# Questions tagged [ho.history-overview]

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

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### Diagrammatic representation of sets as irregular plane figures

I am trying to find the earliest use of plane diagrams of various shapes for representing sets. For example, this is snapshot is from the book called Some Modern Mathematics for Physicists and Other ...
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### Etymology of “real numbers"

I would like to know why the real numbers are called “the real numbers.” I would also like to know the meaning of “real” in the phrase “real number.” Further questions and clarifications: I’d like to ...
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### Hilbert's and Gödel's expanded definition of "Recursive Function"

There is a very interesting comment in this post: I must also make one terminological caveat: Hilbert, and later Godel, used the phrase "recursive function" in a way very different from the ...
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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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### What's the earliest result (outside of logic) that cannot be proven constructively?

Although mathematicians usually do not work in constructive mathematics per se, their results often are constructively valid (even if the original proof isn't). An obvious counter-example is the law ...
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### History of knot enumeration tables

There is much arbitraryness in the Rolfsen (and later) tables. Of course anyone would name $7_1$ to be the first knot with $n=7$ crossings, but already my own "natural" ordering attempt (...
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### About the exact origin of a binomial congruence

Given a prime $p$ and an integer $0 \leq k \leq p-1$, a famous congruence on binomial coefficients states: $$\binom{p-1}{k} \equiv (-1)^k \pmod{p}$$ It is generally taught as a consequence of Pascal’s ...
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### Connection of principal fiber bundles — history

I wonder who was the first to discover the notion of principal fiber bundle and its connection (gauge field in the physical language). Wikipedia cites the book by Steenrod (1951). But was he the ...
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### What was the "stormy discussion" about differential Galois theory at IHES?

In Kazuo Okamoto and Yousuke Ohyama's paper "Mathematical works of Hiroshi Umemura", Annales de la faculté des sciences de Toulouse Mathématiques, XXIX, no. 5 (2020) pp. 1053-1062, there is ...
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### What is the status of the theory of motives?

It has been almost 60 years since Grothendieck conceived the conjectural theory of motives in order to grasp the common behavior of the most important (Weil) cohomology theories. But what is the ...
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### Minkowski problem for polytopes: the origin of necessary condition

Minkowski's uniqueness theorem for polytopes concerns the specification of the shape of a polytope by the directions and measures of its facets. Theorem (Minkowski). Let $A_i$ be positive faces areas ...
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### How are Lie groups and polynomial resolvents related?

I came across the following sentence in Stevenhagen and Lenstra's wonderful little article Chebotarëv and his density theorem: Nikolai's interest in [polynomial] resolvents led him to study Lie ...
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### Video abstracts for mathematical papers

I recently published a video abstract of a manuscript of mine (number theory), finding that more people are interested in its content than when I uploaded the preprint on arXiv. Now, my main question ...
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### Geometric construction of real root of quintic using marked ruler and compass

My question is motivated by a geometry problem about special folded rectangle: 'A rectangle with sides a, b (a<b) is folded along the line that passes through the center of the rectangle in order ...
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### Meaning of a result of Gauss on "Mensura" of cyclotomic numbers

(This question was asked before on mathstackexchange. I received a few useful comments there, which helped me answer it for a special case, but I did not succeed in proving the general case.) In an ...
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### ID needed for one mathematician in group photo

The photo below was taken at MSRI in 1984 and MSRI has asked me to try to find out (on behalf of Lou Kauffman, Sofia Lambropoulou and Martha Jones) the identity of the mathematician farthest left, in ...
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### Explicit character tables of non-existent finite simple groups

In connection with the historical development of the classification of finite simple groups, I am interested in a particular aspect that seems to be less well-documented than the main narrative of ...
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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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### When has the scaffolding been more important than the completed building?

Niels Abel once said(1) of Gauss, "He is like the fox, who effaces his tracks in the sand with his tail." to which Gauss replied, "No self-respecting architect leaves the scaffolding in ...
1 vote
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### "On models of elementary elliptic geometry"

While perusing p. 237 of the 3rd ed. of Marvin Greenberg's book on Euclidean and non-Euclidean geometries, I learned that it can actually be proven that "all possible models of hyperbolic ...
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### History of asymptotic expansion of Laplace’s method between Laplace and Erdélyi

In 1774 Laplace understood that $I≔∫\textrm{d}x \exp kf(x)$ for $k≫0$ can be estimated if one knows 2-jet of $f$ at its point of maximum (as $I₀ ≔ ∫\textrm{d}x \exp kf₀(x)$ with $f₀$ quadratic with ...
1 vote
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### Who introduced the concept of beyond planar graphs?

The concept of planar graphs seems to be standard (I'm also not sure who first used this term), and recently, beyond planar graphs attract a lot of interest in the field of graph drawing. I know that ...
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### History of right hand rule

I am not sure if this is the right place to ask, but many mathematicians are knowledgeable and interested also in history of math, so here I am. I am curious to know when the right-hand-rule for ...
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### How did the term "space" in mathematics started to be understood as a set with a structure?

In mathematical literature, the term 'space' is often used to describe a set endowed with additional structure, such as a metric space or a vector space. What is the historical evolution of the ...
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### Nash–Moser–De Giorgi differences

The names of Nash, Moser and De Giorgi are associated to elliptic and parabolic regularity theory. But what are the differences in the approach between the three contributions? Can you briefly sketch ...
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### What's the unspoken history of compactly generated topological spaces?

Usually, the alleged motivation for the definition of compactly generated topological spaces is Cartesian closedness, which fails for general spaces. Of course, from a contemporary perspective, this ...
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### Mention of Bernoulli principle by Bill Lawvere

In the Author Commentary to the reprint of the paper paper Diagonal Arguments and Cartesian Closed Categories in Theory and Applications of Categories Bill Lawvere wrote: Although the cartesian-...