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

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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 ...
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1answer
21 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 ...
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39 views

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 ...
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1answer
266 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 ...
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1answer
28 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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57 views

Have most popular(famous) mathematicians been determinists? [on hold]

From what I have seen, most mathematicians are/were hard determinists. Has someone done research on this topic? Later edit: The mathematicians which I've seen as hard determinists are the ...
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62 views

What actually happened to Cantor?

I saw this answer and its comments while browsing Math SE, and it made me tempted to ask: What actually happened to Cantor? Did he really, as it's usually claimed, be called blasphemous and ridiculed ...
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115 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 ...
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2answers
104 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 ...
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1answer
38 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?
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2answers
142 views

Friends and Enemies of Infinities

Infinity is a dividing line in the community of mathematicians. There is a long standing contest between those who believe in rich theory of infinite mathematics and large infinite numbers and those ...
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3answers
5k 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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3answers
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 ...
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4answers
156 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 ...
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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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14answers
9k 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
17 views

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 ...
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0answers
34 views

Are there any functions which were proposed as elementary by mathematicians but not considered elementary now?

Are there any functions which were proposed by various mathematicians to be included in the set of elementary functions because of their properties but not considered elementary as of now?
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1answer
32 views

Diophantus problem

I was given following problem as an example of early mathematics with the solutions. But it seems i can't understand from where they are getting the 35z^2 = 5 from in the solutions. Could someone ...
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0answers
86 views

The history of summations

How did summations evolve? For instance, is there an article, book, webpage, etc. that talks about how mathematicians came up with using $\sum_x{ f(x) }$? I'm very interested on how summations came ...
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1answer
45 views

In Whitehead & Russell's PM, if $P$ is an infinite well-ordered series, can $P$ have a last term?

If I'm not mistaken, $B‘\overset{\smile}{P}$ is the last term of $P$. If it does not exist, there is no need to put ~$(B‘\overset{\smile}{P}) \in C‘∇‘P $ in the hypothesis. Chances are I missed ...
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1answer
44 views

Some questions on the formation of the BSD conjecture

I'm quite curious how Birch and Swinnerton-Dyer formed their famous conjecture in the beginning of 1960s. I read some paper of Birch and Swinnerton-Dyer, as well as some paper of Tate and several ...
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3answers
103 views

In Whitehead & Russell's PM, does every Series contain a $P_1$ (immedeately precedes)?

✳204.7 $\vdash: P \in Ser .\supset. P_1 \in 1 \rightarrow 1$ Which says if $P$ is a series, then $P_1$ is one-one. ✳201.63 $\vdash: P \in trans \cap Rl‘J .\supset. P_1 = P \overset{.}{-}P^2$ ...
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1answer
84 views

History of the three “impossible” compass-and-straightedge problems

I'm preparing a presentation about constructible numbers and I wanted to know some of the history about it to motivate the topic. I wanted to know if the classical Greek problems (doubling the cube, ...
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52 views

A finite generalization of differentials and weird 'modular like mathematical space'?

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 ...
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1answer
57 views

Definition of a function and the notation $f:A\to B$.

In some textbooks on analysis, I have encountered a definition of function/mapping that distinguishes the terminology mapping on $A$ to $B$ and mapping from $A$ to $B$; the first one refers to a ...
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2answers
135 views

Shape made by Beltrami

Beltrami made (out of thin paper or stiff cloth) a model of a surface of constant negative Gauss curvature. The original might have resembled a large saddle shaped Pringles chip, and frills might have ...
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0answers
118 views

Isaac Newton did number theory?!

I was reading Whiteside's article called "Newton the Mathemtician", where he says that Newton did Number Theory (e.g. inverstigating which numbers are expressible as a sum of two cubes). If this is ...
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0answers
45 views

Historical motivation for Hilbert's Third problem

What was the historical motivation for Hilbert's third problem? Why did Hilbert feel it was worthy of including on his published list? Hilbert's Third problem: Say that two polyhedra are scissors ...
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0answers
32 views

$A(x+p)²-B(x-p)²=y$, historical/math reference

I'm trying to build a reminder of all that I found about the quadratic function over the years. Here I came across this form of quadratic equation that I did not know: A(x+p)²-B(x-p)²=y I have no ...
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2answers
84 views

Does axiom of foundation/regularity protect against Russell-like paradoxes?

In ZF set theory the axiom of regularity (also called axiom of foundation) says that: In all nonempty sets x there is an element y such that x∩y=∅ As I been told that the intention of the axiom ...
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1answer
46 views

Geometry and land

The word "geometry" in Greek means "measurement of Earth/land". This may imply that geometry was originally invented in order to solve problems related to land. Are there historical accounts of ...
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4answers
114 views

What is a good book, or article, that explains the history of fourier analysis?

What is a good book on the history of Fourier Analysis? I'm looking for a book which explains how it came to be and what the mathematicians (or physicists) were thinking when they came up with it. If ...
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4answers
115 views

Which was defined first to represent $\underbrace{a+a+a+\cdots+a+a+a}_{n \text{ terms}}$? $n\times a$ or $a \times n$?

When we are talking about multiplication, we often use it without knowing which one was defined first and which one was defined because of its commutative property. Here I want to know which one was ...
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2answers
73 views

How did Newton calculate 3x7 by logarithm?

This is a story about Newton I read once when I was a child. Now that book is lost and I can only tell you what I remember. When Newton was young, he had been already famous in curiosity and ...
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0answers
64 views

Hard-to-put-together but easy-to-prove results

What are the most important examples of theorems and definitions which are post factum obvious, i.e., hard to put together but easy to understand and use (and prove, in the case of theorems) once you ...
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2answers
171 views

What does it mean by acta?

There are a lot math journals with title "acta" includes, for instance, Acta Mathematica, acta arithmetica, etc. Would you explain what "acta" means?
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0answers
41 views

Where do divisors on curves come from?

I've been learning about Riemann surfaces and the Riemann-Roch theorem, and I've been able to experience some of its great power. However, I'm curious as to what the history behind divisors on curves ...
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0answers
36 views

Cambridge Maths Tripos Papers

Does anyone know where I can find Cambridge Maths Tripos Papers for the 1980s?
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0answers
81 views

$\sin$ vs. $sin$ - history and usage

One thing newcomers to TeX or MathJax often get wrong is that they write something like $sin(x)$ instead of $\sin(x)$ - the point being that common mathematical functions with names consisting of ...
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0answers
64 views

math historian who don't belong to academia

Is there examples of math historian who don't belong to academia? Is it possible for professionally non-academician to perform good work in the field of the history of mathematics and publish? Does ...
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0answers
51 views

When do two points coincide in euclidean geometry?

The 4° common notion in the Elements of Euclid says: "Things which coincide with one another equal one another". Many authors have interpreted this sentence as a principle of superposition that could ...
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0answers
48 views

Who did first use the concept of “supremum”?

Is there one specific person, who first defined the concept of "supremum"? If so: In which work? In my textbooks or by a quick search on the internet, I did not find an answer to my question.
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1answer
59 views

In Whitehead&Russell's PM's ✳210, how can the product of $\lambda$ be not a member of $\lambda$?

Take ✳210.23 for example: Assuming $\kappa$ is a classes of classes such that, of any two, one is contained in the other, i.e. $\alpha, \beta \in \kappa .\supset_{\alpha, \beta} : \alpha \subset ...
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1answer
32 views

Etymology of the word “function” in mathematics

What is the etymology of the word "function" (i.e. a map) in mathematics. How does (historically) the etymology of the word function relate to the mathematical definition and the mathematical concept ...
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1answer
30 views

In Whitehead&Russell's PM, What is $\max_p$'s converse domain?

Here is the definition of upper limit. If I'm not mistaken, $\max_P$'s converse domain is the universal set $V$. The definition appears to be limiting the converse domain of $\operatorname{seq}_P$ ...
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2answers
111 views

Motivating mathematics(particularly algebraic number theory) through historical problems.

Most mathematical textbooks start a subject by going backwards, historically. They will define the terms that were invented to solve a problem in their polished form and then use these definitions and ...
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3answers
116 views

History of category theory

I am searching some information about the origins of the category theory. Anyone know where can I read about those topics? Thanks!
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0answers
33 views

first example of backwards induction?

In Mathematics Magazine 28(1954/55), 21-46, Richard Bellman presents a proof for the theorem which says that the geometric mean of $n$ numbers is always not greater than the arithmetic mean: the proof ...
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recommend me some texts on the history of the non-western mathematics

I would like to self study the detailed history of the non-western mathematics. I have started the literature of Barton (7th Ed.) but it primarily concentrated on Western and American Mathematics. ...