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

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3
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0answers
59 views

Reference request for Grothendieck's work on “Integration with values in a topological group”

Recently I was reading the available part of the second part of W. Scharlau's book on Alexandre Grothendieck (see here). There I found, An anecdote survives about Grothendieck's arrival in Nancy: ...
3
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0answers
26 views

Why did the number of types of integrals got lower from the beginning of the $20^{th}$ to this day?

There is an old $(\text{circa } 1930)$ and interesting book in calculus: Edwards' Treatise on Integral Calculus. This book has a very complete list of cases of integrals, for example, these ...
2
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1answer
52 views

Cauchy's real line and math philosophy till XIX

I have to write an essay concerning philosophy of mathematics until the end of $XIX$ century. I've heard that the reason why the Cauchy's theorem (if continuous functions $f_n \rightarrow f$ then $f$ ...
35
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2answers
3k views

What concept does an open set axiomatise?

In the context of metric (and in general first-countable) topologies, it's reasonably clear what a closed set is: a set $F$ is closed if and only if every convergent sequence of points in $F$ ...
-1
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0answers
43 views

Left and right inverse

Does anybody knows who is the first person to coin the term "left inverse" and "right Inverse" ? And why is it named that way?
2
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0answers
29 views

What came first: pythagoras number or pythagorean fields? [migrated]

Which concept was first introduced: the pythagoras number of a field or pythagorean fields? I have not found anything on this matter, but my gut feeling says the latter. One can more directly link the ...
4
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0answers
68 views

Who introduced the notation $\lesssim$?

Who in history introduced the notation $X\lesssim Y$ for meaning $X\leq CY$ for some constant $C$? I've seen this notation in modern literature in PDE a lot. (See for instance the notation section of ...
76
votes
25answers
12k views

Mathematicians ahead of their time?

In every field there's always that person who's just years ahead of their time. For instance, Paul Morphy (born 1837) is said to have retired from chess because he found no one to match his technique ...
2
votes
1answer
254 views

What is the origin of the (nearly obsolete) term “binary decimal”?

What is the origin of the (nearly obsolete) term "binary decimal"? At least two important publications in the 1930s used this oxymoron to mean what is now ...
1
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1answer
33 views

Eulers identity history

When Euler discovered/invented $e^{ix} = \cos(x)+i\sin(x)$. Did he doubt his calculations for a length of time? Was it Readily accepted by the mathematical community quickly or did they object at ...
2
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0answers
63 views

Is Leibnizian calculus embeddable in first order logic?

We just published an article making what we feel is a plausible case in favor of an affirmative answer in Foundations of Science, see preprint here. The basic argument is that while such a requirement ...
4
votes
1answer
66 views

History and future of algebraic curves and the like?

Now that Fermat's last theorem has been proven, and also elliptic curves see widespread use in simple everyday applications, I would love to learn how the related theories came into beeing, how they ...
2
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1answer
45 views

Have humans ever used the Log Scale convention in the past rather than the Linear one?

There are many examples where our senses are based off of log scales such as volume of a noise, ability to guess (i.e.) plus or minus a power of 10 with Fermi, and even when we measure pain on 1 to 10 ...
1
vote
1answer
38 views

Ratio vs division

I remember reading somewhere that in ancient times they were not treating a ratio like a division as we do. I was wondering is there a subtle distinction between the concept of the ratio and the idea ...
4
votes
0answers
71 views
+50

Connection of Fourier's work with Fredholm's

Im trying to formulate for myself in what sense Fredholms work on the Dirichlet problem is connected to Fouriers work on the heat equation. Fourier idea seems to have fundamental problems with ...
6
votes
3answers
197 views

Product of permutation cycles, transpositions. Are there different conventions in the order?

From this answer I get that within each cycle you map each element to the one on the right, when taking the product of cycles the one on the right should be performed first, as a typical operator. ...
36
votes
6answers
3k views

What are Some 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 ...
0
votes
1answer
57 views

Why wasn't Mahāvīra's definition of division by zero accepted?

He wrote a book (Ganita Sara Samgraha) where he defined the result of operation of division by zero A number remains unchanged when divided by zero. I think this kind of makes sense. I know ...
0
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0answers
55 views

What is “Squaring the Circle”

I am unclear about what "Squaring the Circle" is, let alone how people tried to solve it. Please tell me if "Squaring the Circle" means finding square and circle with same area OR finding square and ...
6
votes
1answer
450 views

Chinese estimate for $\pi$. Were they lucky?

The famous chinese estimate $\pi\approx\frac{355}{113}$ is good. I think that is too good. As a continued fraction: $$\pi=[3:7,15,1,292,\ldots]$$ That $292$ is a bit too big. Is there a reason for a ...
0
votes
5answers
80 views

Can we prove that plumb line is vertical to ground?

Using a plumb line to make sure a wall is vertical for instance, is as far as I know one of the most primary tools in the sense that the very-very ancient builders used it as an instrument. I was ...
5
votes
1answer
85 views

Was there a golden age of industrial mathematics that is now over?

I read "The Man Who Loved Only Numbers," a great book about Paul Erdős, last summer. The book describes Ronald Graham, a super interesting character who worked on discrete math and graph theory at ...
2
votes
1answer
38 views

What does the word “Comprehension” mean in the Axiom of Comprehension?

I understand roughly what the Axiom of Comprehension means, that any predicate can be used to construct a set of the elements that satisfy the predicate. But in English terms, where does the word ...
6
votes
2answers
73 views

Original proof of Zorn's Lemma

On the wiki page for Zorn's Lemma it says that this lemma was Proved by Kuratowski in 1922 and independently by Zorn in 1935 but then it says: Zorn's lemma is equivalent to the well-ordering ...
3
votes
1answer
104 views

When did Liouville come up with the first transcendental numbers?

There are some conflicting sources regarding this. It is a matter of fact that Liouville defined what it was for a number to be approximated to degree $n$ by rational numbers. He then effectively ...
0
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2answers
96 views

What are some of the Hardest Unsolved Mathematics Problems? [closed]

At the moment, are there any major unsolved mathematical problems yet to be solved, and do they have any prize associated with the solving of them? Furthermore, is there any particular reason that ...
7
votes
2answers
164 views

How did the name “The Calculus” come about, was there a reason or just good marketing?

This is a historical and lighthearted question about etymology. The area of mathematics that deals with limiting processes over real numbers (Real Analysis) or real vector spaces, or even complex ...
1
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1answer
169 views

Galois false solution to the quintic equation

I am looking for the false solution Galois gave to the quintic equation before discovering group theory.
11
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2answers
332 views

The three unsolved problems of antiquity

In Sidelights on the Cardan-Tartaglia Controversy (Apr., 1938) by Martin A. Nordgaard in the National Mathematics Magazine, Vol. 12, No. 7, pp. 327-364, it is written on the first page The ...
5
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0answers
51 views

Understanding a medieval approximation

A medieval text (Maimonides's commentary to chapter 2 of Eruvin in my retranslation from the Hebrew) discusses a rectangle whose area is $5000$ square cubits. It reads in relevant part: … that the ...
2
votes
0answers
35 views

German translation needed - final sentences of a paper by Hilbert

I am translating a paper by Hilbert into English. I am finished except for the last few sentences, which are confusing me. If anyone can give me a rough/quick translation it would greatly appreciated. ...
4
votes
1answer
307 views

Is Euler's Introductio in analysin infinitorum suitable for studying analysis today?

I've read the following quote on Wanner's Analysis by Its History: ... our students of mathematics would profit much more from a study of Euler's Introductio in analysin infinitorum, rather than ...
4
votes
1answer
255 views

History of incenter and Euler line

It is easy to see that if a triangle is isosceles, then its incenter lies on its Euler line. Who first proved the converse of this result and what technique was used? (See the post "The incenter and ...
9
votes
1answer
275 views

Did Field's Medalist Klaus Roth suffer from test anxiety?

I remember hearing the story that Fields Medalist Klaus Roth was convinced that he could not pass a qualifying exam when he was a graduate student. He was then given a so called practice exam for him ...
1
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1answer
42 views

How has the teaching of (undergraduate) Set Theory changed over time?

I'm writing an Essay on Set Theory, and realized it was formulated quite recently, so I thought it might be cool to have some first person accounts. Russell's Paradox was discovered just around a ...
0
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0answers
37 views

Is there any way to retain Russell's original proof of induction in Appendix B of PM 1925?

Recently I was reading this question again and the following question occurred to me, Can there be some new interpretation of the system of PM $1925$ so that Russell's proof of $^\ast89.16$ is not ...
3
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0answers
25 views

history of holomorphic implies analytic and goursat theorem

I'm studing complex analysis and am curious about its history. Did Cauchy know that holomorphic functions (to have derivative in every point of an open set) are infinitely derivable? and that they ...
-3
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1answer
136 views

How values of the constants are derived mathematically? [closed]

As said by Jan regarding constant value $\pi$ ,Imagine you have a circle and you are able to measure its circumference "c". Then, you can also find out what its diameter "d" is. When you divide ...
3
votes
1answer
101 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 ...
12
votes
5answers
493 views

When can ZFC be said to have been “born”?

The "History" section of the Wikipedia article on ZFC isn't particularly helpful. The only thing I have understood from it is that ZFC had appeared after 1922. In what book or paper was ZFC first ...
1
vote
1answer
45 views

How to graph in hyperbolic geometry?

I was given the following question regarding hyperbolic geometry: In the hyperbolic geometry in the upper half plane, construct two lines through the point $(3,1)$ that are parallel to the line ...
0
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2answers
62 views

why soh cah toa is right?

i am confused by the sine of an angle, (it might appear evident for some of you but please i am not an expert ). sine of an angle is says to be the half of the magnitude of the chord of 2 time the ...
19
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3answers
2k views

What is the origin of the expression “Yoneda Lemma”?

Thank you very much in advance for telling where the expression “Yoneda Lemma” comes from. EDIT 1. On page -14 of Reprints in Theory and Applications of Categories, No. 3, 2003. Abelian Categories, ...
2
votes
1answer
72 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
votes
1answer
33 views

What is the example called, where someone was wrongly convinced of a sequence function because of naive induction.

I remember I have seen a classical example of a mistake, where someone was convinced that a sequence defined somehow had a close form, which did in turn work until some very high $n$. I think the ...
13
votes
2answers
348 views

Before Abel's proof, what did they used for trying to find the general solution for quintics?

Whenever I read about the history of algebra, I end up with the same conclusion: They solved the general cubic, then the general quartic and then spent lots of years trying to solve the general ...
15
votes
9answers
2k views

Why are the Trig functions defined by the counterclockwise path of a circle?

My understanding is that $\cos$ is defined by the value of $x$ as you trace the graph of a circle counterclockwise, starting at the point $(1, 0)$. Similarly, $\sin$ traces the $y$ value. I understand ...
0
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1answer
44 views

How are gigantic primes actually defined in the 1992 article by Samuel Yates?

The Prime Glossary states: In a 1992 article, Samuel Yates coined the name gigantic prime for any prime with 10,000 or more decimal digits (he had also coined the term titanic primes a decade ...
1
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1answer
249 views

Why must there be an infinite number of lines in an absolute geometry?

Why must there be an infinite number of lines in an absolute geometry? I see that there must be an infinite number of points pretty trivially due to the protractor postulate, and there are an infinite ...