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

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18
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2answers
787 views

History of Geometric Analogies in Number Theory

My question, put simply, is: When did mathematicians/number theorists begin viewing questions in number theory through a geometric lens? For example, was it before Grothendieck introduced schemes to ...
22
votes
0answers
386 views

Next steps on formal proof of classification of finite simple groups

While people are steaming ahead on finessing the proof of the classification of finite simple groups (CFSG), we have a formal proof in Coq of one of the first major components: the Feit-Thompson ...
15
votes
1answer
942 views

The list of problems for Grothendieck's thesis

Is the list of open problems which were given by Dieudonne and Schwartz to Grothendieck for his thesis published somewhere? I know a quotation of Dieudonne that the problems concerned duality theory ...
3
votes
1answer
146 views

Blow-up as polar coordinates?

While doing some explicit calculations involving a blow-up of the plane in a point, I realised what I was doing was basically writing things in polar coordinates. Somewhat astonished that I hadn't ...
20
votes
1answer
916 views

What is $\infty^6$?

The title of this question may make you want to close it immediately, but bear with me a moment. In several older mathematics papers (early 20th century) I have seen statements such as The ...
1
vote
0answers
92 views

First to note the relation between Stasheff polytopes (associahedra) and compositional inversion?

In my answer to MO-Q: Enumerative geometry and nonlinear waves, I outline the relation between the refined face polynomials of the Stasheff polytopes (associahedra) and the partition polynomials for ...
14
votes
2answers
735 views

Origin of the term “Diophantine equation”

It seems that the term "Diophantine equation" has been around at least since the second half of the 19th century, since the historian Hermann Hankel writes (polemically) in the chapter on Diophantus ...
41
votes
4answers
1k views

How did Cole factor $2^{67}-1$ in 1903

I just heard a This American Life episode which recounted the famous anecdote about Frank Nelson Cole factoring $N:=2^{67}-1$ as $193707721 \times 761838257287$. There doesn't seem to be a historical ...
16
votes
1answer
359 views

What sort of models did Bolyai and Lobachevsky use to demonstrate the consistency of their models of non-Euclidean Geometry?

As is well-known, in the 1820s both Bolyai and Lobachevsky showed, at long last, the independence of the Parallel Postulate from the rest of the axioms of Euclidean geometry by developing what we now ...
1
vote
1answer
156 views

Non-Pythagorean proof for the square root of 2 and solution to YBC7289 [closed]

My name is J. Frederic Teubner I am an independent researcher. I wish to publish a proof for the non-Pythagorean solution to the Babylonian tablet YBC7289 and am currently inquiring as to whether or ...
6
votes
1answer
355 views

Who introduced the concept of topological mixing?

I am writing an introduction and I want to know who introduced the concept of topological mixing?
3
votes
1answer
143 views

What kind of role has Functional Analysis played in Signal Processing? [closed]

Does it serve mainly as a narration or is there any substantive consequence which might not be derived without tools of functional analysis?
11
votes
2answers
763 views

Describe the desired features of a “Mathematics Colloquium”?

I'm now a member of my department's colloquium committee. Our task is to make a great colloquium series. I thought that the first step would be to come up with an appropriate definition of ...
5
votes
0answers
148 views

Reference to forcing with a sigma ideal $\cong$ Cohen forcing

This is a historical question: Who was the first person to notice the following? If $V \models \kappa$ is measurable and $P$ adds $\kappa$ Cohen reals, then in $V^P$, letting $\hat{I}$ to be the ...
19
votes
1answer
764 views

Steinhaus's Easter Egg Problem

The following is the text of Steinhaus's so-called Easter egg problem. According to this article of Roman Duda, this was recorded in the New Scottish Book around Easter 1955 and "Steinhaus offered an ...
12
votes
4answers
928 views

“Epicycles” (Ptolemy style) in math theory?

By analogy: The epicycles of Ptolemy explained the known facts in the sun system and in this sense were not "wrong". But they distracted from a better insight. From another viewpoint, everything fell ...
16
votes
7answers
2k views

Are there any Algebraic Geometry Theorems that were proved using Combinatorics?

I'm collaborating with some algebraic geometers in a paper, and when writing the introduction I mentioned the interaction of Combinatorics and Algebraic Geometry, and gave some examples like the ...
21
votes
1answer
983 views

Homeomorphism historically: When did it reach its modern formulation?

Q. When did the notion of homeomorphism reach its modern formulation as a bicontinuous bijection, i.e., a continuous bijection between topological spaces whose inverse is also continuous? ...
38
votes
1answer
2k views

Did Bourbaki write a text on algebraic geometry?

Certainly Bourbaki never wrote an introduction to algebraic geometry: we would have heard about it, right?
1
vote
1answer
2k views

Famous examples of PhD advisors younger than their student [closed]

What are the most famous examples of PhD advisors in mathematics, younger than their student? (if possible put the date of birth and/or the difference in age).
5
votes
1answer
666 views

Cricket and the Hardy-Littlewod maximal function

I'v read somewhere that one motivation for Hardy to define his maximal function is the game of cricket. But I can't see how they are related. Could anyone provide some more information on their ...
0
votes
1answer
683 views

The most cited paper in Mathematics [closed]

I am wondering about the most cited papers/books in Mathematics. I always had the impression that the number of citations in the mathematical community is several orders of magnitude below the number ...
11
votes
4answers
727 views

Brandt's definition of groupoids (1926)

The definition of a category is usually attributed to Mac Lane and Eilenberg (1945). What seems to be less known is that the german mathematician Heinrich Brandt has developed the notion of a groupoid ...
14
votes
2answers
575 views

Scott-Solovay unpublished paper on ``Boolean valued models of set theory''

I have read some papers from 1970$^{th}$, and in some of them, the paper of Scott and Solovay on ``Boolean valued models of set theory'' is given as a main reference, with many references to the ...
10
votes
2answers
458 views

History of Tarski's problems on free groups

As is known, Tarski posed his questions about first-order theories of non-abelian free groups around 1945. However, the questions were not published in his papers or books. What is the original ...
23
votes
4answers
867 views

Communal problem books

A certain class of books is defined as follows: (1) the book was kept for years in a cafe or mathematics library; (2) the primary contents are research problems and comments, handwritten by resident ...
8
votes
0answers
167 views

History of preservation theorems in forcing theory

For my honours thesis, I am studying a general preservation theorem using a framework provided by Shelah. I am mainly concerned about revised countable support iteration of $\dot{S}$-semiproper ...
0
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0answers
95 views

Filmed lectures by Hassler Whitney

Are there any filmed lectures by outstanding American mathematician Hassler Whitney, besides the two Einstein Chair lectures below? Old lectures, from the 1940s onwards, would be particularly ...
3
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0answers
251 views

Galois correspondence subgroups/subsystems

In this paper (1998) by M. Izumi, R. Longo, S. Popa, there is the following result (page 49) on compact groups: Lemma 3.16. Let $G$ be a compact group and $Rep(G)$ the category of finite ...
3
votes
1answer
826 views

Who coined “mob” and “clan” and why these words?

A mob is a word used for a topological semigroup which is a Hausdorff space. A clan is a compact connected mob with a two-sided identity element. Who used these words with these meanings first and ...
6
votes
1answer
166 views

Did Lucas discover Lucas circles?

MathWord's article on Lucas circles traces the name to a little-known 1973 publication. These interesting circles have found their way into several 21st century publications, including the online ...
2
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0answers
110 views

Examples of Geometric Constructions in Higher Dimensions

The classical problem of geometric construction seems to be restricted to planar Euclidean Geometry with straight edge and compass as the only admissible "construction-tools". I would like to ...
3
votes
1answer
224 views

Was $\Sigma x$ used as quantifier?

Kurt Gödel in 1931 used $x\Pi a$ where we in contemporary notation would use $(\forall x) A$ or $(x)A$, and $Ex a$ where we would use $(\exists x) A$. I believe that I remember that $\Sigma xA$ has ...
5
votes
2answers
221 views

History of the orientation of Cartesian coordinates in drawing

Is there any actual historical example in which a Cartesian plane with all four quadrants has been used, but with all axes marked with positive numbers? [Please see Sawyer's paper below for a ...
0
votes
1answer
275 views

History of Poincare conjecture in higher dimension [closed]

As far as I know, when Poincare formulated his well known conjecture, the original statement was the follwoing: if a closed manifold has the same homology groups as the sphere it is homoeomorphic to ...
11
votes
2answers
870 views

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. ...
1
vote
0answers
168 views

Filmed lectures by Jürgen Moser

Are there any filmed lectures by outstanding German mathematician Jürgen Moser (July 4, 1928 – December 17, 1999)?
51
votes
2answers
1k views

History of $\frac d{dt}\tan^{-1}(t)=\frac 1{1+t^2}$

Let $\theta = \tan^{-1}(t)$. Nowadays it is taught: 1º that $$ \frac{d\theta}{dt} = \frac 1{dt\,/\,d\theta} = \frac 1{1+t^2}, \tag1 $$ 2º that, via the fundamental theorem of calculus, this is ...
11
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0answers
285 views

Why is a matrix pencil called a pencil?

I'm trying to understand the historical context behind the word pencil in matrix pencils, or pencil of curves so on. I am aware that even Gantmacher 1959 has this terminology however I don't know ...
12
votes
0answers
269 views

Grothendieck on polyhedra over finite fields

In Grothendieck's Sketch of a Programme he spends a few pages discussing polyhedra over arbitrary rings and concludes with some intriguing remarks on specializing polyhedra over their "most singular ...
2
votes
1answer
144 views

Two questions on substitutability

(1) The condition that a term $a$ be substitutable for another term in an expression can be given a recursive definition. Who first developed such a definition? (2) One sometimes see the phrase "$a$ ...
1
vote
0answers
371 views

Why did Grothendieck say stop publishing his works? [closed]

Why did Grothendieck say stop publishing his works? https://sbseminar.wordpress.com/2010/02/09/grothendiecks-letter/ Any edition or dissemination of such texts which have been made in the past ...
0
votes
0answers
69 views

Shuffle multiplication and generalized Leibniz rule in tensor calculus

The headline already says it: Is anybody (except me) aware of this formula for higher total covariant derivatives of tensor products? It is the simplest application of the commutative shuffle product ...
1
vote
0answers
104 views

Why are they called 'pernicious' numbers?

The definition of a pernicious number: In number theory, a pernicious number is a positive integer where the Hamming weight (or digit sum) of its binary representation is prime. The meaning of ...
3
votes
1answer
216 views

When was the “arrow notation” for functions first introduced?

When was the "arrow notation" $f: X \to Y$ for functions first introduced? Who introduced it and with which motivation? I ask this question in order to understand whether it was, in part, this ...
5
votes
2answers
259 views

Convention about “long” roots for simple Lie algebras of types ADE?

The classification of simple Lie algebras (over $\mathbb{C}$ or other sufficiently large field of characteristic 0) correlates these Lie algebras with the irreducible reduced root systems (in ...
4
votes
1answer
434 views

Did Brouwer evade uncountability?

I have the distinct memory of having often heard and read that intuitionism was inter alia geared to avoid Cantor's uncountable sets, and it may be that this was Brouwer's plan. But are there accounts ...
10
votes
1answer
446 views

Metric $d(A,B) = \mathbb P(\overline A\cup\overline B\mid A\cup B)$

I'm wondering where the relative probabilistic distance was first studied: $$d(A,B) =\mathbb P(\overline A\cup\overline B\mid A\cup B)$$ where $\overline A$ is the complement of $A$. A web search ...
52
votes
5answers
4k views

Are there any serious investigations of whether “mathematicians do their best work when they're young”?

There is no shortage of anecdotes and conjectures on both sides of this widespread belief, but good supporting data either way is harder to find. Can anyone provide any references for serious ...
12
votes
2answers
578 views

Discovery and Study of Conic Sections in Ancient Greece

Is there anything known about what drew the attention of ancient greek mathematicians to conic sections and, what were the models they used to study conic sections? What I would like to know, is ...