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

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I would like to see the historical references for the following sequence of events: 1) When outer measure defined first time? 2) When it is proved that the outer measure is not countable additive?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

When can ZFC be said to be “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 ...
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1answer
56 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 ...
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0answers
36 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, ...
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1answer
79 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 ...
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0answers
36 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
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1answer
49 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
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0answers
31 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 ...
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4answers
93 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 ...
3
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1answer
50 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 ...
2
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0answers
89 views

Grothendieck's works [closed]

I heard today that Alexander Grothendieck has passed away. I have encountered his name in some things I have studied, but does not know much about his contribution in mathematics and why he was ...
18
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5answers
283 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 ...
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0answers
79 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 ...
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0answers
17 views

About Galois Covering Theory

so I am studying somethings about Galois Covering and I am writing a beamer to present for my friends of the university. But I would like of somethings about the author of Covering Galois Theory to ...
3
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1answer
68 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 ...
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0answers
28 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
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1answer
23 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 ...
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2answers
75 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 ...
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2answers
543 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
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1answer
40 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 ...
2
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0answers
67 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
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1answer
20 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 ...
5
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1answer
134 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 ...
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22answers
16k 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 ...
4
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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 ...
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2answers
65 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
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0answers
50 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 ...
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0answers
46 views

Why is the natural logarithm 'natural'? [duplicate]

Simple question: Why is it that the natural logarithm is called 'natural'?
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3answers
48 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 ...
6
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0answers
38 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 ...
4
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2answers
112 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, ...
8
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1answer
73 views

Newton's way of getting a Taylor expansion

I don't understand how Newton find the Taylor expansion of $\frac{a^2}{b+x}$ by the following method : **This screenshot is from : The method of fluxions and infinite series Any idea ?
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3answers
49 views

How come leap years don't occur on years divisible by 100 that aren't divisible by 400? [closed]

I read this and I was surprised that years like 1900 and 1400, which aren't divisible by 400, aren't leap years, even though they are divisible by four. I wonder when this started happening on years ...
1
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1answer
43 views

How did Fourier series lead to the development of rigorous analysis?

Once I've heard that the studies of Fourier series have lead to rigorous definitions of such concepts as function, convergence, integral, limit. And also that Cantor's study of Fourier series led him ...
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3answers
210 views

Mathematical results that were generally accepted but later proven wrong?

I am giving a presentation on mathematical results that were widely accepted for a period of time and then later proven wrong, or vice versa. This talk is geared towards undergraduates who are likely ...
2
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1answer
46 views

Why can real variable methods take place of complex variable methods in harmonic analysis' research?

We know that one complex variable methods have been largely used in the early research of (real variable) harmonic analysis. But, as is known to me, there is much difficulty when mathematicians ...
3
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1answer
99 views

What is the incorrect proof by Euler that $\pi = 0$ (or something like that)?

I seem to remember a proof by Euler, involving infinite series, which was really complex (for a maths hobbyist). I believe it was sent in a letter to someone, and that it ended up with $\pi = 0$ or ...
0
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1answer
38 views

Discovering the mathematical nature of Nature - Galileo's inclined plane experiment

In 1638 Galileo published Two New Sciences, in which he described his inclined plane experiment. He discovered that the acceleration of gravity was uniform, and could be modeled mathematically by the ...
2
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0answers
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Pell's Equation and the Pigeon Hole Principle

David Speyer gave a beautiful application of the pigeon hole principle here to show that Pell's equation $$x^2-Dy^2=1$$ has infinitely many integral solutions. I was wondering if anybody knows the ...
30
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1answer
449 views

What did mathematicians study as an undergraduate/graduate before modern mathematics such as modern algebra and analysis?

I am curious as to what mathematicians such as Leibnitz and Gauss and the Bernoulli's studied when they were students in university. I find it fascinating how we are taught calculus and abstract ...
2
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1answer
30 views

Different proofs for two squares theorem for primes

There is a proof of two squares theorem for primes of form $4k+1$ from quadratic forms and there is a proof from Bolyai using Gaussian integers. I am reasonably sure such a nice simple statement has ...
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0answers
145 views

Why is $J$ sometimes used to denote $\mathbb{Z}_{>0}$?

In older books, such as Rudin's Principles of Mathematical Analysis and Herstein's Topics in Algebra, I've noticed that authors tended to use $J$ to denote $\mathbb{Z}_{>0}$. Does anyone have any ...
4
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2answers
117 views

What happens to a great mathematician's unpublished works when they die?

When a great mathematician dies, they often leave plenty of unpublished and incomplete works in their manuscripts. As we assumed that they were a really good mathematician, most of the ideas in these ...
0
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1answer
40 views

Name for LDC: Lebesgue?

Is there also a name associated to the Lebesgue dominated convergence theorem like Beppo-Levi or Fatou? Would Lebesgue be reasonable? Who did originally prove it?
83
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3answers
6k views

A 1,400 years old approximation to the sine function by Mahabhaskariya of Bhaskara I

The approximation $$\sin(x) \simeq \frac{16 (\pi -x) x}{5 \pi ^2-4 (\pi -x) x}\qquad (0\leq x\leq\pi)$$ was proposed by Mahabhaskariya of Bhaskara I, a seventh-century Indian mathematician. I ...
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5answers
2k views

“Stick it to the man!” Mathematical discoveries that resulted in persecution.

As the old story goes, Pythagoras and his followers were adamant that all numbers were rational, until Hippasus came along and proved that $\sqrt{2}$ (the length of the diagonal of the unit square) is ...
2
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4answers
175 views

Theorems in number theory whose first proofs were long and difficult

What are the examples of important theorems of number theory that has been shown to have surprisingly simple proofs though their first demonstration wasn't at all simple enough. Now simple proof is an ...
2
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0answers
38 views

Some Logo and Stamp on Mathematics and Mathematicians

I don't know whether this question is allowed to post of stackexchange, but I don't know other any other so good sources of mathematics community other than this website. I also thought that the ...
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16answers
10k views

Do mathematicians, in the end, always agree?

I've been trying to study some different sciences in my life, ranging from biology to mathematics, and if I try to explain to people why I like mathematics above the others, I think the most important ...
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0answers
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The name of $fusc$ (Calkin-Wilf sequence)

I was just wondering where $fusc$ got its name (where $fusc(2n) = fusc(n), fusc(2n + 1) = fusc(n) + fusc(n + 1)$, seeds: $fusc(0) = 0, fusc(1) = 1$). The function is of some importance in the ...