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

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2
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1answer
22 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 ...
0
votes
0answers
54 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 ...
-1
votes
0answers
59 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 ...
10
votes
0answers
97 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
votes
2answers
99 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What happens to a great mathematician's unpublished works when they die?

When a great mathematician dies, they often leave plenty of unpublished and incomplete works in their manuscripts.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
votes
1answer
36 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?
0
votes
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 ...
2
votes
2answers
136 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 ...
73
votes
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 ...
3
votes
3answers
152 views

The Historical Importance of Keynes' A Treatise on Probability

A visiting speaker in Economics recently happened to mention that John Maynard Keynes' A Treatise on Probability revolutionized probability theory. I have not heard any such claim before and it struck ...
2
votes
4answers
153 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 ...
28
votes
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 ...
7
votes
4answers
600 views

Can Leibniz Notation Be Treated As a Quotient?

Why is saying $\frac{dy}{dx}\frac{dy}{dx}=y\frac{d^2y}{(dx)^2 }$ not valid? Does Leibniz notation (and thinking of it as an infinitesimal quotient) not work for higher-order derivatives?
65
votes
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 ...
1
vote
2answers
163 views

Have any definitions in mathematics been redefined

Based on certain intuitions and motivations we make certain definitions and then proceed to use these concepts in further developing our intuition. For example, we have an intuition that a line has ...
87
votes
31answers
16k views

Examples of mathematical results discovered “late”

What are examples of mathematical results that were discovered surprisingly late in history? Maybe the result is a straightforward corollary of an established theorem, or maybe it's just so simple ...
1
vote
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 ...
3
votes
1answer
218 views

Tips on writing a History of Mathematics Essay

I'm a third year maths undergrad currently taking a 'History and Development of Mathematics' module. As a maths student, you can probably guess my skills at writing an essay are a little (if not ...
10
votes
4answers
113 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 ...
0
votes
2answers
134 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 ...
2
votes
3answers
99 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 $\vdash: P \in trans \cap Rl‘J .\supset. P_1 = P \overset{.}{-}P^2$ ...
1
vote
1answer
44 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 ...
2
votes
0answers
37 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 ...
3
votes
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 ...
5
votes
1answer
227 views

Maths controversies due to an empty universe?

In France, most math/CS grad students hear the following story: On the day of his defense, Jay, a PhD candidate in pure Maths, presents his results, a series of highly non-trivial theorems which ...
1
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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?
0
votes
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 ...
2
votes
0answers
84 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 ...
5
votes
1answer
80 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, ...
1
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0answers
51 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 ...
3
votes
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 ...
21
votes
3answers
827 views

Who came up with the $\varepsilon$-$\delta$ definitions and the axioms in Real Analysis?

I've seen a lot of definitions of things like boundary points, accumulation points, continuity, etc, and axioms of the real numbers. But I have a hard time accepting these as "true" definitions or ...
6
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0answers
117 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 ...
2
votes
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 ...
1
vote
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 ...
0
votes
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 ...
8
votes
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 ...
16
votes
2answers
718 views

A problem V.I. Arnold solved as a primary school student

According to a 1995 interview that Vladimir I. Arnold gave to the Notices of the AMS, his primary school teacher I.V. Morozkin gave in 1949 (when Arnold was 12 years old) to a Soviet classroom, most ...
8
votes
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 ...
0
votes
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 ...
12
votes
1answer
401 views

Fibonacci, compositions, history

There are three basic families of restricted compositions (ordered partitions) that are enumerated by the Fibonacci numbers (with offsets): a) compositions with parts from the set {1,2} (e.g., 2+2 = ...
3
votes
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?
2
votes
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 ...
14
votes
5answers
545 views

Reflections on math education

Why is there such a big difference in math education between The Americas and (Europe and Asia) ? except for a few privileged who have the opportunity to access to math much earlier than the ordinary ...
32
votes
13answers
3k views

Research done by high-school students

I'm giving a talk soon to a group of high-school students about open problems in mathematics that high-school students could understand. To inspire them, I would like to give them examples of ...
1
vote
3answers
159 views

When and where the concept of valid logic formula was defined?

I was stimulated by a recent question about Gödel Completeness Theorem. All my citations are from Jean van Heijenoort (editor) From Frege to Gödel A Source Book in Mathematical Logic (1967). Gödel's ...
32
votes
5answers
2k views

Examples of “Non-Logical Theorems” Proven by Logic

I am still an undergraduate student, and so perhaps I just haven't seen enough of the mathematical world. Question: What are some examples of mathematical logic solving open problem outside of ...
3
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0answers
33 views

Cambridge Maths Tripos Papers

Does anyone know where I can find Cambridge Maths Tripos Papers for the 1980s?
6
votes
2answers
878 views

Mathematics celebrities that every mathematician should know? [closed]

As a mathematician, sometimes I meet across very embarrassing questions which were posted by who does not learn of mathematics, for example, my wife and so on. She or he always posted such questions: ...
8
votes
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 ...