Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [math-history]

Use this tag for questions concerning history of mathematics, historical primacies of results, and evolution of terminology, symbols, and notations. Consider if History of Science and Mathematics Stack Exchange is a better place to ask your question.

4
votes
0answers
53 views

Name for “the kernel lemma”?

Lately I've been fascinated by the result that one might state slightly informally Lemma. (In the context of linear algebra over a field.) If $p$ and $q$ are relatively prime polynomials and $...
0
votes
0answers
52 views

Is there any method known in the Mathematical Statistics that proves that the prime numbers are not randomly distributed?

I am asking for my curiosity. Maybe everyone knows the answer to that question. I do not know. I don't have a maths education. Is there any method known in the Mathematical Statistics that proves ...
0
votes
0answers
23 views

de Mere's Dice Game

In an exchange between Pascal and Fermat concerning de Mere's Dice Game, Fermat gives a different solution than Pascal, and Pascal concedes that Fermat had the correct one (see text https://www.york....
0
votes
0answers
34 views

What is the timeline of the sets of real, rational, integer, and natural numbers?

Historically, did mathematicians: 1) construct the set of real numbers using rationals, integers, and naturals? Or 2) did they already know the set of reals existed and partitioned it into ...
2
votes
5answers
52 views

How do we mathematically define the meaning of the word “undecidable”?

I need to understand the meaning of this mathematical concept: "undecided/undecidable". I know what it means in the English dictionary. But, I don't know what it means mathematically. If You ...
0
votes
0answers
19 views

History of the Barzilai-Borwein method

I seem to recall hearing the story that the Barzilai-Borwein method (a first-order optimization method with superlinear convergence) was discovered by accident, involving some indexing error in some ...
2
votes
0answers
21 views

The Hahn-Kolmogorov Extension Theorem

How did Hahn and Kolmogorov prove the Hahn-Kolmogorov Extension Theorem? Did they contruct the extension in a similar way to what Carathéodory did?
1
vote
0answers
19 views

an evolutive graph of the number

the idea that "wanting to do something new" sometimes led to "the need for a new kind of number" is clearly stated in both Morris Kline's book and in several videos in this playlist, both about ...
0
votes
1answer
66 views

What are the arguments of the mathematicians who objected against the ontological proof Gödel offered?

Q: What are the arguments of the mathematicians who objected against the ontological argument/proof Gödel offered? $$ \begin{array}{rl} \text{Ax. 1.} & \left\{P(\varphi) \wedge \Box \; \forall ...
0
votes
1answer
39 views

Origin of infix notation

Wondering where the infix notation of things like 1 + 2 came from, when roughly it came about, and if it was before/after prefix or postfix notation. I know the ...
2
votes
0answers
47 views

Why are categories and monads called that way?

The words "category" and "monad" existed already in philosophy. The usage of the terms in category theory seems to be slightly influenced by the philosophical meaning, but actually the concepts are by ...
0
votes
0answers
17 views

Moderators help required [migrated]

Can someone please illustrate how to use the sigma symbol using mathjax and other such symbols please help? By the way the moderators of this site are extremely helpful so thank you.
0
votes
0answers
67 views

Which one is the correct/standard mathematical notation?

I want to learn that, which one is the correct/standart mathematical notation? $f:\mathbb{R}\rightarrow \mathbb{R^{+}}$ or $f:\mathbb{R}\rightarrow (0,\infty)?$ What is the standard mathematical ...
2
votes
1answer
69 views

Why is “antiderivative” also known as “primitive”?

If I had to guess, I would say that calling the antiderivative as primitive is of French origin. Is one term more popular than the other?
12
votes
1answer
242 views

History of definitions for an ellipse?

Recently I've been learning about ellipses. It seems as though there are four (from what I've learned of so far) different ways to define ellipses, all which seem to be connected in kind of obscure ...
1
vote
0answers
52 views

Is finitary method for Hilbert and modern logic - Turing computability?

It is known that Hilbert proposed in the state of crisis of foundations of mathematics that we create formal theories which we analyze using "proof theory" or "metamathematics". He then also said that ...
1
vote
0answers
51 views

Who, when, and why invented the symmetric derivative?

When computing an approximate derivative of a function on a computer, engineers use the symmetric derivative for reduced error. Who came up with the symmetric derivative? Who proved it? When? Why was ...
1
vote
1answer
79 views

Hilbert Program: Consistency vs Soundness

I have been wondering why exactly Hilbert asked for a decidable, complete, and consistent set of axioms for mathematics, rather than a decidable, complete, and sound set of axioms. Consistency being: ...
6
votes
2answers
327 views

Hilbert program: Does Consistency and Completeness imply Decidability?

I have a question regarding the Hilbert Program. Below I will express my current understanding of it $($... if I get something wrong, please correct me!$)$ ... followed by my question. Roughly put, ...
2
votes
1answer
89 views

Why do we call it Bayes' theorem?

I'm not a historian, nor would I claim to be one, but I've seen a lot of people say that it was Laplace who formalized the theorem: $$P(A|B)=\frac{P(B|A)P(A)}{P(B)}$$ Why don't we call it "Laplace'...
0
votes
0answers
25 views

What does N stand for in Thomas Bayes' publication “An Essay towards solving a Problem in the Doctrine of Chances”

For example, in Prop 1, the beginning of the second paragraph. Suppose there be three such events, and which ever of them happens I am to receive N, and that the probability of the 1st, 2d, and 3d ...
4
votes
1answer
83 views

Why do we notate the greatest common divisor of $a$ and $b$ as $(a,b)$?

In my textbook on elementary number theory from a class last year, as well as elsewhere through my academic experience and even posts here, I often see the greatest common divisor notated as $(a,b)$ (...
4
votes
4answers
1k views

Why don't we subtract out / ignore the leap year every 128 years? [closed]

When we add the extra day to the calendar every 4 years it's to "correct" the calendar under the assumption that the year's length is 365.25 days. Every year, you're .25 days off, so after 4 years, ...
2
votes
1answer
79 views

Oldest discovered maths notes [closed]

What are the oldest discovered mathematics notes ? Which country was it discovered in and by who was it discovered ? What topic/topics did it cover mostly and how has this contributed to modern day ...
-1
votes
2answers
42 views

How is it that a third line segment doesn't always divide the first two?

How can it be shown by the pythagorean theorem that it's not always possible to find a third line segment that evenly divides into the first two? I'm using the unit square as an example. Does this ...
1
vote
1answer
75 views

Who was Dalzell? $\pi$ < 22/7

The Dalzell-Integral reads: $$0<\int_0^1\frac{x^4(1-x)^4}{1+x^2}dx=\frac{22}{7}-\pi$$ It proves that $\pi<\frac{22}{7}$. See also Wikipedia. It was introduced by D.P.Dalzell in 1944 (see ...
6
votes
3answers
1k views

Why is it called commutative property?

I can see why distributive is called distributive (distribute whatever you are multiplying to everything within the brackets). Associative because when the same associative operator appear in a row, ...
1
vote
0answers
21 views

Weird Rice distribution

In an old engineer online course (DNV Ocean), they derive the probability of local maxima of a joint gaussian process. From Equation 4.1.82: $$ f(x,w) = \frac{1}{(2\pi)^{3/2}\varepsilon\sqrt{...
6
votes
1answer
75 views

How did Euler show that number is idoneal?

Euler famously showed that there are at least 65 idoneal (convenient) numbers. This was Euler's definition of idoneal number: Number $n$ is idoneal if following holds: Let $m>1$ be an odd number ...
3
votes
3answers
47 views

Why do we order our numbers from most significant digit and not the least significant?

Not sure if this belongs here, but it occurred to me that when I add two numbers, I start adding them from the left to the right. Probably because of the simple fact that I read from left to right, or ...
9
votes
5answers
276 views

Why is it Euler's 'Totient' Function?

The function $\phi(n)$ calculates the number of positive integers $k \leqslant n \space , \gcd(k,n)=1$. It was found by mathematician Leonhard Euler. In 1879, mathematician J.J.Sylvester coined the ...
0
votes
1answer
135 views

Why still people are searching for elementary proof of Fermat's Last Theorem?

I was searching in SE and Google for elementary proofs of Fermat's Last Theorem (FLT) and I found a lot of false claims about an elementary proof is found for FLT. I'm wondering: why still there are ...
1
vote
2answers
64 views

Mathematical Development

I have two questions regarding the development of mathematics: 1) Is there an example where in mathematics, a collaboration has led to the discovery of another result? I already know something like ...
2
votes
0answers
40 views

Why do we use $Df$ rather than $f'$ for the derivative of a multivariable function?

Is there any reason we use $Df$ for derivatives of multivariable functions but $f'$ derivatives of single variable functions despite having a definition that works for both: $$Df(c) = f'(c) = L \iff \...
13
votes
2answers
131 views

The general proposition of Fermat

In his letter to Frenicle, dated 18th October, 1640, Fermat states the following (Point 8, translated) : If you subtract $2$ from a square, the remaining value cannot be divided by a prime which ...
3
votes
2answers
66 views

Why are open sets denoted $U$, $G$, and measurable sets $E$?

Why are open sets usually denoted by $U$? Is there a reference about this? Sometimes open set uses the letter $G$, such as $G_{\delta} $ set. I also wonder the meaning of $G$. Additional question: ...
1
vote
1answer
101 views

Why is Euler's reasoning correct in his proof that $\sum_n n^{-2}=\frac{\pi^2}{6}$? [duplicate]

I was reading Euler's proof that $\sum_n n^{-2}=\frac{\pi^2}{6}$ and I don't agree with his reasoning. My issue is outlined below. First, Euler observed that the function $\sin x$ has roots at $x = 0,...
0
votes
0answers
75 views

Soundness of Calculus?

In this wikipedia article. It talks about the "soundness of calculus", but it seems to talk about soundness in an informal sense and how analysis/calculus was not very rigorous and not the soundness ...
2
votes
1answer
121 views

Why are permutations (nPr) called variations in non-English languages?

First of all, you should be at least a little familiar with combinatorics to understand that question. Some often used calculator keys in stochastic are the nCr and nPr ones. Edit: I've first asked ...
3
votes
1answer
103 views

Why is it called “$e$”?

So I'm sure you have all heard of the number $e$ which is approximately $2.71828...$ . But why is it called $e$? It isn't due to Leonhard Euler, since he didn't name the number after himself, the ...
4
votes
0answers
59 views

What's the historical origin of the left-to-right order of operations?

I would assume this question has been answered before, but no combination of Googling and searching StackExchange yielded an actual response. The Facebook problem 6/2(1+2) is boring to discuss in ...
70
votes
1answer
4k views

What does the mysterious constant marked by C on a slide rule indicate?

Years ago, before everyone (or anyone) had electronic calculators, I had a pocket slide rule which I used in secondary school until the first TI-30 cane out. Recently I dug it out. Here's a photo of ...
1
vote
0answers
41 views

Relationship between Null Homotopy and Homology of Spheres

I am reading about some of the historical motivations leading up to the discovery of the Hopf Fibration in 1931, but I am having some trouble with some intuition behind why the map was such a shock to ...
5
votes
1answer
115 views

Who said (a variation of) this? “Mathematics didn't teach me how to reason correctly, but […] how easy it is to make an error when reasoning.”

I remember I once read a quote of a mathematician at the beginning of a book, or article, which said a (possibly) small variation of: Mathematics didn't teach me how to reason correctly, but at ...
2
votes
0answers
140 views

Principia Mathematica, chapter *117: a false proposition?

I was reading Principia Mathematica of Whitehead and Russell and I have found what I think is a false proposition. The proposition in question is *117.632 click on the link to see the formula and the "...
0
votes
1answer
27 views

Original Source for Norbert Wiener quote “A pattern is essentially an arrangement…” ?

I found this quote blow supposedly said by Norbert Wiener in at least two books : "Digital image processing" by R. Gonzales and "Pattern Formation and Pattern Recognition — An Attempt at a Synthesis" ...
0
votes
1answer
79 views

Will Math Ever Stop Using Paper? [closed]

This is an odd question, yet I must still inquire: will math ever stop using paper? In the writing industry, paper is dead; we do all our writing on computers. Yet with all of mathematics' complex ...
0
votes
0answers
37 views

Which term came first, “open set” or “open interval”?

As anyone familiar with toplogy may know, open/closed intervals are closely related with open/closed sets in the standard topology on $\mathbb{R}$. I am interested in the mathematical history behind ...
1
vote
2answers
274 views

Reference request: where is it written explicitly that the paradoxes of the early 20th century were overcame in the current mathematics?

Excuse me for this question, it continues this one. I wonder if there is a text where it is written explicitly that the old paradoxes (like the Russell paradox, and the others) do not appear in the ...
1
vote
0answers
61 views

Why is (or was) it necessary to rigorously define the concept of a limit?

I've been revisiting calculus for the fun of it and trying to "reconstruct" over history to understand what forces led to the creation of various topics. The reason for rigorously defining limits is ...