nate's user avatar
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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 ...
Speakpigeon's user avatar
1 vote
0 answers
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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
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 ...
Igor F.'s user avatar
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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?
Prelude's user avatar
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2 votes
1 answer
176 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
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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 ...
Sam Sanders's user avatar
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 ...
pie's user avatar
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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 ...
pie's user avatar
  • 263
0 votes
0 answers
77 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 ...
Mozibur Ullah's user avatar
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 ...
Addem's user avatar
  • 511
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 ...
Fraser's user avatar
  • 11
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 ...
Humberto José Bortolossi's user avatar
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 ...
SRobertJames's user avatar
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 ...
0-1's user avatar
  • 141
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 ...
User303131's user avatar
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 ...
Frode Alfson Bjørdal's user avatar
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 ...
Frode Alfson Bjørdal's user avatar
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?
bzm3r's user avatar
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4 votes
2 answers
466 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 ...
pie's user avatar
  • 263
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 (...
pie's user avatar
  • 263
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, ...
Antoine Chambert-Loir's user avatar
1 vote
0 answers
313 views

Attributed quote to Nikola Tesla

In many serious engineering and scientific publications including IEEE publications, we see a quote attributed to Nikola Tesla which goes like this If you want to find the secrets of the universe, ...
ACR's user avatar
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3 votes
0 answers
142 views

Is there a comprehensive list of Ancient Greek mathematical writings?

Much of the Ancient Greek's mathematical philosophy texts have survived from antiquity and passed to modern times. Also, texts previously thought to be lost are being occasionally rediscovered (...
0-1's user avatar
  • 141
3 votes
0 answers
86 views

Did the Romans really use the binomial formula to calculate products?

I'm not quite sure if this is the right place to ask this question (in fact, I was redirected to this SE from the Math Stackexchange), but it's probably more fitting than the original posting place. I ...
Cornelius Brand's user avatar
2 votes
0 answers
79 views

History behind Serre's conditions $\mathrm{S}_k$ and $\mathrm{R}_k$ for a commutative Noetherian ring

In 033Q we find defined what some sources call “Serre's conditions $\mathrm{S}_k$ and $\mathrm{R}_k$” (if you don't know what a scheme is, you can read the definition for a commutative Noetherian ring ...
Elías Guisado Villalgordo's user avatar
5 votes
0 answers
169 views

Early illustrations of topological notions in published work

Since I've not gotten any answers after a bit more than a week, I've now cross-posted to MathOverFlow. EDIT 2023-08-15: Several commenters here and at MO have asked me to sharpen the original question....
Sam Nead's user avatar
  • 151
7 votes
1 answer
248 views

The Original Title of "Euclid's Elements"

What did Euclid originally call his treatise of thirteen books that we now refer to as "Euclid's Elements" ? Was it "The Elements" ? Was it something else ? Does anyone know the ...
DDS's user avatar
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1 vote
0 answers
126 views

Scientific articles discovered false and useless several years after their publication

I am looking for examples of important scientific articles that have been discovered to be false and useless several years after their publication. I mean: they stated something interesting and ...
Marco Disce's user avatar
0 votes
2 answers
65 views

What's the name of P C Gilmore?

I have several times come across the name P C Gilmore, and even made use of a publication by her, or him, viz. "The consistency of partial set theory without extensionality", which was ...
Frode Alfson Bjørdal's user avatar
4 votes
2 answers
772 views

Provenance of mathematics quote from Robert Musil, 1913

The quote is as follows: "Nur wenn man nicht auf den Nutzen nach aussen sieht, sondern in der Mathematik selbst auf das Verhältnis der unbenutzten Teile, bemerkt man das andere und eigentliche ...
Frode Alfson Bjørdal's user avatar
1 vote
0 answers
106 views

Early results on the Fourier transform

Published tables of Fourier transform pairs have been available for many years. One such example is the paper by George Campbell in the Bell Systems Technical Journal in 1928. Most such tables simply ...
CrimsonDark's user avatar
8 votes
1 answer
312 views

What research articles were inspired by web comics?

Currently, I'm doing a PhD on the applications of algorithms to generate timelines of textual content. Recently, I found an article entitled StoryFlow: Tracking the Evolution of Stories by S. Liu et ...
Max Muller's user avatar
4 votes
1 answer
243 views

History of visualization in science and math - where may I read of it?

I am looking to inquire into the role of visualization in sciences and math and wish to read about the history of visualization in those fields and also wonder where I might read about the ...
Rumi's user avatar
  • 49
3 votes
0 answers
125 views

References on the role of diagrams in scientific advancement

A number of diagrammatic formulations have played an important role in the advancement of science. Some embody representations of physical phenomena, while others model mathematical or logical ideas ...
Max Muller's user avatar
4 votes
1 answer
95 views

Where can I find the early proofs for the simplicity of $\text{PSL}(n,q)$?

I am doing a research project on the history of group theory, and want to know about the early developments on the subject. There are plenty of proofs about why the projective special linear group ...
Void's user avatar
  • 41
7 votes
0 answers
188 views

History of group actions as their own structures

I'm interested in when (and how) the modern idea of a group action developed and how group actions became their own algebraic structures. As far as I can tell in the 19th century group actions were ...
paidresolution's user avatar
0 votes
0 answers
95 views

The history and origin of the Argument Principle ( or Cauchy's argument principle)

I am looking for a book that discusses The history and origin of the Argument Principle ( or Cauchy's argument principle) Thanks!
user17825's user avatar
4 votes
0 answers
146 views

Finding the Letter from Freeman Dyson to Gerald Gabrielse in 2006

In 2006, the renowned physicist Freeman Dyson wrote a letter to his colleague Gerald Gabrielse regarding an advance in precision about measuring the magnetic moment of an electron. An excerpt of his ...
Talmsmen's user avatar
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