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When was the unit circle formalised

I am wondering about the origins of the Unit Circle. Of course it is part of trigonometry, which goes back many centuries. But since it uses Cartesian coordinates, it should be after Descartes. So, ...
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1answer
20 views

A question in understanding some part of paper of Frobenius

I am learning German, and reading German paper of Frobenius (click here). It is "Verallgemeinerung des Sylow'schen Satzes / G. Frobenius" I didn't understand few things, and I didn't find the answer ...
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0answers
66 views

Generlization of Riesz Representation Theorem until now

I am writing on Riesz Representation Theorem. How this theorem was motivated and what further generalizations were done while it was on its way to where it is now. Starting from the begining, ...
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1answer
55 views

Origin of alternate base annotation

In modern arithmetic textbooks, students are taught about alternate numeric bases. The notation for indicating the base of a number is to attach the base as a subscript. The subscript is itself a ...
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3answers
297 views

How do mathematicians invented and introduced $\pi$ term in the case of circle?

This is basic question. Since childhood I am mugging the mathematical formulae areas of square, rectangle and circle etc. Now,it is possible for me to understand formula of area of square I.e. ...
5
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1answer
183 views

Did Russell correct his proof of Peano Postulates as was in the second edition of Principia Mathematica?

In the second edition of Principia Mathematica Russell attempts to show in a new Appendix B that the Peano postulates for the natural numbers, including the scheme of mathematical induction, can be ...
3
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1answer
138 views

How did the ancient Greeks discover formulas for volume and surface area?

How did the ancient Greeks discover formulas for volume and surface area of different objects, e.g. of a sphere? They did not know about integrals, so there must another way?
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2answers
139 views

What is the latest work being done in the field of Mathematics? 6/8/2015 [closed]

Young mathematics enthusiast here. I'm very curious to know what the top research is in the field of pure mathematics. Physics seems to take all the glory with quarks, then gravitons, Higgs boson,......
6
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0answers
159 views

Is Bourbaki unique?

So my understanding is that a while back a group of mostly French mathematicians, under the pseudonym Bourbaki, wrote a somewhat austerely written series titled "Elements of Mathematic(s)" covering a ...
20
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11answers
1k views

What are some results that shook the foundations of one or more fields of mathematics? [closed]

An example would be the proof that $\sqrt{2}$ is not rational, which was a violation of some fundamental assumptions that mathematicians at the time made about numbers. Another would be Russell's ...
1
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1answer
122 views

Difference between the formula of Roger Cotes and Euler

What was the difference between the formula that Roger cotes derived and that euler got? I mean to say that Euler got the following formula : $$e^{ix} = \cos x+i \sin x$$ And Cotes got the following ...
76
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15answers
12k views

What is the smallest unknown natural number?

There are several unknown numbers in mathematics, such as optimal constants in some inequalities. Often it is enough to some estimates for these numbers from above and below, but finding the exact ...
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1answer
9k views

Strange old multiplication table found in Oklahoma school

Today I read an article about chalk boards from 1917 discovered in an Oklahoma school. One of the chalkboards included the following curious image: (Oklahoma City Public Schools) The article ...
5
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0answers
185 views

What is the likely future of Univalent Foundations?

Univalent foundations has been hyped up as the foundation for mathematics for the future in articles such as this one. Now I've given HoTT a brief look, and at least seen that it appears on the face ...
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0answers
44 views

Lasker-Noether Theorem and Kummer-Dedekind

I would like to know about the relations between Ernst Kummer's invention of complex ideal numbers (and Dedekind's development of them into what is now called ideals) regarding the unique ...
9
votes
1answer
317 views

Work of Ted Kaczynski

I hope this question is not too crazy sounding, but I was wondering if anyone is familiar with the work of Ted Kaczynski (or even has cited/used it before). After reading in Lars Ahlfors' Complex ...
2
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2answers
113 views

How do you pronounce Richard Courant's surname?

Since his surname looks rather French than German, I started wondering how you pronounce his name. In particular, I'd be interested in how he would have pronounced his name himself (since I already ...
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2answers
529 views

Why are Natural Numbers called Natural Numbers?

When we say $1,2,3...$ are natural numbers, why don't we include rational and irrational numbers? Isn't $\pi$ something natural? Shouldn't we say all real numbers the Natural numbers? Shouldn't we,...
2
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0answers
53 views

Who first used the notation $\mathcal{O}_K$ for ring of integers?

I think this is a standard notation since almost every author uses it, but who came up with the notation? After all, what does $\mathcal{O}$ in $\mathcal{O}_K$ stand for? Thanks in advance.
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2answers
135 views

What is the poetry of mathematics? [closed]

In computer science it's often noted, said or agreed on that algorithms are the poetry of computer science. What is considered the poetry of mathematics? Is it statistics? If there is something agreed ...
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0answers
54 views

On the origins of Homological algebra

In Martin Krieger's book "Doing Mathematics: Convention Subject, Calculation, Analogy" (2003) I find the following statement (apparently, a quote from somone else) : "Homological algebra starts from ...
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0answers
26 views

Origins of the Cesaro Operator

I am wondering when the Cesaro Operator was first studied. I can find an article from 1965 but I'm wondering if there are any previous ones.
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0answers
234 views

Did Guinness Book of Records screw this up? [closed]

Crossposted on HSM See Guinness Book of Records. Did they screw this up? It says that Fermat's Last Theorem was the longest open problem - with only 365 years. However, there are Greek problems that ...
6
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0answers
95 views

What did John Nash publish post-illness?

I've searched for this from time to time and never been able to find a single research paper he published since 1960. Every account of his later work seems to finesse this. The Abel prize page for ...
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1answer
70 views

Inverse functions multivalued or not?

The square root of $y$ is usually defined as the positive solution $x$ to $y=x^2$, so the negative variant is not considered. In the same way, the inverse cosinus and sinus give the solution on ...
2
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2answers
107 views

Why Cantor set removes one third?

I found the derivation of Cantor-like set in Understanding Analysis by Abbott. There he removes one fourth, and most properties (length, cardinality, compactness, uncountableness) are preserved (...
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0answers
62 views

Who coined ideals in Set Theory?

One of the meanings of the word "ideal" in maths refers to Set Theory. Even though handbooks say that concept can be translated to Order Theory or to Algebra effortelssly, I am interested in: 1) ...
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0answers
72 views

Who was the first to use right and left ideals in a ring?

I know Emmy Noether defined the terms right and left ideal of a ring and made extensive use of them. However, I am interested in knowing whether someone had already coined the term (in the very ...
2
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0answers
44 views

Relation of ideals in probability with other kinds of ideals?

It seems that there are at least 5 kinds of ideals in maths: Ideals in number theory (Kummer, Dedekind) Ideals in abstract algebra (Dedekind, Noether), as kernels of homomorphisms Ideals in order ...
5
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1answer
77 views

Number of squarefree numbers and the Basel problem

Who discovered/proved that there are about $$ \frac{x}{\zeta(2)} $$ squarefree numbers up to $x$, or (roughly) when was this first known? Today I think this is considered 'obvious', but I don't know ...
6
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1answer
198 views

Where did the German term “Spur” of a matrix come from?

I wonder the origin of the term "trace" of a matrix. As I googled, it was the English translation of the German word "Spur" and it appeared in the translation of H. Weyl's Raum, Zeit, Materie. http://...
3
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1answer
101 views

Book recommendation: History of the foundations of analysis

I'm looking for a book for a friend. I'd like to find a mostly historical, non-technical treatment of the story of Weierstrass, Cauchy, Riemann, and their work placing Newton and Leibniz' calculus on ...
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0answers
22 views

Relation between Noether's one-sided ideals and Polish notation?

Given the definitions of one-sided ideals (right ideals; left ideals) bu Emmy Noether, as referred in this answer Noether's definition of right and left ideals?, I would like to raise the ...
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1answer
45 views

Noether's definition of right and left ideals?

could anyone provide me with Emmy Noether's definition of right and left ideals? The German original and references would be welcome. I am assuming she was the one who first coined those two kinds ...
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0answers
55 views

Rudolff's symbol for unknown

I have read Florian Cajori's book "A history of mathematical notations." Cajori explained about several symbols for unknown. Rudolff used weird symbols. I could identify some symbols: "z" for ...
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1answer
66 views

Where does the term “affine space” come from?

I'm wondering since few years what its origin is. The adjective affinis means neighbouring, allied to, kindred and the noun derived from it affinitas means relationship, connection, union, affinity. I'...
2
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1answer
88 views

Riemann's genus???

Could anyone provide me with Riemann's original definition of genus? It would be great if, apart from the definiton in English and some example he may have illustrated the notion with, you could also ...
5
votes
1answer
134 views

Why are these functions called “kernels”?

In the last years while studying numerical analysis I came across different "kernels", like the Dirichlet Kernel $$D_n(x) = \sum_{k=-n}^n e^{ikx}$$ the Fejer-Kernel $$F_n(x) = \frac{1}{n} \sum_{k=0}...
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4answers
250 views

Can we still learn from the old masters?

So, let me first describe how my doubt originated: out of curiosity I started to study Newton's Opticks, a book written more than 300 years ago. I was doing some of the experiments described on it, ...
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1answer
52 views

Why did mathematicians name a functional that assigns number to function as a “distribution”?

Why did people name it as a "distribution"? I don't see the reason. My instructor told us don't bother with this strange name, but I guess maybe I will have a better understanding if I know the ...
1
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1answer
91 views

Who was the first person to use logarithmic differentiation?

This is a math history question. And I'm curious if it was Euler or someone else. In what mathematical work did it first appear? I don't have the resources/resourcefulness to answer this question.
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0answers
57 views

Reference request: history of analytic geometry

I am searching a book in the domain of the history of math, that describes the historical origins of analytic geometry, starting from Descartes (?), and that describes also its development (e.g. the ...
5
votes
1answer
381 views

Traveling salesman problem: why visit each city only once?

According to wikipedia, the Traveling Salesman Problem (TSP) is: Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city ...
12
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4answers
502 views

Elementary problems that would've been hard for past mathematicians, but are easy to solve today? [closed]

I'm looking for problems that due to modern developments in mathematics would nowadays be reduced to a rote computation or at least an exercise in a textbook, but that past mathematicians (even famous ...
0
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0answers
88 views

Khayyam's method of solving a cubic equation

Can someone offer a worked example of how Omar Khayyam would have a solved a cubic equation with geometric solutions by means of intersecting conics?
2
votes
1answer
171 views

Famous Problems the Experts Could not Solve [closed]

After Yitang Zhang stunned the mathematics world by establishing the first finite bound on gaps between prime numbers, it got me thinking about the following question: $\underline{\text{Question}}:$ ...
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0answers
129 views

History of differential and integral calculus

My math teacher told me that the research in differential calculus and integral calculus began on two separate tracks.Apparently people didn't know there was a relation between the two until some ...
0
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0answers
36 views

Historical use of geometry to solve polynomial equations

I'm researching historical use of geometry to find solutions to polynomial equations. I'd like to ask for those familiar with this topic, could you describe the use of geometry by early mathematicians ...
93
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6answers
11k views

What did Alan Turing mean when he said he didn't fully understand dy/dx?

Alan Turing's notebook has recently been sold at an auction house in London. In it he says this: Written out: The Leibniz notation $\frac{\mathrm{d}y}{\mathrm{d}x}$ I find extremely difficult ...
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3answers
410 views

Famous smoking mathematicians [closed]

I know Banach was an incessant smoker. I would like to know about the post 1950 famous smoking mathematicians? This is a math-sociological question. Please do not view this as promoting anything. ...