20 votes
Accepted

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

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

George Bergman, "A number system with an irrational base," Mathematics Magazine, Vol. 31, No. 2, Nov.-Dec. 1957, pp. 98-110. George Mark Bergman is an American mathematician who was born on ...
njuffa's user avatar
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17 votes
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Did Newton say: "If I have ever made any valuable discoveries, it has been due more to patient attention, than to any other talent"?

So far I have been unable to find substantially identical words in Newton's writings, and as usual, authors that use this quotation do not cite a source. The origin may be a remark of Newton's in ...
njuffa's user avatar
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14 votes
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DeMorgan's commentary on Euclid's Elements

De Morgan's "Short Supplementary Remarks on the first Six Books of Euclid's Elements" is contained in the Companion to the (British) Almanac for the year 1849, pp.5–20, published by the ...
Alexander Campbell's user avatar
13 votes

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

Arthur Leonard Rubin submitted the following paper at age 12.5 -- he was born in Feb 1956 and the paper was submitted in Nov 1968: Arthur L. Rubin and Jean E. Rubin, Extended operations and relations ...
Dave L Renfro's user avatar
10 votes
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The Original Title of "Euclid's Elements"

It is "Στοιχεῖα" [ Stoikheîa ] in Ancient Greek. https://en.wikipedia.org/wiki/Euclid%27s_Elements : Euclid's Elements (Ancient Greek: Στοιχεῖα Stoikheîa) is a mathematical treatise ...
Prem's user avatar
  • 396
8 votes
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What were the obstacles that made the discovery of calculus very late?

I would like to make several points with regard to this interesting question. The discovery of some Taylor series of trig functions by the Kerala school is a very impressive early breakthrough. ...
Mikhail Katz's user avatar
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8 votes

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

Daniel Larsen published his "Bertrand's Postulate for Carmichael Numbers" in International Mathematics Research Notices at age 19.
José Hdz. Stgo.'s user avatar
6 votes

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

John von Neumann published his first co-authored paper ''On the position of zeroes of certain minimum polynomials'' with Michael Fekete at the age of 18. His first solo paper ''On the introduction of ...
Hollis Williams's user avatar
6 votes

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

The problem with accepting complex numbers, when your only experience with "numbers" is the real number line, is lacking a visualization of them. No ordinary (i.e., real) number can square ...
KCd's user avatar
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6 votes

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

Mathematics is a tiny part of human activities, and its historical development cannot be considered in isolation. Since the 2nd century AD, there was a decline in all intellectual activities. ...
Alexandre Eremenko's user avatar
6 votes

Translated articles of Fatou and Julia

I was pointed to this chain of messages and I would then like giving you my version of facts. The translations project was the very very early version of the contents that ended up in the book I ...
Sandro Rosa's user avatar
5 votes

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

Leo Corry's recent text, A Brief History of Numbers, offers an authoritative account of these matters. According to Corry, Bombelli's attitude to negative numbers was the same as Cardano's. Bombelli ...
nwr's user avatar
  • 6,859
5 votes
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Reference request: What were the problems of accepting zero, negative numbers, and complex numbers? And how were they solved?

What you write suggests that you still have difficulty with complex numbers. I would suggest that you overcome such difficulties before you proceed to the next step such as delving deeply into real ...
Mikhail Katz's user avatar
  • 5,772
4 votes
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Was "potency set" used for power set?

The paper Rieger, L. "On the consistency of the generalized continuum hypothesis." Rozprawy Mat. 31 (1963) described in MR0146091, which can be downloaded from http://pldml.icm.edu.pl/pldml/...
kimchi lover's user avatar
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4 votes

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

Katherine Knox recently published Billiard circuits in quadrilaterals in the American Mathematical Monthly, and the paper contains original research results. I'm not sure of her exact age, but she is ...
Timothy Chow's user avatar
  • 1,506
4 votes
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Height function following Borel

As usual, it is very difficult to identify the first occurrence of a term, but in this case it is Borel's own article that can help us. The full note can be found here, we read: Étant donné un ...
user6530's user avatar
  • 3,870
4 votes

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

Perhaps the question ought to be turned on its head: why did mathematical learning hit the accelerator in Ancient Greece and during the modern era in Western Europe (17th century to present)? Some ...
RobertF's user avatar
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4 votes

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

It's well known that Blaise Pascal published his Essai pour les coniques in February of 1640 at the age of 16. Galois' Démonstration d’un théorème sur les fractions continues périodiques paper was ...
Mark Yasuda's user avatar
  • 1,548
3 votes

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

There reason for the speed-up in the 1600s was Vieta's development of an algebraic formalism that allowed mathematicians for the first time to write down mathematical formulas rather than merely ...
Mikhail Katz's user avatar
  • 5,772
3 votes

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

Lajos Posa wrote one 1 with Erdos and was submitted for publication in September 1961. At the time of submission Posa was not 14 yet. [1] Erdos and Posa : On the maximal number of disjoint circuits of ...
hyportnex's user avatar
  • 347
3 votes

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

Certainly not as young as Arthur Rubin, but Carl Størmer was also very precocious. Størmer entered the University of Christiana (Oslo) in 1892 and in the same year, at the age of 18, he published his ...
user6530's user avatar
  • 3,870
3 votes

Translated articles of Fatou and Julia

Before posting my thoughts I would like to thank everyone for contributing to this inquiry and express my sincere appreciation for Mr Rosa's answer. I have read parts of two books on the history of ...
Prelude's user avatar
  • 201
2 votes

What research articles were inspired by web comics?

If we ignore research on webcomics themselves, xkcd seems to be the most common webcomic inspiration for science and mathematical research, and these are pretty much all in computer science and ...
David Bailey's user avatar
  • 1,222
2 votes

What is the earliest use of the $\perp\!\!\!\!\perp$ symbol in statistics to denote statistical independence?

An early reference that uses this notation and (at a minimum) introduced many people to this notation is the following publication. Dawid, A. P. “Conditional Independence in Statistical Theory.” ...
Chris Meek's user avatar
2 votes

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

Other examples of articles published by mathematicians at an early age: High-schooler Britney Gallivan was born in 1985 and published a paper early 2002 in which she established a formula for the &...
Max Muller's user avatar
2 votes

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

An aspect that has not been mentioned and is at least a partial answer is that progress must strongly depend on the number of people working in the field, which is the product of the population and ...
Peter - Reinstate Monica's user avatar
2 votes

The history of motivations

"The Origins of Cauchy's Rigorous Calculus" by Judith Grabiner discusses some of the motivations of mathematicians involved in the development of calculus, starting in the eighteenth century ...
Michael E2's user avatar
  • 1,861
2 votes

Translated articles of Fatou and Julia

This is a longer comment rather than an answer to the question specifically about Fatou and Julia papers. Having been given green light by Sandro, let me add some more details about his project of &...
Margaret Friedland's user avatar
2 votes

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

While the wiki article mentions Desargues, it is inaccurate in that it implies that Desargues only had the notion of a point at infinity, whereas he went much further, including the line at infinity. ...
Mikhail Katz's user avatar
  • 5,772

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