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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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16 votes

Why did Hilbert believe consistency implies existence?

Hilbert wrote this observation some decades before the formal theories of completeness (and incompleteness) took shape, so you can't expect him to be overly precise with regard to such notions. The ...
Mikhail Katz's user avatar
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14 votes
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What was the role of Schmidt in derivation of the Gram-Schmidt process?

A detailed history can be found in Gram-Schmidt orthogonalization: 100 years and more by Leon, Björck and Gander, see also their slides for a brief version. In short, Schmidt's 1907 presentation was ...
Conifold'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
12 votes

How do we explain the lack of activity in the study of Latin mathematics?

Since the full professor in question certainly hasn't read all of "the mathematics written in Latin over the last 1000 years," one can assert with certainty that he literally does not know ...
Mikhail Katz's user avatar
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12 votes
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When did "neighbourhood of a point" first appear in the history of Taylor series?

The terminology "neighbourhood of a point" (in German, "Umgebung einer bestimmten Stelle") with its current meaning, dates back at least to 1841 when Weierstrass wrote his Zur ...
user6530's user avatar
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11 votes
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Source of a Poincaré quote: "Logic sometimes makes monsters..."

McTutor most likely took the passage from Kline's Mathematical Thought From Ancient to Modern Times, v.3, p.973, they reproduced his translation verbatim. Kline references Poincare's essay Dans la ...
Conifold's user avatar
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11 votes

How come there is no portrait of Legendre?

Because (Adrien-Marie) Legendre, the mathematician, wanted it this way, see Duren, Changing Faces: The Mistaken Portrait of Legendre, who quotes Poisson: "We know from testimony of Poisson that ...
Conifold's user avatar
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10 votes
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Was there an intentional purge of all audio recordings of Alan Turing?

There is no evidence for an intentional purge of all audio recordings of Alan Turing. The BBC recordings seem to be the only ones ever made by Turing, so there wasn't really anything to "purge&...
David Bailey's user avatar
  • 1,242
10 votes

How does the science community decide which scientist to credit for a particular discovery?

Squabbles over honor are just as common among scientists as elsewhere in society. Memorable examples include: Leibniz-Newton; Manifold destiny. Plain facts are usually not sufficient to resolve ...
Mikhail Katz's user avatar
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9 votes
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How to find the first appearance of a theorem?

Finding out who stated and proved some theorem first can require a more serious research than reading history of mathematics books and textbooks. Many examples can be given. I give only a couple. ...
Alexandre Eremenko's user avatar
8 votes
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Did ancient Greeks have a numerical value for the Golden Ratio

First of all, Greeks were not fascinated with Golden ratio as we are. Modern golden-ratio hype started about from the time of Leonardo da Vinci. Second, Greek mathematicians were not very interested ...
Alexei Kopylov's user avatar
8 votes

Why did Hilbert believe consistency implies existence?

I just want to add some context to Katz's very nice answer. Hilbert's work on foundations occurred in the aftermath of the intuitionistic criticisms by Brouwer and Weyl. (Weyl in particular must have ...
Michael Weiss's user avatar
8 votes
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Who first stated the "uncertainty principle" for Fourier transforms?

It seems that Heisenberg was the first to notice this phenomenon in 1927. He did not use the terminology of Fourier transform. Heisenberg's principle was rigorously stated and proved by Kennard in ...
Alexandre Eremenko's user avatar
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
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When and why was the concept of "having a least upper bound" dubbed "completeness", as in Axiom of Completeness?

According to Burn, Irrational numbers in English language textbooks, 1890–1915: Constructions and postulates for the completeness of the real numbers, "completeness" was first used by ...
Conifold's user avatar
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8 votes
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Why Isaac Newton published his discoveries so much later than he discovered them?

The question virtually quotes some blanket statements about Newton's willingness (or not) to publish, and about when he made certain discoveries, etc. It is true that such statements certainly have ...
terry-s's user avatar
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8 votes
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Is it true that Aryabhata explicitly understood or stated the irrationality of $\pi$?

No, certainly not "explicitly". The question would have made sense already to ancient Greeks in the ratio form: is the ratio of the circumference to the diameter incommensurable? Did they ...
Conifold's user avatar
  • 77.7k
8 votes

Was it after Riemann's death that Weierstrass gave a counterexample to Riemann's mapping theorem?

Yes, but there were other criticisms already during Riemann's lifetime, see Bottazzini, "Algebraic truths" vs "geometric fantasies" which gives a detailed story. In 1864, when ...
Conifold's user avatar
  • 77.7k
7 votes

Where does the term elasticity (of a function) come from?

The term elasticity was first used in print by Alfred Marshall (1885, p. 260): We may want to find a measure of what may be called the elasticity of demand; that is, when a fall of price leads to an ...
user103496's user avatar
7 votes
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Cantor, set theory and foundations

Cantor was interested in, and developed, a theory of ordinal numbers and cardinalities. This was a significant accomplishment, in part because it overcame traditional resistance to working with ...
Mikhail Katz's user avatar
  • 6,162
7 votes

Can I find the number e in the tables of Napier?

Q: "Can I find the number e in the tables of Napier?" (and) "The number that I find on the last row of the last table is 3,465,735 rather than 3,678,794. Is there a number closer to e ...
terry-s's user avatar
  • 4,600
7 votes

Origin of exact and closed differential expressions

From Bottazzini U., Gray J., Hidden Harmony-Geometric Fantasies. The rise of Complex Functions, Springer, 2013 (from which it seems that the terms 'exact' and 'complete' for differentials were used ...
BakerStreet's user avatar
  • 1,065
7 votes
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Ancient drawing board in mathematics

I do not know Winter's text, at any rate I think the references to Iamblichus and Apuleius. For Iamblichus, the reference is definitely to Life of Pythagoras, Chapter V: Though no one therefore ...
user6530's user avatar
  • 4,010
7 votes
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Origin of modern definition of a function as a graph

The precise definition can be found into Bourbaki's Elements of Mathematics: Theory of sets (1968; but the 1st French edition is dated 1939), page 76: A correspondence between a set $A$ and a set $B$ ...
Mauro ALLEGRANZA's user avatar
7 votes
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From which university did Riemann acquired Ph.D?

Math genealogy says Bernhard Riemann received the Dr. phil. degree in 1851 from Georg-August-Universität, Göttingen. His advisor was C. F. Gauß . Dissertation title: "Grundlagen für eine ...
Gerald Edgar's user avatar
  • 10.4k
6 votes

Etymology of "power" (math.)

The Greek word δύναμις is, I believe, an ordinary (Ancient) Greek word meaning power, ability, strength, etc. The first entry in Liddell/Scott/Jones (click on LSJ) cites Homer: ἦ τ᾽ἂν ἀμυναίμην, εἴ ...
Michael E2's user avatar
  • 1,911
6 votes

When did mathematicians realize that theory of algebraically closed fields admits quantifier elimination?

A useful sketch of history is given in Alfred Tarski's Elimination Theory for Real Closed Fields by van den Dries. The result was known to Tarski by 1948 (when his Decision Method for Elementary ...
Conifold's user avatar
  • 77.7k
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
  • 5,689
6 votes
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Which geometer first compared a length (one dimensional) to an area (two dimensional)?

Al Khwarizmi, one of the first written sources of the general solution to quadratics, does exactly that: I observed that the numbers which are required in calculating by Completion and Reduction are ...
SRobertJames's user avatar

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