Questions tagged [ho.history-overview]
History and philosophy of mathematics, biographies of mathematicians, mathematics education, recreational mathematics, communication of mathematics.
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Can I find Fermat's complete works anywhere?
I admire the mathematician very much and want to look at his writings. Is there anywhere in book or web form that has a collection of his writings?
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The fundamental theorem of Galois theory
Who proved the modern form of the fundamental theorem of Galois theory?. Was it in the original Galois' manuscript?
user6976
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Who first defined locally convex topological vector spaces?
Who first defined the class of locally convex topological vector spaces?
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Why are they called Specht Modules?
I know that the simple modules of $\mathbb{C}S_n$ are called Specht Modules, and they are named after the German Mathematician Wilhelm Specht because he studied them, but I think these modules were ...
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At what point in history did it become impossible for a person to understand most of mathematics?
Disclaimer:
I am asking this question as an improvement to this question, which should be community wiki. This is in line with the actions taken by Andy Putman in a similar case (cf. meta).
See the ...
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Erich Stiemke biography
Can someone provide some biographical details, especially the dates of birth and death, about Erich Stiemke? According to the Mathematics Genealogy Project, he obtained his Dr. phil at Universität ...
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History question - why h in the definition of derivative?
Does anyone have a clue where the "h" came from?
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Where does the $\hat A$ class get its name?
In K-theory we have the Todd class and the $\hat A$ class.
The Todd class is named after the Cambridge geometer John Arthur Todd.
Where does the name $\hat A$ come from? Does the A stand for Atiyah?...
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reference request: rational points on the unit sphere
I wonder what would be a good/early reference for the fact:
rational points on the unit sphere (centered at the origin) are dense.
Stereographic projection (from a rational point in the sphere) ...
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The first complete proof of the Kronecker-Weber theorem
While the Kronecker-Weber theorem —that every finite abelian extension of $\mathbb Q$ is contained in a cyclotomic field— is always attributed to, well, Leopold Kronecker and Heinrich Martin Weber, ...
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How quickly did Gödel's Incompleteness Theorem become known and heeded throughout mathematics
Does anyone know how news of Gödel's incompleteness theorem spread? Did it do so little by little, or was it shouted in dramatic headlines throughout mathematical literature? If anyone can point me to ...
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Can Fuchsian functions solve the general equation of degree n?
In the classic textbook Introduction to the Theory of Equations (Conkwright, 1941), on p. 85, the author writes that “the algebraic solution of the general equation of degree n is impossible if n is ...
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Up-to-date version of Principia Mathematica?
Background: I found this interesting translation of Godel's On formally undecidable propositions of Principia Mathematica and related systems I that, along with translating it into English, uses more ...
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Reference request: Leonardo Da Vinci's supposed math results
Many reputable sources (I can give as many as you want) describe Da Vinci as a mathematician, but they never mention a single theorem, result, or lemma that he proved. There's the golden ratio spiral, ...
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Why did Alonzo Church choose the letter $\lambda$ as the "binding operator"?
Is there any known reason why Alonzo Church chose Greek $\lambda$ as the "binding operator" for the Lambda Calculus?
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At what point does number theory stop playing with finite rings?
Basic results in number theory, like the Chinese remainder theorem, the Euclidean algorithm and Euler's theorem, are really about finite structures, namely the rings $\mathbb{Z}/n\mathbb{Z}$ for ...
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Is there something I am missing about the computation of the $p$-part of the class groups of cyclotomic fields?
Well, the answer of the question in the title in certainly Yes, many things in fact, but let me be more precise.
In 1958, Serre gave a Bourbaki talk on the recent works of Iwasawa on class groups in ...
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Why is the Dyck language/Dyck paths named after von Dyck?
The Dyck language is defined as the language of balanced parenthesis expressions on the alphabet consisting of the symbols $($ and $)$. For example, $()$ and $()(()())$ are both elements of the Dyck ...
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English translation of Wilhelm Killing's 1889 paper
In the paper The greatest mathematical paper of all time, by A. J. Coleman (The Mathematical Intelligencer 11 (1989) pp29-38, https://doi.org/10.1007/BF03025189) the author argues that Wilhelm Killing'...
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History of the classification of mathematical subjects
I would like to know if there are sources on the history of the classification of mathematical subjects.
Gérard Lang
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Smallest dimension of nontrivial representation of a simple Lie algebra over `$\mathbb{C}$`
The question involved here is natural and very classical, but I'm unsure what has been formally stated and proved in the literature. The only approach I know involves assembling facts that apparently ...
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Higgs paper ``A category approach to Boolean valued set theory''
As Philip Scott says
about Denis Higgs:
In category theory, he wrote an influential and beautiful long paper, "A
category approach to Boolean valued set theory", which initiated many
early students ...
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Is there evidence whether undergraduate math courses improve problem-solving?
The most commonly stated reason for why mathematics should be a required condition for graduating is }to improve problem-solving skills". Usually it's taken for granted that taking a mathematics ...
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Ehresmann's approach to differential geometry
I have come accross this brief description of Charles Ehresmann's life given by his wife: http://www.cs.le.ac.uk/people/ah83/cat-myths/myth0002.html
I quote the part from the text relevant to my ...
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What's the role of $H^{p}(\mathbb{R}^{n})$ in modern (harmonic) analysis?
The classical theory of $H^p$,due to it's heavy dependence on the complex function theory(such as Blaschke products), seemed to have an insurmountable obstacle barrying its extension to several ...
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History of use of "=" symbol to mean "is canonically isomorphic to"
Let $A$ be a commutative ring, and let $f$ and $g$ denote elements of $A$ such that the prime ideals of $A$ containing $f$ are precisely the prime ideals containing $g$ (a not completely trivial ...
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What is the reason that $\sigma$-algebra replaced $\sigma$-ring in introductory measure theory?
May I ask what is the (historical) reason we adopted the $\sigma$-algebra rhetoric instead of $\sigma$-rings (like used in Halmos)? To my knowledge almost all modern measure theory or real analysis ...
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Who first showed that $SL(n,O_K)$ is a lattice for a number ring $O_K$?
Let $O_K$ be the ring of integers in an algebraic number field $K$. Assume that $K$ has $r$ real embeddings and $s$ pairs of complex conjugate complex embeddings. There is then an injective ...
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Continuous extension of Riemann maps and the Caratheodory-Torhorst Theorem
If $G\subsetneq\mathbb{C}$ is a simply-connected plane domain, then by the Riemann mapping theorem there is a conformal isomorphism $\newcommand{\D}{\mathbb{D}}\varphi:\D\to G$, where $\D$ is the unit ...
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Wikipedia story about Bill Thurston's death [closed]
I did not know whom to ask about this rather unsettling piece of news. Apparently Wikipedia has announced Bill Thurston's death on August 21, 2012. I could not independently verify it. Is this true?
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What is the history of the notion of subdivision of categories?
A recent answer by Peter May prompts me to ask a question which I have been considering to ask for several months. (The reason why I have not asked it before is that it is not directly related to my ...
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Where can you find Grothendieck's "Récoltes et Semailles"?
Where can you find Grothendieck's "Récoltes et Semailles"?
Is it available anywhere?
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Selberg's advisor?
Does anybody know who was Atle Selberg's advisor?
I find it interesting to know the advisor's impact on his students.
Unfortunately, in Selberg case, this information (even his advisor's name) seems ...
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Dehn's solution to Hilbert's 3rd: 1901 or 1902?
This is a simple bibliographic request that I have been unable to pin down. Max Dehn's
solution to Hilbert's 3rd problem is:
Max Dehn, "Über den Rauminhalt." Mathematische Annalen 55 (190x)...
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Algebraic geometry over the complex numbers, and beyond
My question basically is very simple: when did mathematicians start to do algebraic geometry "outside the complex numbers" ?
In the old days, algebraic geometry was solely done over the ...
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Early examples of mathematicians publishing (from home) in a foreign language?
Today this is common, but how exactly did it start? I am looking for examples in various languages, and suggest:
Exclude Latin (as more “ancient” or “international” than “foreign”)
Exclude French ...
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Why do mathematicians prefer one definition over the other when they both define the same concept?
Here is a basic, though very important, example:
Hilbert takes as primary the notion of “congruence” (or “equal”) between segments. His first axiom of congruence “requires the possibility of ...
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Emergence of the discrete from the continuum
An almost eternal theme in Mathematics is the approximation of the Continuum by the Discrete. This core idea goes back at least to Archimedes, and remains active to these very days (and quite likely ...
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History of the Frobenius Endomorphism?
The existence of the Frobenius endomorphism probably goes back to Euler's proof of Fermat's little theorem. But why is it named after Frobenius? Who gave it this name? When was it first stated in full ...
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Is GCH useful in proving theorems?
By GCH I mean the Generalized Continuum Hypothesis. Let me give some context before presenting my question.
When the axiom of choice was introduced by Zermelo in his 1904 proof of Well-Ordering ...
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Oldest photographed mathematician [closed]
Who is the most ancient mathematician of which we have a photograph?
(or, in the same vein, what is the oldest photograph of a mathematician)
A quick search on MacTutor History of Mathematics gives ...
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Texts on the General History of Contemporary Combinatorics
I am looking for some core texts (books, book chapters, papers) about the general history of contemporary combinatorics, starting, say, from the interwar period up to today.
Texts about the history ...
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Origin of the noun "mathematician" [closed]
I have read that Pythagoras's fraternity had two kinds of members, the 'acousmaticians', who were allowed to attend the lectures, and the 'mathematicians', who had been initiated. Is this the origin ...
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Early successes of Schwartz distribution theory
What are the early successes of Schwartz distributions theory?
What are the hard theorems that became simple and what
open problems were solved with this new tool soon after Laurent
Schwartz released ...
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Did human computers use floating-point arithmetics?
Before the proliferation of computers in the 1950s, did human computers use floating-point formats for their computations?
Floating-point calculation was reportedly implemented already in the 1910s (...
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Russell and Whitehead's types: ramified and unramified
I was reading Logicomix (a fictionalised account of logic from Frege to Gödel through Russell's eyes) and there was mention about two different versions of types developed by Russell and Whitehead for ...
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Earliest diagonal proof of the uncountability of the reals.
I cited the diagonal proof of the uncountability of the reals as an example of a `common false belief' in mathematics, not because there is anything wrong with the proof but because it is commonly ...
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An Euler-proof that cannot be repaired?
Ed Sandifer writes on Euler's wonderful work on prime numbers: The sum of the series of reciprocals of prime numbers $\frac{1}{2}+\frac{1}{3}+\frac{1}{5}+...$ is infinitely large, and is infinitely ...
user36182
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What are Central Limit Theorems and why are they called so?
I know two opinions:
1) "Central" means "very important" (as it was central problem in probability for many decades), and CLT is a statement about Gaussian limit distribution. If the limit ...
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Banach-Zarecki theorem - who was Zarecki?
I'm writing a paper for real analysis seminar, a paper about Banach-Zarecki theorem and I need some information about the authors.
Stefan Banach - there is no problem to find information about him.
...
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