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

Hilbert was influenced especially by Dedekind's 1888 essay The Nature and Meaning of Numbers, but he shared only half of Dedekind's approach. To keep things in perspective, it is important to note the ...
Conifold's user avatar
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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
2 votes

Origin of modern definition of a function as a graph

This is definitely not 200 years old. The first definitions of the modern function concept are from Dedekind, Cantor, Peano and Frege from around 1890, and even those definitions are not encoded ...
Michael Bächtold's user avatar
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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2 votes

When and why was the concept of "having a least upper bound" dubbed "completeness", as in Axiom of Completeness?

Michael E2 suggests the first usage of the Axiom of Completeness was Hilbert (p.21) in 1899 (!!!), who writes: Remark. To the preceeding five groups of axioms, we may add the following one, which, ...
SRobertJames's user avatar
4 votes

Is Gauss the first who introduced congruences?

It is worth noting that Gauss himself did not claim to be the first to invent the concept of congruence. In Disquisitiones Arithmeticae, after giving his definition of congruence and introducing his ...
TranslatesGauss's user avatar
5 votes
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What were Auguste Comte's contributions to mathematics (if any)?

Comte's main contribution to mathematics is the careful set of notes he kept of Cauchy's course in analysis in the 1820s. This is mentioned in Schubring's book Schubring, Gert. Conflicts between ...
Mikhail Katz's user avatar
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4 votes

Is it true that Empress Elisabeth of Austria did math?

She didn't do any math. From my research about her, it seems that the user you are referring to is teasing the fact that her nickname was "Sisi" which looks similar to the integrand. I also ...
Kamal Saleh's user avatar
3 votes

Why and how did the study of complex numbers progress despite the denial of negative numbers?

Those mathematicians who worked with complex numbers, of course did accept negative numbers. When you say that "negative numbers were not accepted", you mean that they were not UNIVERSALLY ...
Alexandre Eremenko'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
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5 votes

Is there any example of a long-standing mathematical conjecture whose resolution did not require advanced knowledge?

The Gaussian correlation inequality was first conjectured in the 1950s, and not proved until 2014 by Thomas Royen. As Wikipedia puts it, The proof did not gain attention when it was published in 2014,...
Timothy Chow's user avatar
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3 votes

History of cohomology theory

Cohomology theories were introduced independently by A. Kolmogorov, Ueber die Dualitat im Aufbau der kombinatorischen Topologie, Mat. Sbornik, vol. 1, 1936, 97-102, and by J. W. Alexander, On the ...
Alexandre Eremenko's user avatar
2 votes

What new mathematics was inspired by biology and chemistry?

In his article, Can biology lead to new theorems?, Bernd Sturmfels gives four theorems that were inspired by biology. As one example, Andreas Dress and his collaborators have developed a theory of ...
Timothy Chow's user avatar
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1 vote

Mathematization of natural sciences

Pythagoras discovered that simple mathematical ratios were important to harmony. As Xenocrates put it: Pythagoras discovered also that the intervals in music do not come into being apart from number;...
Mary's user avatar
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