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.

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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 $f$ ...
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55 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?
5
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1answer
104 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 ...
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1answer
36 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 ...
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1answer
77 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 ...
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0answers
69 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 ...
2
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1answer
51 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 ...
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3answers
220 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. ...
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1answer
48 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 ...
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1answer
62 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 ...
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0answers
62 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 ...
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5answers
105 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
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1answer
90 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 AT&...
2
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1answer
41 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
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2answers
85 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 ...
0
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2answers
197 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
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2answers
166 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 ...
5
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0answers
52 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 ...
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0answers
40 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. ...
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1answer
43 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 ...
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0answers
38 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 ...
11
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2answers
350 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 ...
3
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0answers
28 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 ...
0
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2answers
64 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 ...
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1answer
49 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 $x=7$....
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1answer
35 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 ...
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 ...
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4answers
216 views

Why do we use degrees? [closed]

I see a lot of people who ask why we use radians instead of degrees. But why do we use degrees instead of radians. In the cases we use degrees instead of radians, what convenience does it bring? The ...
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0answers
38 views

Weak convergence in probability and functional analysis

Let $X$ be a metric space. By definition, the sequence of Borel measures $\mu_n$ on $X$ converges weakly to a measure $\mu$, if for all bounded continuous functions $f:X\to\mathbb{R}$ we have $$\int\...
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0answers
61 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: ...
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1answer
63 views

What is the first absolutely normal number to be discovered?

What is the first absolutely normal number to be discovered? Is it the Chaitin's constant? $$\Omega_F = \sum_{p \in P_F} 2^{-|p|}$$
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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 ...
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0answers
26 views

Oka's coherence theorem and Cartan's theorem A and B

So reading up on some articles I've found that whilst attempting to characterize Oka's coherence theorem in sheaf-theoretic language, Cartan was ultimately led to formulating his theorem A and B in ...
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2answers
88 views

Mathematic books with historical and original view

I am looking for books along the lines of history of mathematics but I have some conditions; History must not be the main aim of the book, the main aim of using historical context should be ...
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2answers
392 views

Is PA the first axiomatization of arithmetic to be discovered? [closed]

Is Peano Arithmetic the first axiomatization of arithmetic to be discovered?
6
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1answer
151 views

Personal notebooks of a Fields medalist

I once read that some Fields medalist published all of his personal handwritten notebooks, and that they are freely available somewhere on the net. I can't remember whose mathematician it was, so I ...
4
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1answer
93 views

Why isn't '&' used for logical conjunction?

There is a beautiful and well-established logogram for "and" that is known to virtually every more or less educated person in the world - it's the ampersand '&'. It's completely unambiguous, as ...
3
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1answer
39 views

Why can we identify complex numbers as points on a plane?

Modern mathematicians seem to define the complex number $a+bi$ as the ordered pair $(a,b)$, with the usual rules for complex addition and multiplication. I'm reading a book on the history of the ...
3
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1answer
61 views

Gauss: The study of Euler's works…

I keep coming across this quote by Gauss but I haven't actually been able to locate the original source: “The Study of Euler’s works will remain the best school for the various fields of mathematics ...
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2answers
86 views

Cauchy's contribution

Sometime, I believe perhaps 2 years, ago I asked a question about breakthroughs, such as those within mathematics and physics which may lead a whole discipline forwards in many ways. One example from ...
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7answers
395 views

On a definition of manifold

In the book Mathematical Masterpiece, on page 160, the authors wrote that A manifold, in Riemann's words, is a continuous transition of an instance I know a manifold is something glued by ...
3
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1answer
114 views

why can't quintics be solved by radicals and the relevance of permutations of roots of polynomials

I am seeking to learn about the motivation in the development of group theory. It has been a few years since algebra, and we got as far as rings and fields. I am aware that there were several ...
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4answers
2k views

Why weren't continuous functions defined as Darboux functions?

When we were in primary school, teachers showed us graphs of 'continuous' functions and said something like "Continuous functions are those you can draw without lifting your pen" With this in ...
3
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0answers
40 views

Historical use of k in proof by induction

Does anybody know the history of why the symbol k is used in proof by induction? As an example, in physics the symbol p is used for momentum because Newton called it impetus, and the letters i and m ...
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2answers
191 views

Andrew Wiles' Abel Prize for FLT - delayed or not? [closed]

Andrew Wiles was recently awarded the Abel Prize for his work proving Fermat's Last Theorem (FLT). The Abel Prize has existed for 14 years. From my layperson's perspective, it would seem that he ...
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1answer
60 views

Mersenne numbers fail primality test at 2047 itself. How could we believe Mersennes are primes?

M$_{11}=2047$ is a composite number. How could one, not check the primaility of such a small number and believe that all Mersenne numbers are primes?
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1answer
48 views

Why is it called the *Inverse* Galois Problem?

This is just a very quick question and hopefully not poorly received. Question: Why is it called the inverse galois problem? The very brief statement given on wikipedia says Is every finite ...
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0answers
83 views

Largest prime known to ancients

As is well known, Fermat couldn't check the primality of $F_{5} = 2^{2^{5}} + 1$. This raises an interesting question : what was the largest prime number that was known to ancients (particularly ...
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Why is the Weierstrass test called the M-Test [duplicate]

Is there any reason why we call this test an $M$-test? The presence of $M_n$'s in the standard formulation?
3
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4answers
137 views

Who found the expression $n^2 - n + 41 $ for generating prime numbers?

I am doing some research and I cannot seem to find the answer anywhere so does anyone know who found the expression $n^2 - n + 41 $ for generating prime numbers?