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

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481 views

Early proofs of Leibniz's formula

Wikipedia attributes Leibniz's formula to Madhava of Sangamagrama, James Gregory and Gottfried Leibniz. But what were their proofs?
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3k views

Good examples for mathemathical problems/statements that are easely solvable/provable in one theory and hard to solve/prove in another

Let $P$ be a mathematical statement or a mathematical problem. I am looking for a couple of nice examples for $P$ that satisfy the following criteria: Given two (or more) mathematical points of view ...
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1answer
341 views

Early history of lower bounds on the prime counting function

Let $\pi (x)$ be the number of prime numbers less than or equal to $x$. Euclid's proof of the infinitude of primes gives a horrible lower bound of the type $ \pi (x)>> \sqrt{\log{x}} $. ...
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1answer
272 views

Who first discovered that the torus supports a flat structure?

Who first recognized that there exists a homogenous metric on the closed genus 1 orientable surface?
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1answer
171 views

Original Proof of Riesz-Thorin

Wikipedia says that Riesz proved the Riesz-Thorin theorem in 1926 without using any complex methods. Does anyone know where the original proof can be found? ...
6
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1answer
308 views

Did Euler have an alpha function

I've heard of Euler Gamma function: $\Gamma(x)$, and Euler's beta function: $\text{B}(x,y)$. Did Euler have an alpha function?
6
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1answer
654 views

An updated alternative to “A Panorama of Pure Mathematics”

Dieudonne's A Panorama of Pure Mathematics serves as a nice, brisk overview of the state of pure mathematics at its time, but it would be nice if there were an updated version of this book. Is there ...
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8answers
2k views

Original works of great mathematicians

In almost every mathematical text there is a line as This was first proved by Gauss or This formula first appeared in a work of Riemann, but for me it's more like My friend told me once that... For ...
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1answer
237 views

Who is “Euclide Paracelso Bombasto Umbugio”?

I just browsed through the book Foundations of Algebra and Analysis by C. Dodge, which contains a very short biography of a very famous mathematician at the beginning of each chapter, together with ...
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1answer
508 views

Who was Hermann Künneth?

Question as in the title: Who was Hermann Künneth? Where can I find some biographical information beyond what is available on Wikipedia? The well-known Künneth formula, for example in the form of ...
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0answers
135 views

Etymology of algebra (as k-algebra)?

Why algebra (over a field) is called "algebra?" (My random guess is that it's a back-formation of some algebras, chopping adjectives from say Lie algebra or Clifford algebra, etc.) And when was that ...
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4answers
461 views

Real World Usage Examples and Historical Origin of Beginning Algebra (HS Algebra I and II)

I have a high schooler who I need to get energized about math. She excels in other sciences, but does not in math. The issue, I learned after some discussion, is that she doesn't find math interesting ...
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0answers
430 views

On the geometric arguments used in Newton's *Principia Mathematica Naturalis Philosophae*

When one reads Newton's Principia Mathematica, one is immediately aware of the complexity of the synthetic geometry that he uses to prove his propositions. This I understand because all of the ...
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2answers
565 views

Was there a culture/number system with negative numbers but without zero?

In the history of numbers, negative numbers as well as zero appear relatively late, possibly because the concepts represented are not really 'quantities' in a straightforward sense. However, even ...
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1answer
457 views

Old versus New enunciation of Taylor's Theorem.

I am studying from Spivak' Calculus, and he states Taylor's Theorem as follows: THEOREM Let $f',\cdots,f^{(n+1)}$ be defined on $[a,x]$ and let $R_{n,a}(x)$ be defined by ...
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2answers
907 views

What do Greek Mathematicians use when they use our equivalent Greek letters in formulas and equations?

Like for example, it's common to use the Greek letter $\theta$ to represent an angle right? So what would a Greek person doing math use to represent an angle? Would they also use $\theta$? Or is there ...
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4answers
695 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 ...
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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 ...
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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 ...
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1answer
407 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?
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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): ...
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5answers
916 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 ...
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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 ...
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1answer
210 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 ...
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1answer
253 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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2k 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 ...
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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 ...
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2answers
717 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 ...
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2answers
147 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
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2answers
389 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: $$f\colon \mathbb{R}^2\rightarrow \mathbb{R}$$ ...
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2answers
593 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 ...
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0answers
157 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 ...
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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 ...
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3answers
951 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 ...
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1answer
429 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 ...
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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 ...
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3answers
947 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 ...
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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 ...
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2answers
420 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
674 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 ...
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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 ...
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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 $IX$?
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1answer
627 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 ...
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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 ...
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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 ...