Use this tag for questions concerning history of mathematics, historical primacies of results, and evolution of terminology, symbols, and notations.

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7
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5answers
238 views

Why do we first introduce the open set definition for continuity instead of the neighborhood definition?

After (nearly) completing my course in topology, something weird just stuck out to me which I hadn't considered before. When first discussing continuity, we often use the following definition: Let ...
0
votes
1answer
77 views

Who introduced the term indefinite integral and the notation $\int f(x)dx$?

I find the notation $\int f(x)dx$ for the indefinite integral of $f(x)$ on some interval $I$ is both suggestive and confusing. On the one hand, this notation is very suggestive when we calculate ...
0
votes
1answer
61 views

Lagrange's original proof of Remainder Theorem?

Where can I find Lagrange's original proof of the Remainder Theorem?
2
votes
2answers
47 views

St.Petersburg Paradox and Bernoulli's quote

I was reading about St.Petersburg paradox, and understood the proof that $\frac{S_n}{n\log n} \overset{P}{\rightarrow}1$. The textbook then quotes Bernoulli: "There ought not to exist any even ...
4
votes
1answer
304 views

When was it realized that complex numbers can't lie on a number line?

When I first learned about representation of a complex number by a point in a $2D$ plane, I wondered: what if it's redundant? What if a line is sufficient? Apparently, it's not, but I still wonder: ...
28
votes
7answers
5k views

Genius mathematicians who never published anything

Amongst philosophers, Socrates is an example of a genius with a great influence on human history who never wrote anything. Almost all facts which are known about his revolutionary ideas are written by ...
3
votes
1answer
82 views

What exactly is the 'tension' between arithmetic and geometry?

We all know Pythagorean theorem, $a^2+b^2 = c^2 $ Im reading John Stillwell, Mathematics and its history at the moment, and during the greek antiquity they had some trouble by interpretating ...
3
votes
1answer
111 views

When was contemporary logical notation established

When contemporary fundamental logical notation was established? I mean basic symbols as used nowadays $\iff\implies\land\lor\lnot\forall\exists\vdash\models$.
7
votes
0answers
96 views

History of the term “anodyne” in homotopy theory

There is a notion of an anodyne morphism (usually of simplicial sets). This type of morphisms is used, for instance, to establish basic properties of quasicategories. But the name is quite mysterious. ...
3
votes
1answer
81 views

Original Papers on Singular Homology/Cohomology.

I am currently reading Singular Homology Theory and Cohomology on my own mainly from Hatcher's "Algebriac Topology" and "Topology and Geometry" by Bredon. Quite often it happens that it takes a lot of ...
36
votes
11answers
4k views

Why are integers subset of reals?

In most programming languages, integer and real (or float, rational, whatever) types are usually disjoint; 2 is not the same as 2.0 (although most languages do an automatic conversion when necessary). ...
1
vote
1answer
60 views

Who are the two men credited with inventing logarithms?

This is a bonus question on a pre-calculus quiz I've been tasked with grading. Napier is clearly one of the answers. Who should I accept for the second inventor? In particular, should Newton be ...
2
votes
0answers
65 views

Development of measure and probability theory

I am interested in a reference (article, maybe a book chapter) on the development of mathematical probability theory - that is, mostly starting from the beginning of the 20th century. It is surprising ...
10
votes
1answer
264 views

Does anyone know about Ramanujan's method of solving the quartic? [closed]

I have read (probably) in Kanigel's book The Man Who Knew Infinity that S. Ramanujan devised his own method of solving the Quartic Equation after he learnt to solve the Cubic Equation. Does anyone ...
2
votes
0answers
68 views

What did homogeneous coordinates allow 19th century mathematicians to do?

I read about Mobius developing Barycentric and homogeneous coordinates, and I read about homogeneous coordinates and what they are and I'm totally on board with taking a line from the origin and ...
2
votes
2answers
161 views

The Big Picture of Commutative Ring

For final assignment on my Abstract Algebra class $-$ which is about Commutative Rings with Unity covering roughly Modules, Field of Fractions of an Integral Domain, Integrality and Fields, Prime ...
2
votes
0answers
45 views

Why are there so many different symbols to represent the Heaviside (unit step) function

In signal processing, the unit step function is typically written as $u(t)$. In other references though I have seen it represented as $H(t)$ and even $\theta(t)$. The unit impulse is fairly ...
1
vote
0answers
52 views

In which years in the prefaces to mathematical books thanks to secretaries for typing text books have disappeared?

In which years in the prefaces to mathematical books thanks to secretaries for typing text books have disappeared? Just interesting. When latex won?
8
votes
1answer
268 views

Meaning of the word “conjugate” across mathematics?

Clearly, the word conjugate or conjugation is used for a myriad of different concepts across mathematics and even in science (see the Wikipedia page). Its meaning can range from the fraction used to ...
2
votes
0answers
36 views

International Awards for Roger Apery?

Roger Apery stunned the math community when he proved that $\zeta(3)$ is irrational, in a truly elementary fashion. I wonder if he received any international awards specifically for this achievement. ...
1
vote
0answers
30 views

A finite generalization of differentials?

So basically, in trying to make sense of a certain math aspect of a thermodynamic problem (how to manipulate differentials) I end up reading this ...
2
votes
1answer
86 views

Development of Measure Theory

I would like to see the historical references for the following sequence of events: 1) When outer measure defined first time? 2) When it is proved that the outer measure is not countable additive? ...
9
votes
5answers
423 views

When can ZFC be said to have been “born”?

The "History" section of the Wikipedia article on ZFC isn't particularly helpful. The only thing I understood from it is that ZFC appeared after 1922. In what book or paper was ZFC first explicitly ...
5
votes
1answer
96 views

What are some good references on how probability theory got mathematically rigorous?

I am working on a term paper for an analysis course and I thought it would be interesting to talk about the connection between analysis and probability theory. Honestly, it would also benefit me a lot ...
1
vote
0answers
39 views

Did Hamilton have a proof that $\mathbb{R}^3$ is cannot be turned into an $\mathbb{R}$-division algebra?

It is well-known that $\mathbb{R}^n$ cannot be made into a non-commutative $\mathbb{R}$-division algebra if $n\ne 4$. My question is whether there is a (slick) proof of this for $n=3$; in particular, ...
4
votes
1answer
105 views

Theorems which later turned out to be vacuous

Has it ever happened that a theorem of the form If $P$, then $Q$ was proven and published, perhaps with great difficulty, only for someone to realize later that the condition $P$ of the theorem ...
0
votes
0answers
47 views

Dedekind(?) representation lemma on posets?

Here's an easy lemma: Any poset $(S, \preceq)$ is order-isomorphic to a subset of the powerset $\mathcal{P}(S)$ ordered by set-inclusion. I seem to recall having seen this attributed to Dedekind. ...
2
votes
1answer
63 views

suggest a topic about history of mathematics

Can you suggest a topic (the history of mathematics) concerning the evolution of a given concept from a document written in English from varied scientific resources What do you think of the ...
2
votes
0answers
33 views

Synonyms for “Theorem”

Some mathematical results, despite being formally proven, are not actually called "theorem". Examples include: Bertrand's postulate Pigeonhole principle Law of large numbers Do these names imply ...
1
vote
4answers
122 views

math-biography of mathematicians

Some of the mathematicians agree that reading Biography(Or more specifically, math-autobiography, scientific-biography ) gives lot of inspiration for working; and I am one of them. One book which I ...
6
votes
1answer
73 views

The convention for speakers to refer to themselves at the board with a single initial

This question is being asked on behalf of a graduate student in my department. When and where did the tradition start of a seminar or colloquium speaker using just the first initial of the speaker's ...
23
votes
5answers
379 views

Examples of Mathematics in Court

In court trials, natural sciences such as physics and biology routinely make an appearance, e.g. when estimating the speed of a vehicle based on impact damage or trying to deduce from the condition of ...
0
votes
0answers
83 views

What is the name of this proof of, “$\sqrt{2}$ is irrational”?

Usually the proof of $\sqrt2$ is irrational is done by contradiction(e.g. here), but I found another similar but short proof in the book "Beginning Algebra for College Students" by Lloyd Lincoln ...
3
votes
1answer
86 views

Did Gauss find the formula for $1+2+3+\ldots+(n-2)+(n-1)+n$ in elementary school?

I heard Gauss's primary school teacher gave some busy-work to his class: to add all the numbers between 1 and 100 up. Gauss immediately wrote 5050. His teacher was shocked, so she told him to add up ...
1
vote
0answers
37 views

How old is the distinction of right homotopy from left homotopy?

Going into the 1960s it seems to me that topologists saw path spaces as an advanced idea, useful in come contexts but not fundamental. So they took homotopy of maps as basically what is now called ...
0
votes
1answer
38 views

Functions of Matrices History

I'm currently looking for some books or papers that talk about the history of the functions of matrices. Specifically, I'm looking for the history regarding sine and cosine of a matrix. I've already ...
1
vote
2answers
87 views

A thought on Ancient Math

Is there a good site that I can see/ learn all the great work of mathematicians from all over the world? I am interested in reading those ancient book in a modern language. Suggestion? "Knowledge of ...
19
votes
4answers
691 views

Was there anybody before Cantor who conjectured existence of infinities of different sizes?

Georg Cantor is formally known as the first one who discovered existence of infinities of different sizes. But the history of thinking about the concept of "infinity" in maths and philosophy goes back ...
2
votes
1answer
59 views

Why is the nuclear norm called so?

A simple question. Why is the sum of the singular values of a matrix called its nuclear norm? What is the origin of, and motivation for, this term? Apparently the term nucleus is sometimes used to ...
20
votes
10answers
417 views

What are the theorems in mathematics which can be proved using completely different ideas?

I would like to know about theorems which can give different proofs using completely different techniques. For example: When I read from the book Proof from the Book, I saw there were ...
2
votes
0answers
107 views

Who first proved Fermat's Last Theorem for polynomials and when?

Who first proved Fermat's Last Theorem for polynomials and when? I have a proof using the Mason-Stothers Theroem, but the result is much older. Does anyone know the original proof or prover? Or at ...
1
vote
1answer
39 views

Open and closed localization of sheaves

In this paper: http://www-math.mit.edu/~hrm/papers/ss.pdf the author claims that Leray originally developed sheaves over closed sets rather than open sets and that it was Cartan who later realized ...
6
votes
1answer
163 views

Ramanujan's False Claims

"During his short life, Ramanujan independently compiled nearly 3900 results (mostly identities and equations). Nearly all his claims have now been proven correct, although a small number of these ...
115
votes
22answers
18k views

Examples of mathematical discoveries which were kept as a secret

There could be several personal, social, philosophical and even political reasons to keep a mathematical discovery as a secret. For example it is completely expected that if some mathematician find ...
5
votes
6answers
1k views

The Largest Gaps in the History of Mathematics

Edit: Based on the useful comments below. I edited the original post in order to seek for other important historical gaps in mathematics. Mathematics is full of the historical gaps. The first type ...
2
votes
2answers
123 views

Widespread, persistent mathematical disagreement?

My question is related to this one about whether mathematicians always ultimately agree, with a slight variation. I'm curious not whether mathematicians always ultimately agree, but whether there are ...
2
votes
0answers
123 views

History of the neusis construction of cube roots?

A simple neusis (marked ruler) construction of $\sqrt[3]{2}$ is given in many places, for example wikipedia. My question is: what is the history of this construction? As far as I can determine, all ...
2
votes
3answers
59 views

Where did the sum-of-divisors function come from?

Doing a research project on a few number-theoretic functions, and I was curious, where does the sum-of-divisors function come from? Surely someone thought it up and made it a possibility. I'm talking ...
9
votes
1answer
111 views

How are Hilbert Space methods used in number theory?

In N. Young's book An Introduction to Hilbert Space, there is an interlude in which the author remarks that the theory of Hilbert spaces is "routinely used in differential geometry, complex analysis, ...
4
votes
2answers
164 views

Etymology of “flabby” or “flasque” sheaf

I just started working with flasque, or flabby sheaves, that is sheaves whose restriction maps are surjective for any two open set of the space. I wonder about the etymology of the term. In French, ...