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

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5
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4answers
692 views

Euler and infinity

What do people mean when they say that Euler treated infinity differently? I read in various books that, today, mathematicians would not approve of Euler's methods and his proofs lacked rigor. Can ...
0
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3answers
249 views

Resource request: history of and interconnections between math and physics

Reading this article I became curious to learn more of (- study more thoroughly and *seriously*$^{\star}$-) the topic. Is / are there some good references - either papers, books and/or other ...
3
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0answers
73 views

analogy between etale sites and Riemann surfaces

I recently read that Grothendieck originally introduced the etale site of a scheme as an analog of the formation of Riemann surfaces over the complex numbers (the salient point being that the latter ...
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5answers
131 views

integer constants.

Are there some examples of mathematocal constants which are integer numbers. I know of one that is called Kaprekars constant but thats just a base 10 curiosity. Aret there some more important ...
3
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1answer
399 views

Why were Lie algebras called infinitesimal groups?

Why were Lie algebras called infinitesimal groups in the past? And why did mathematicians begin to avoid calling them infinitesimal groups and switch to calling them Lie algebras?
3
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1answer
259 views

History of the study of rational points on the circle

What is the first known instance of a mathematician parameterizing rational points on the unit circle by the slopes of rational lines going through a rational point on the circle?
4
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1answer
372 views

Motivation behind Theory of Relations?

I looked through the nice paper by Tarski On the Calculus of Relations. In the beginning he touched a motivation behind Theory of Relations but this part was not clear to me (page 1, very beginning): ...
18
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5answers
911 views

history of the double root solution of $ay''+by'+cy=0$

Motivation: It is a well-known fact that $ay''+by'+cy=0$ has solutions which are found from substituting the ansatz $y=e^{\lambda t}$ into the DEqn. It turns out that we replace the calculus problem ...
0
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1answer
88 views

Two $\psi$ functions

This is either a notation/history question or a point of confusion. In (for example) Ramanujan's proof of Bertrand's postulate, he uses the following notation: $\log [x]!$ means $\log ([x]!),$ in ...
9
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1answer
208 views

Which definition of dimension came first?

In my algebraic geometry class, the dimension of an affine variety $X=V(I)$ was defined as the supremum of the length of chains of prime ideals in the coordinate ring $R=k[x_1,\ldots,x_n]/\sqrt{I}$, ...
4
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1answer
137 views

Nagura's paper--can we substitute for the original upper bound?

This question concerns two results about primes. The first is J. Nagura's 1952 result, that there is a prime on the interval $[x, (1+1/5)x] $ for $x> 2103,$ which depends on the result derived ...
2
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1answer
252 views

Origin of the Notion of a Well-Formed Formula

When was the idea of a well-formed formula first stated or can get inferred as such under another name?
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2answers
1k views

Why are Darboux integrals called Riemann integrals?

As far as I have seen, the majority of modern introductory real analysis texts introduce Darboux integrals, not Riemann integrals. Indeed, many do not even mention Riemann integrals as they are ...
9
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2answers
2k views

Why are even/odd functions called even/odd?

Bit of a silly question, someone told me that the reason even functions are called 'even' and odd functions are called 'odd' is that all (single-variable) monomials with even powers are even functions ...
10
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2answers
707 views

Injection and surjection - origin of words

Can anyone give me a good explanation of how and why words surjection and injection came into use in mathematical community? What do they exactly mean? Who introduced them? I have a feeling students ...
3
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2answers
144 views

Cohen and the axiom of choice

The wikipedia article on Paul Cohen mentions that: Cohen is noted for developing a mathematical technique called forcing, which he used to prove that neither the continuum hypothesis (CH), nor ...
6
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1answer
253 views

History of Lie algebra notation (in Fraktur)?

Does anyone know how it has become the standard to express Lie algebras in fraktur? I'd also like to know how it's established for each era and region, not only the origin. It doesn't seem that ...
4
votes
2answers
382 views

Where does the symbol for a partial deriviate come from?

Does anybody know where the symbol $\partial$ comes from? (preferably with sources or with a document where it was used first) Symbol in context: $$f\colon \mathbb{R}^2\rightarrow \mathbb{R}$$ ...
4
votes
2answers
590 views

How to calculate π [duplicate]

Possible Duplicate: Simple numerical methods for calculating the digits of Pi How do people/computers calculate π? Im sure long ago, someone just took a measurement of the circumference of ...
1
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0answers
156 views

History of calculus-based optimization

I would like to know: - who started with calculus-based optimization problems and when it was, - if there is a book focusing on history of ellipses/ conic sections - if someone ever tried to ...
2
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0answers
226 views

Who invented the breadth-first permutation algorithm?

My initial problem was solved here. It is about enumerating all n-tuples of a permutation in a specific order. The solution algorithm is very simple and I'm sure has been used before. However, I did ...
9
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3answers
942 views

The aim in a course of differential equations?

As I used to understand the primary aim of a student learning differential equations is that given a differential equation he should be able to solve it. However while recently reading a note on the ...
19
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1answer
428 views

When, and by whom, was “$\mathbb{C}$ is algebraically closed” dubbed the “fundamental theorem of algebra”?

Wikipedia has this enigmatic sentence on the page for the fundamental theorem of algebra: ...its name was given at a time when the study of algebra was mainly concerned with the solutions of ...
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9answers
2k views

What mathematical ideas/concepts became obsolete due to technological progress?

As technology evolved, some ideas and methods became obsolete. What mathematical ideas entered this state due to technology progress? We could consider that doing some mathematical operations done by ...
1
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1answer
158 views

Are there any famous number system competely independence from the real number system that show its signifance in math history?

I know that both of the binary number system and complex number system depend on each others with real number system respectively and share some of their conditions and operation properties. My ...
2
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3answers
940 views

How was the quadratic formula found and proven? [duplicate]

Possible Duplicate: Why can ALL quadratic equations be solved by the quadratic formula? History of Quadratic Formula How was the quadratic formula $\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ found ...
22
votes
1answer
2k views

What is magical about Cartan's magic formula?

Why is Cartan's magic formula $$\mathscr{L}_X\omega = i_Xd\omega + d(i_X\omega)$$ called "magic"? Should it be considered a highly surprising result? Does it "magically" prove several other ...
15
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2answers
419 views

Who was the first to use dual space?

Who was the first person who used the dual space? In which paper / book did he or she use the dual space? Who was the first who called it dual space and in which paper / book?
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0answers
669 views

Definitive source about Dirichlet finally proving the Unit Theorem in the Sistine Chapel

There is a remark one can find in various books or survey articles (e.g., page 49 of Helmut Koch's "Number Theory: Algebraic Numbers and Algebraic Functions") saying Dirichlet figured out a proof of ...
10
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2answers
278 views

Articles on ideas in the history of mathematics notation?

I'm teaching a course this term on the history of scripts (writing systems) and rather than talking interminably about Semitic and Chinese and their spawn, I'd like to give students a more varied ...
2
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3answers
254 views

Is there a reasoning behind the depiction of the numbers as they are $\{1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9\}$?

Is there a reasoning behind the depiction of the numbers as they are: $$\{1,2,3,4,5,6,7,8,9\}$$ Is there any other form of depiction for $6$ and $9$ other than $VI$ and $IX$?
15
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1answer
618 views

Hilbert's Original Proof of the Nullstellensatz

Does anyone have a link to Hilbert's Original Proof of the Nullstellensatz, or know a book where it's printed? I'd be interested to see what it was like. I only really know the Noether normalisation ...
11
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2answers
4k views

Which symbol should be used for an empty set?

Currently, a discussion started on the German Wikipedia article for Empty Set (the German discussion), whether $\emptyset$ or $\varnothing$ should be used or is more common as a symbol for an empty ...
59
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1answer
2k views

How was the Monster's existence originally suspected?

I've read in many places that the Monster group was suspected to exist before it was actually proven to exist, and further that many of its properties were deduced contingent upon existence. For ...
6
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1answer
406 views

Historical Development of CW Complexes

I recently started learning about CW complexes. Although my understanding of them is somewhat nascent, I see that one can deduce a number of useful properties of a space if one can show it is a CW ...
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0answers
249 views

Who found this example of continuous nowhere differentiable function?

In many books from mathematical analysis (for example in Rudin) is presented the following example of continuous nowhere differentiable function: $$f(x)=\sum_{n=1}^\infty (\frac{3}{4})^n g(4^n x) ...
0
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3answers
356 views

How did it happen that base 10 went on to be the most popular? [duplicate]

Possible Duplicate: why have we chosen our number system to be decimal (base 10) 0,1,2,3,.......9! What are the reasons fow which this system is the most popular? Why not any other base? It ...
5
votes
2answers
1k 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: ...
10
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0answers
600 views

What is the history of “only if” in mathematics?

A quick search on the use of "only if" returns questions asking about its use and meaning in mathematics, such as here, here and here, revealing confusion in its interpretation and use for some ...
10
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2answers
833 views

Varieties as schemes

Some questions about schemes and varieties, one really basic. I follow the definitions as given in Hartshorne. Firstly, my main question. I understood that Grothendiecks introduction of schemes ...
14
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2answers
3k views

“L'Hôpital's rule” vs. “L'Hospital's rule”?

I know this is not strictly a mathematical question, and I considered putting it on Linguistics SE, but I decided that seeing as this is most probably a mathematical history question, it would be ...
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0answers
156 views

History of operator precendence

I have seen a lot of debates over operator precedence but what is the history of operator precedence and how it evolved over time? Why multiplication precedes addition; Is it just to be definitive? ...
16
votes
4answers
467 views

When was $\pi$ first suggested to be irrational?

When was $\pi$ first suggested to be irrational? According to Wikipedia, this was proved in the 18th century. Who first claimed / suggested (but not necessarily proved) that $\pi$ is irrational? I ...
4
votes
1answer
224 views

Who came up with the Euler-Lagrange equation first?

Could someone explain who came up with the specific equation first? http://en.wikipedia.org/wiki/Euler-Lagrange makes it sound like Lagrange got it first, in 1755, then sent it to Euler. but: ...
3
votes
2answers
247 views

original source for the Borel-Kolmogorov paradox

Does anyone know the original source for the Borel-Kolmogorov paradox? Is it online somewhere? Kolmogorov doesn't give a precise citation. (He does list three works by Borel in his bibliography, ...
0
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2answers
258 views

Why was Newton concerned with finding tangents?

While trying to teach myself calculus, I stumbled upon a BBC documentary called The Birth of Calculus. In the documentary, the narrator explains that Newton and other contemporary mathematicians were ...
0
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1answer
112 views

omar khayyam work on ODE (ordinary differential equation)

I wanted to know if Omar Khayyam did work on ODE and if there is any connection between that and the cubic equations.
2
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1answer
726 views

Weyl's unitarity trick

Weyl's unitarity trick creates from an irreducible representation of a compact group a unitary representation by averaging with a Haar measure. Does anyone know a reference to the paper (or book, ...
46
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13answers
5k 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 ...
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3answers
5k views

how exactly did calculus change our understanding of the world?

I am taking calculus course and I keep wondering if this is really necessary. I know it is the cornerstone of modern science but what I don't understand is why and how. Was it impossible to pursue ...