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

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13
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2answers
273 views

Motivation for introducing algebraic topology?

What kind of topological questions does algebraic topology answer where point set topology is not enough? Phrased differently: Where is the line (or maybe intersection) between point set topology ...
9
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1answer
120 views

The average of the roots of a polynomial equals the average of the roots of its derivative

Background: It's straightforward to check that the average (i.e. the mean) of the roots of a nonlinear polynomial equals the average of the roots of its derivative: if $$f(x) = x^n + a_{n-1} x^{n-1} ...
5
votes
3answers
88 views

Swapping Theorems with definitions

My question is motivated from the following passage of Gian-Carlo Rota's Indiscrete Thoughts, 'Suppose you are given two formal presentations of the same mathematical theory. The definitions of the ...
10
votes
5answers
533 views

What are reasons why some symbols in mathematical logic are not standardized?

Why is so hard to find a standardisation regarding symbolism and/or terminology in Mathematical Logic ? We see again and again students asking if e.g. $\rightarrow$ and $\implies$ means the same ...
5
votes
1answer
97 views

the word “derivative”

When did the word "derivative" come into use in calculus, and why? As in Can the word "derive" be used to mean "take the derivative of"? the word "derivative" in normal English ...
3
votes
0answers
69 views

Is there a link between level of abstraction and use of numbers?

One of my friend who stopped studying maths in high school told me once You study maths, can you help me fill my tax forms? In her mind, advancing in maths studies implied manipulating an ...
5
votes
1answer
110 views

Does Whitehead and Russells' PM distinguish Proof from Demonstration?

I'm currently at Chapter 4, vol. 1 and 1st ed. I have to ask this question because the most important thing about this book is in its minute details. Thanks. Take *3.3 for example. Acording to this ...
3
votes
0answers
124 views

What makes Beal's conjecture “beautiful” enough to make people offer a million dollar prize? [closed]

What makes Beal's conjecture "beautiful" enough to make people offer a million dollar prize? Is it just a challenge or does it have real applications?
7
votes
3answers
575 views

Why are compact sets called “compact” in topology?

Given a topological space $X$ and a subset of it $S$, $S$ is compact iff for every open cover of $S$, there is a finite subcover of $S$. Just curiosity: I've done some search in Internet why compact ...
4
votes
0answers
67 views

Mathematical journals (maybe in the past) with regular competitions?

I just finished reading Yōko Ogawa's "The Housekeeper and the Professor". One of the main characters - "the professor" - is a retired mathematician who regularly takes part in contests published in a ...
4
votes
1answer
109 views

What is Euler's proof of his formula ${e^{ix}=\cos(x)+i\sin(x)}$

I've read several proofs of the Euler's formula $$e^{ix}=\cos(x)+i\sin(x)$$ but I want to know how Euler's himself prove it at the first time, how did he think about it?
2
votes
1answer
104 views

Who first proved that the second-order theory of real numbers is categorical?

The second-order theory of real numbers is obtained by taking the axioms of ordered fields and adding a (Dedekind) completeness axiom, which states that every set which has an upper bound has a least ...
3
votes
2answers
225 views

History of Calculus

Newton/ Leibniz invented calculus on approximately 1680's. Cauchy/Weierstrauss defined the $\epsilon - \delta$ definition of a limit in approximately 1820's. So how did they define derivatives? I ...
5
votes
1answer
77 views

What is $M_x$ in Frege's Basic Law IIb?

Gottlob Frege's magnum opus, "The Basic Laws of Arithmetic" (Die Grundgesetze der Arithmetic in German) constitutes one of most impressive and meticulous attempts at developing a rigorous foundation ...
14
votes
2answers
612 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 ...
18
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1answer
514 views

The most active fields of mathematics?

Which fields of mathematics are the most active at this time -- by number of papers published, grant money, people working in them or by any other measure? Any trends in this regard?
5
votes
1answer
168 views

Could Euclid have bisected a line segment without his method of superposition?

In Book I Proposition 10 of the Elements, Euclid performs the bisection (i.e. finding a midpoint) of a line segment. In the course of doing so, he uses Book I Proposition 4, the Side-Angle-Side ...
3
votes
2answers
105 views

Notation and the name choice for meet and join (in order theory)

I have two simple questions: From where do the names meet and join come from? I don't see any intuition between those names in context of order theory. From where does the notation come? I have to ...
0
votes
2answers
457 views

Mathematics and slavery [closed]

I think that ancient Greek mathematics is a miracle. Think about Euclid. Developing mathematical arguments from a small set of axioms is incredibly modern. And their influence on modern mathematics is ...
3
votes
1answer
75 views

Cauchy's theorem or Frobenius' lemma

A textbook exercises asks: The goal of this exercise is to prove Frobenius's lemma, which asserts that if the order of the group $G$ is divisible by the prime $p$, then $G$ contains an element of ...
21
votes
3answers
773 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 ...
0
votes
1answer
55 views

Who first described commutative algebraic theories explicitly?

Lately, I've been thinking that the concept of a commutative algebraic theory is really, really important. So I'm curious; who had the honor of first discovering this concept? In particular, I'd like ...
2
votes
0answers
90 views

What were some Mexican contributions to high school level algebra and statistics?

I want to do a presentation on Mexican mathematicians' contribution to either high school level algebra or statistics. What kind of resources are out there? Does anyone know of a contribution that I ...
2
votes
1answer
25 views

What is a cofactor in this case?

Im looking at a homework problem I have and I am a bit confused. The first part of the question is to show that 8128 is a perfect number. This is simple enough: $1 + 2 + 4 + 8 + 16 + 32 + 64 + 127 + ...
3
votes
1answer
123 views

Why $\operatorname e$ was named e ? What is the history and reason behind it?

Why the constant that Euler discovered has symbol $\operatorname e$ and not other symbols? What is the history and reason behind it? Thanks.
2
votes
0answers
47 views

Order of operations - is there any standard?

Is there any standard regarding order of mathematical operations? I only found ISO 31-11 that deals with mathematical symbols, but not with the order of operations. If there's not, I'd be interested ...
2
votes
2answers
93 views

why function argument is on right side $f(x)$ rather than on left side as $xf$

Is there an advantage for writing function arguments on the right side as $f(x)$ rather than on the left side as $xf$? The latter looks more natural if we think about it in diagram as $domain ...
1
vote
1answer
82 views

From $\mathsf{O}$ to $\mathsf{I}$ via $\infty$

The following is not true mathematics, but a little imaginary story about mathematical symbols. I wonder if there is - in parts - a true (etymological) story behind it. Once there was a symbol ...
1
vote
2answers
162 views

Is there any surprising elementary probability problem that result in surprising solution like the Monty Hall problem?

For recreational purpose, i haven't seen a interesting elemetary probability question quite a while. Is there any surprising elementary probability problem that result in surprising solution like the ...
1
vote
1answer
76 views

Russell's definition of finite cardinals

whether the thought had been previously adumbrated, perhaps confusedly, i know not, but the name of Bertrand Russell has become associated with the assertion that: the number $2$ is the set of all ...
1
vote
1answer
115 views

Reform of math symbols for high school texts

I am looking for references to papers and resources related to reforming math symbols for introductory courses at middle or high school level. Pointers to other forums also welcome. Eidt: For ...
4
votes
0answers
70 views

The Leibniz rule in Euler's works

Does anyone know if the Leibniz rule (the method of differentiation under the integral sign), or a variation thereof, has ever appeared in any of Euler's papers? Any references would be appreciated. ...
0
votes
2answers
113 views

General questions about theorems and laws

I have doubts about the construction of mathematical elements. There are proofs, that are proven using other theorems (corollaries) and/or axioms or definitions, such as Fermat's Last Theorem, the ...
1
vote
1answer
65 views

Probability of World Series - Using Pascal and Fermat “Problem of Points”

This is a question I have for a history of math class, but I can't figure it out. I need to use the three method that Pascal and Fermat used on their problem of points, and it doesn't seem to work ...
13
votes
1answer
194 views

Why are proofs written in first person plural? Were they ever written differently?

It's probably a silly question but it interests me when was the convention of writing proofs in first person plural introduced? Is there any historical examples of a different POV for proof writing?
8
votes
0answers
88 views

Ludwig Sylow 12 december 1832 [closed]

Not a question, but just to commemorate that Ludwig Sylow was born today exactly 181 years ago, on 12-12-1832. Note that $1832=2^3.229$, and hence by Sylow's theorems there is no simple group of order ...
1
vote
1answer
28 views

Pascals first method

So pascals first method was to first solve a simple problem,this was before the pascal triangle. This is in relation to De Meres problem: Each player stakes $32$ pistoles. One player has 1 round ...
2
votes
1answer
100 views

Mathematician as a title [closed]

After some googling around, I can't seem to find a definite answer to this question. When can someone call themselves a mathematician? Is it after a b.sc. in mathematics? After graduate school? Or ...
3
votes
0answers
51 views

Question about the first step in Mann's original proof of the Schnirelmann-Landau Conjecture

I was reading Henry Mann's proof for the Schnirelmann-Landau Conjecture from 1942 which can be found in JSTOR here Today, the Schnirelmann-Landau Conjecture is known as Mann's Theorem: $$d(C) \ge ...
2
votes
0answers
54 views

How influential was Lorenz' work?

I've recently read an article in Pour la Science (a French equivalent of the Scientific American, with an overall very good quality) on the history of Chaos theory. Essentially, the article goes ...
2
votes
3answers
128 views

Golden ratio / Fibonacci which branch of math?

Friends, The Golden ratio / Fibonacci sequence are studied under which branch of math? Can you recommend some good textbooks on the subject? Thanks
14
votes
4answers
498 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 ...
5
votes
1answer
564 views

History of Compass/Straight Edge Construction

I'm interested in learning the origin of compass/straight-edge constructions. In particular, I am interested in the historical interplay between Euclid's axioms for plane geometry, and ...
3
votes
0answers
106 views

why nineteen is not tenty-nine? [closed]

Professionally I am a web designer but teaching as a part time job. Yesterday, my grade 3 student asked a question which is so nonsense for someone. But I realized that there is a must reason for ...
1
vote
0answers
25 views

Slope of tangent line using Wallis method

Consider the Wallis method of finding the slope of tangent lines where $x = a$. Use the method to find the slope of the line tangent to the graph of $y = x^2 + 3x + 7$. Use the method to find the ...
2
votes
0answers
51 views

Probability of World Series - Pascal and Fermat [closed]

In the World Series, each opponent attempts to win 4 of 7 games. In 1989, Oakland had already won the first two games as the San Francisco Giants and the Oakland Athletics were getting ready to play ...
0
votes
1answer
128 views

Area using Fermat's method of quadratures [closed]

Use Fermat's method of quadratures to find the following: a. The area between the curve $y = x^5$ and the x-axis over the interval $(0,a)$. b. The area between the curve $y = 1/x^2$ and the x-axis ...
1
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0answers
53 views

Weierstrass and Borel summation

In the Wikipedia article on Borel summation, there is the following quote attributed to Gösta Mittag-Leffler: Borel, then an unknown young man, discovered that his summation method gave the ...
0
votes
1answer
54 views

Indeterminate Equations using kuttaka

The question is "find the smallest solution to the indeterminate equation $195y = 221x + 65$ using the Indian method of kuttaka." Factoring out $13$, I got $15y = 17x + 5$ Using kuttaka, I got $x = ...
0
votes
0answers
18 views

History of Logs and/or solving simultaneous equations

I am currently taking a history of mathematics course and am wanting to "sketch" the history of a mathematical topic at an undergraduate level. The sketch must tell a story of some idea, process, ...