**7**

votes

**2**answers

541 views

### Survey of the history of calculus?

Boyer 1939 is a nice readable survey of the history of the calculus, but it's showing its age. Discussing the notion of instantaneous velocity, he has:
Mathematics knows no minimum interval of ...

**9**

votes

**2**answers

516 views

### Origin of the term “generic” in set theory

In set theory, in particular the context of forcing, if $M$ is a model of $\sf ZFC$ and $P\in M$ is a partial order, we say that $G\subseteq P$ is a generic filter (or $M$-generic or generic over $M$) ...

**25**

votes

**3**answers

2k views

### Who invented diagrammatic algebra?

There is a strong and growing trend to do mathematics via diagrammatic algebra, which involves constructing and manipulating equations whose elements are diagrams drawn in the plane. The manipulations ...

**13**

votes

**1**answer

659 views

### Who first dubbed them “expander graphs”?

Expander graphs
("sparse graphs that have strong connectivity properties")
burst onto the mathematical scene around the millennium, but I have not
been successful in tracing the origin of
(a) the ...

**3**

votes

**1**answer

381 views

### Levi's book on Leibnizian calculus

Raphael Levi learned from Leibniz at a late stage in Leibniz's career. This might be a definite advantage for understanding Leibniz. Leibniz did not elaborate some of the philosophical principles ...

**6**

votes

**0**answers

138 views

### Origin of Lie Product Formula

I'm interested in where Lie wrote down the Lie Product formula (for finite matrices)
(the precursor of the Trotter product formula; see http://en.wikipedia.org/wiki/Lie_product_formula). With a ...

**5**

votes

**1**answer

391 views

### What was Seifert's contribution to the Seifert-van Kampen theorem?

The Seifert-van Kampen theorem is the classical theorem of algebraic topology that the fundamental group functor $\pi_1$ preserves pushouts; more often than not this is referred to simply as the van ...

**6**

votes

**1**answer

808 views

### Is there a “big program” in mathematics at the moment? [closed]

I apologize in the event that you should find this question off topic. Please feel free to delete it if that is the case.
Years ago, I studied undergrad mathematics at university. The understanding ...

**5**

votes

**1**answer

249 views

### When was the word “stable” first used to describe stable homotopy theory?

The word "stable" has many uses in mathematics, but in the context of stable homotopy theory, one might take it to mean one of two things:
Homotopy groups stabilize after taking suspensions ...

**43**

votes

**4**answers

3k views

### History of “without loss of generality”

"Without loss of generality" is a standard in the mathematical lexicon, and I am writing to ask if anyone knows where the expression was popularized. (The idea has been around since antiquity, I'm ...

**11**

votes

**3**answers

2k views

### Why are smooth numbers called “smooth”?

"Adleman refers to integers which factor completely into small primes as “smooth” numbers." (ME Hellman, JM Reyneri. Advances in Cryptology, 1983: citation link.)
Does anyone know what is the ...

**15**

votes

**4**answers

795 views

### Who first used the multiplication operator version of spectral theory

This is another history question.
Hilbert phrased the spectral theorem in terms of resolutions of the identity.
While this remained the form of Stone and von Neumann, they did also have the ...

**11**

votes

**3**answers

282 views

### Origin of number theoretic invariants associated to hyperbolic 3-manifolds

I've been studying number theoretic methods of classifying hyperbolic 3-manifolds for over a year now. In particular, there is are the trace field, invariant trace field, quaternion algebra, and ...

**52**

votes

**8**answers

5k views

### Have you solved problems in your sleep? [closed]

I have hit upon major (for me—relative to my trivial accomplishments)
insights in my research
in various sleep-deprived altered states of consciousness,
e.g., long solo car-drives extending ...

**17**

votes

**1**answer

805 views

### Reference for Diagonalization Trick

There is a standard trick in analysis, where one chooses a subsequence, then a subsequence of that... and wants to get an eventual subsubsequence of all of them and you take the diagonal. I've always ...

**2**

votes

**3**answers

622 views

### The Hidden Aspect of Set Theory [closed]

This question is inspired by a similar question at the beginning of Kunen's new book, "Set Theory".
Many mathematicians believe they are exploring a "real" universe. In such a Platonic point of ...

**1**

vote

**1**answer

104 views

### Original sources for two theorems by Bass, Matlis and Papp

It is an interesting fact that a commutative ring $R$ is noetherian if and only if direct sums of injective $R$-modules are injective, and if and only if every injective $R$-module is a direct sum of ...

**13**

votes

**2**answers

566 views

### What was the Question that led Euler to his Investigations on Polyhedra?

The question that led Euler to his investigations on graphs is the well-known question related to the seven bridges of Königsberg, and that story is a must in every introduction to graph theory.
...

**4**

votes

**1**answer

160 views

### What is the early history of the concepts of probabilistic independence and conditional probability/expectation?

In the 1738 second edition of The Doctrine of Chances, de Moivre writes,
Two Events are independent, when they have no connexion one with the other, and that the happening of one neither forwards ...

**7**

votes

**2**answers

556 views

### $\aleph$ looks like $\mathbb N$?

We all know the notation $\aleph_\lambda$ for the $\lambda$th (or, I guess, $\lambda+1$st) infinite cardinal number; in particular $\aleph_0$ is the cardinality of the the set of natural numbers ...

**1**

vote

**0**answers

441 views

### Is it possible to give a fair assessment of the influence of Bourbaki's “Eléments de mathématique”? [closed]

Well, I apologize if this "soft-question" (related to the "Arnold-Serre" debate) is considered as irrelevant for MO, and for possible misunderstandings in the two earlier versions of this post (which ...

**1**

vote

**1**answer

159 views

### First Parameterized Subset of Primes that was Related to a Mathematical Result

To my knowledge, Fermat primes, i.e. primes of the form $2^{2^n}+1$ were the first to play a role in a mathematical result, namely in the characterization of constructible regular n-gons. Gauss ...

**23**

votes

**2**answers

1k views

### Was Vinogradov's 1937 proof of the three-prime theorem effective?

Was Vinogradov's first proof of the three-prime theorem effective?
Reasons for my question: Vinogradov presented his proof in 1937 in a monograph; the English translation by K.F. Roth and A. ...

**10**

votes

**1**answer

375 views

### Who first resolved Hilbert's 20th problem?

Hilbert's 20th problem concerns the existence of solutions to the fundamental problem in the calculus of variations. I understand that Hilbert, Lesbesgue and Tonelli were pioneers in this area.
In ...

**6**

votes

**2**answers

1k views

### Ramanujan's tau function

Why was Ramanujan interested in the his tau function before the advent of modular forms? The machinery of modular forms used by Mordel to solve the multiplicative property seems out of context until I ...

**13**

votes

**2**answers

841 views

### Who first defined _simply connected_, reference?

The following definition is due to Donald J. Newman:
A connected open subset $D$ of the plane $\mathbb C$
is simply connected
if and only if its complement $\widetilde D = \mathbb C \setminus D$
...

**71**

votes

**9**answers

8k views

### Analogues of P vs. NP in the history of mathematics

Recently I wrote a blog post entitled "The Scientific Case for P≠NP". The argument I tried to articulate there is that there seems to be an "invisible electric fence" separating the problems in P ...

**6**

votes

**1**answer

770 views

### Source for Derogatory Quote About Graph Theory

(Edited in accordance with suggestions in comments.)
I remember once I read a quote that sounded like "graph theory is the scum of topology" (please approximate). I can not find it on the web, and I ...

**0**

votes

**3**answers

578 views

### Definition of Prime Numbers [duplicate]

The first time I heard of prime numbers, they were defined as natural numbers $n$ that can only be divided by 1 and themselves without remainder; later, when prime factorization was introduced, I ...

**24**

votes

**1**answer

5k views

### Who made the famous error in calculation that 'wasted' the final years of his life?

Sorry, I am merely a Middle School maths teacher at an Australian secondary school. I remember reading years ago about a famous mathematician (18th or 19th Century?) who calculated table upon table of ...

**9**

votes

**2**answers

402 views

### Historical quotation search: Equations/formulae in (Latin?) prose, before modern symbolic notation

I have been trying, without success, to find a vaguely-remembered quotation: the quadratic equation (or perhaps the quadratic formula), given in (Latin?) prose, along lines like “Consider that ...

**10**

votes

**1**answer

672 views

### 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 ...

**4**

votes

**1**answer

533 views

### Origin of “Woodin cardinal”

Sorry if this is a completely stupid question (I'm a not a set-theorist, though I've been doing some reading in the subject), but I was wondering, specifically, about the exact provenance of the name. ...

**16**

votes

**2**answers

629 views

### Felix Klein on infinitesimals

This is a reference request prompted by some intriguing comments made by Felix Klein.
In 1908, Felix Klein formulated a criterion of what it would take for a theory of infinitesimals to be ...

**11**

votes

**2**answers

537 views

### Riemann's quote cited by Lakatos: what is the context?

"If only I had the theorems! Then I should find the proofs easily enough."
This quote is generally attributed to Bernhard Riemann. In particular,
on page 9 in Proofs and refutations by Imre ...

**12**

votes

**0**answers

478 views

### How come Cartan did not notice the close relationship between symmetric spaces and isoparametric hypersurfaces?

Elie Cartan made fundamental contributions to the theory of Lie groups and their geometrical applications. Among those, we can list the introduction of the remarkable family of Riemannian symmetric ...

**3**

votes

**2**answers

290 views

### Is there a source linking Robinson's work in wing theory with his theory of infinitesimals?

Abraham Robinson worked in applied mathematics for several decades. MathSciNet lists 12 articles by Robinson in wing theory. His production included the book
Robinson, A.; Laurmann, J. A. Wing ...

**5**

votes

**0**answers

181 views

### Did the notion of “angle” originate with Thales?

Thales (circa 600BC—roughly 50 years before Pythagoras, 200 years before Plato,
and 300 years before Euclid)
certainly knew and reasoned with the concept of a planar angle.
Are there earlier ...

**12**

votes

**0**answers

262 views

### Who stated and proved the “Hopf lemma” on bilinear maps?

If $A\otimes B\rightarrow C$ is a nondegenerate linear map, where $A, B, C$ are vector spaces over an algebraically closed field, then $\dim C\ge \dim A + \dim B -1$.
Nondegenerate here means ...

**12**

votes

**2**answers

1k views

### Original manuscript of Archimedes' cattle problem

Wikipedia states that
[Archimedes' cattle problem] was discovered by Gotthold Ephraim Lessing in a Greek manuscript containing a poem of forty-four lines, in the Herzog August Library in ...

**2**

votes

**1**answer

263 views

### What are the Reasons for the Ambiguous Meaning of “Distribution” in Mathematics

The term "distribution" is commonly associated with statistics and, less commonly known, to generalized functions.
Questions:
what is known about the origin of the term in the two fields?
are the ...

**5**

votes

**1**answer

373 views

### Why does the gamma function use the symbol $\Gamma(\,)$?

I am aware of some of the history of the gamma function $\Gamma(z)$, partly through
a 2009(!) MO question "Who invented the gamma function?"—Euler, Bernoulli, etc.
My question does not seem to ...

**9**

votes

**0**answers

248 views

### From Frege to Gödel - German equivalent?

I know this question does not quite fit here, but I felt it could best be answered here. I recently stumbled upon the book From Frege to Gödel, which is a sourcebook containing some of the most ...

**16**

votes

**1**answer

877 views

### history of quaternion algebras

Who is responsible for the generalization of Hamilton's quaternions to other types of quaternion algebras, and when did this occur? In particular, Hamilton's quaternions are the 4-dimensional algebra ...

**7**

votes

**3**answers

640 views

### history of calculus of several variables

Everybody knows that Leibniz and Newton (or Newton and Leibniz, if you wish) invented calculus, i.e. they developed the notion of differentiability for a function of one real variable. But who had for ...

**36**

votes

**3**answers

1k views

### Why aren't fields called “bodies” instead?

The discrepancy regarding the names of commutative division algebras in German and English has always startled me. In English they are called fields, whereas their original German name is Körper ...

**12**

votes

**4**answers

861 views

### What properties of knots lead Lord Kelvin to hypothesize that atoms were knots in the ether?

I've often heard that Lord Kelvin was one of the first people to study knot theory, as he hypothesized that atoms were knots in the ether. I assume that he had some compelling evidence for this fact.
...

**2**

votes

**2**answers

301 views

### Origin of the name “Torelli group”

The genus $g$ Torelli group $I_g$ is the kernel of the action of the mapping class group of a genus $g$ surface on the first homology group of the surface.
The first paper I am aware of that uses the ...

**5**

votes

**2**answers

478 views

### How was Christoffel a 'whimsical eccentric'?

I've seen several citations of a letter from Weierstrass, talking about his dispute with Kronecker, in which he refers to Christoffel as a 'whimsical eccentric' (presumably the German original is ...

**6**

votes

**1**answer

419 views

### Origin of the term “weight” in representation theory

In representation theory, there are the related concepts of weights and roots. Since both are kinds of generalised eigenvalues, and eigenvalues are roots of e.g. the characteristic polynomial, the ...