Questions tagged [ho.history-overview]

History and philosophy of mathematics, biographies of mathematicians, mathematics education, recreational mathematics, communication of mathematics.

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Fantappie transform(ation)s in Gelfand et al. “Generalized functions”

In the 6-volume "Generalized functions" a treatment of Fantappie transformations is promised in Vol. 1 (bottom of p.461 of the Russian edition) to come in Vol. 5. However, there is no Fantappie ...
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How much is MathOverflow exposed to recent events on StackeExchange? [migrated]

[Long-time 10k+ MO user here, asking this question anonymously for reasons that should be obvious. I can't ask this question on meta.MO without logging in, despite the sidebar telling me to go ask ...
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1answer
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Is Van der Waerden's conjecture really due to Van der Waerden?

Van der Waerden's conjecture (now a theorem of Egorychev and Falikman) states that the permanent of a doubly stochastic matrix is at least $n!/n^n$. The Wikipedia article, as well as many other ...
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Frégier and Frégier's Theorem

A curious and interesting gem is Frégier's theorem, quoted here from David Wells: Choose any point $P$ on a conic, and make it the vertex of a right angle which rotates about $P$. Then the ...
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1answer
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Why is the inertia stack of a smooth Deligne-Mumford stacks called inertia?

Let $\mathcal{X}$ be a smooth Deligne-Mumford stack. Then there is an associated stack $I\mathcal{X}$, called the inertia stack of $\mathcal{X}$. Why is the inertia stack called "inertia"? We can ...
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Skolem's proof of Konig's infinity lemma

I am trying to understand the following passage from Skolem’s (1922) proof of the Lowenheim-Skolem theorem by reference to the contemporary proof of Konig’s infinity lemma: Let $L_{1,n},L_{2,n},...,...
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Motivation for considering cyclic and separating vectors

Is there a natural motivation which would lead someone to consider the notion of cyclic or separating vectors to study representations of $C^*$-algebras? It only arouses a vague feeling about ...
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Thurston on the Robertson-Seymour theorem

Danny Calegari recounts here that Bill Thurston "gave one talk explaining his idea of a new proof of (some version of) the Robertson-Seymour theorem" at MSRI in 1996-1997. I could not find it in the ...
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1answer
197 views

Possible to prove a lemma from Godel's completeness theorem in intuitionistic logic?

I am trying to determine whether a particular theorem used in the course of Godel’s (1930) proof of the completeness of predicate logic could be proven in an intuitionistic metatheory. Theorem VI (p....
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3answers
568 views

Lesser known examples of perseverance with a successful ending [closed]

The stories of Wiles, of Perelman, and of Zhang, are very well-known to illustrate that sometimes great results are achieved through particularly long perseverance. What are lesser known-examples ...
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Examples of “unsuccessful” theories with afterlives

I am looking for examples of mathematical theories which were introduced with a certain goal in mind, and which failed to achieved this goal, but which nevertheless developed on their own and ...
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305 views

Contributions of Mary Cartwright to Theory of Entire Functions

I have seen on the Wikipedia page for the mathematician Mary Cartwright that she achieved many new results in the field of entire functions and the zeroes of entire functions and that many of these ...
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Completeness or soundness? Understanding a claim by Gödel

My question concerns a statement by Gödel in 1967. Commenting on Skolem’s failure to infer completeness from his (1922) proof of the Lowenheim-Skolem theorem, Gödel observes that Skolem did not ...
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Origin of the term “sinc” function

Is the sinc function defined here, really a short form of "sinus cardinalis" as proposed by Wikipedia? This information is deleted now but it existed some time ago. Even if we search Google Books for ...
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Origin of the standard result on convex hull of weights of an irreducible finite dimensional representation?

What is the earliest published statement and proof of the well-known result: for a simple Lie algebra over $\mathbb{C}$ or other algebraically closed field of characteristic 0, the convex hull (in the ...
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409 views

Character theory and Quantum Chemistry

Who (presumably a chemist) realized first the efficiency of character theory in calculations of orbitals of atoms? In which year?
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Spelling König's Lemma

I was surprised to learn here that the man responsible for "König's Lemma" was Hungarian, and spelled his last name Kőnig (with a different accent on the o), presumably with the same accent that ...
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Who proved that the Mandelbrot set's Julia sets are locally connected?

I'd be greatly interested in a reference to the respective article. Was it Douady? Julia? Hubbard? Fatou? Bonus question: Who gave the proof that can be found in the Orsay notes? EDIT: The question ...
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14answers
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Why doesn't mathematics collapse even though humans quite often make mistakes in their proofs?

To begin with, I am aware of these questions, which seems to be related: How do I fix someone's published error?, Examples of common false beliefs in mathematics, When have we lost a body of ...
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260 views

Why “monoidal” transformation?

In Carlo Beenakker's answer to this recent MO question, it turns out that the name "monoid" was first used in mathematics by Arthur Cayley for a surface of order $𝑛$ which has a multiple point of ...
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1answer
945 views

Who invented Monoid?

I was trying to find (and failed) the original author of either the concept of Monoid (set with binary associative operation and identity) the name (which sounds french ? and also Dioid (for what ...
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Asymptotically periodic potentials

Who came up with the idea of solving elliptic equations with periodic potentials and from there solving elliptic equations with asymptotically periodic potentials?
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2answers
340 views

When were triples called monads for the first time?

I am fine-tuning a short note on basic category theory; any such course must introduce monads, and I want to give a bit of history of the subject. I soon realized that I don't know the precise series ...
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1answer
241 views

Problem Understanding Euclid Book 10 Proposition 1 [closed]

this is embarrassing, but I am having trouble reading through Proposition 1 of Book 10 of Euclid's elements. I'm struggling with Euclid's terminology and don't have a clear picture of what divisions ...
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2answers
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Moving frames method for non-matrix Lie group

I am having troubles in understanding the modern definition of moving frames method. Classically, the idea of moving frames is "to express the variation in terms of the moving frame itiself". This ...
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Equivalence between Lowenheim-Skolem Theorem and Godel Completeness

In papers published 1920 and 1922, Skolem offered two separate proofs of a result due to Lowenheim. On this basis we can distinguish a strong and a weak version of the Lowenheim-Skolem theorem as ...
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1answer
271 views

O. Leroy's thesis on Fundamental groupoids

Does someone have a copy of the O. Leroy's thesis: Groupoïde fondamental et théorème de van Kampen en théorie des topos or has the ability to make a digitalization ? The thesis was done at ...
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Examples of simultaneous independent breakthroughs

I'm looking for examples where, after a long time with little progress, a simultaneous mathematical discovery, solution, or breakthrough was made independently by at least two different people/groups. ...
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2answers
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Origins of substitutional quantification

Substitutional quantification is an alternative to the objectual or referential interpretation of the quantifiers $\forall$ and $\exists$. The truth-conditions for objectual quantifiers are given in ...
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1answer
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Infinitary reasoning in Godel's Completeness Proof

Godel's Completeness Theorem is a straightforward consequence of Skolem 1922 and yet this conclusion was not drawn by Skolem himself. In a letter to Wang (Dec. 7, 1967 in Godel 2003) Godel gives an ...
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Was Jacobi the first to notice the ambiguity in the partial derivatives notation? And did anyone object to his fix?

In his 1841 article De determinantibus, Jacobi remarked that the notation $\frac{\partial z}{\partial x}$ for partial derivatives is ambiguous. He observed that when $z$ is a function of $x,y$ as well ...
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1answer
145 views

Origin of the theorem related to the integral transform pair

The development of Fast Fourier transform is attributed to Cooley & Tukey, both have written a lot about it is historical development. Both Cooley and Tukey call it a re-discovery rather. However,...
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On earlier references for $P=BPP$ and Kolmogorov's possible view on modern breakthroughs involving randomness?

Kolmogorov and Uspenskii in this paper 'http://epubs.siam.org/doi/pdf/10.1137/1132060' speculate $P=BPP$ in $1986$. They do this without getting into circuit lower bounds and from a different view ...
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1answer
458 views

Origin of the convolution theorem

I am a chemist, with some interest in signal processing. Sometimes, we use the deconvolution process to remove the instruments response from the desired signals. I am looking for the earliest ...
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1answer
984 views

Divergent Series & Continued Fraction (from Gauss' Mathematical Diary)

I've asked that question before on History of Science and Mathematics but haven't received an answer Does someone have a reference or further explanation on Gauß' entry from May 24, 1796 in his ...
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How did Lefschetz do mathematics without hands?

If people think this is the wrong forum for this question, I'll cheerfully take it elsewhere. But: How did Solomon Lefschetz do mathematics with no hands? Presumably there was an amanuensis to ...
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The meaning of this mysterious remark in Littlewood's Miscellany

In the well known book by Littlewood (Mathematician's Miscellany, or the later edition called Littlewood's Miscellany) there is a remark made in the chapter 'A Mathematical education', the meaning of ...
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366 views

Why are algebraic schemes called algebraic?

In scheme theory, an algebraic scheme is the data of a scheme + a morphism of finite type to the spectrum of a field. Where does the term "algebraic scheme" come from? It does not seem intuitive to me ...
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Historically, how were Grothendieck topoi motivated?

The question is about how did the person who invented Grothendieck topoi (presumably Grothendieck) arrive at the necessity of a such a notion. I do not know much about the history of the subject. What ...
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239 views

Do we know what the impulse to “introduce” the Jordan canonical form was?

Mo-ers, Do you know how it was that the study of the Jordan canonical form began? There are certain things that may be said once one has thought about the matter: for instance, one can say that the ...
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1answer
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Why is the Eisenstein ideal paper so great?

I am currently trying to decipher Mazur's Eisenstein ideal paper (not a comment about his clarity, rather about my current abilities). One of the reasons I am doing that is that many people told me ...
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402 views

History of the notion of $(G,X)$-structure

I'm currently searching for sources and historical basis on the notion of $(G,X)$-structure as it appears in Thurston's work. So far, it appears that he was the first to set it. Many mathematicans ...
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2k views

Status of proof by contradiction and excluded middle throughout the history of mathematics?

Occasionally I see the claim, that mathematics was constructive before the rise of formal logic and set theory. I'd like to understand the history better. When did proofs by contradiction or by ...
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Why not adopt the constructibility axiom $V=L$?

Gödelian incompleteness seems to ruin the idea of mathematics offering absolute certainty and objectivity. But Gödel‘s proof gives examples of independent statements that are often remarked as having ...
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1answer
169 views

History of algebraic graph theory

I need a source about the history of algebraic graph theory. I mean for solving which problems or responding to what needs it was created? Indeed, I want to write a note about the history of the ...
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1answer
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Yau's problem: Construct a triangle given a side, an angle, and an angle bisector

In Shing-Tung Yau's autobiography The Shape of a Life, he mentions a problem that he came up with as a teenager. Suppose you know the length of one side of a triangle, one angle, and the length of ...
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868 views

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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Telling right from left

I know a lot of people, some of them mathematicians, who have trouble telling right from left. This can lead to problems when you are composing functions, for example. When did this seemingly ...
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Why are Thompson's groups called $F$, $T$ and $V$?

Why are Thompson's groups called $F$, $T$ and $V$? I never saw Thompson's unpublished notes, in which he introduces these groups; maybe an explanation can be found there?
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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?...