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

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4k views

Strange old multiplication table

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 ...
3
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0answers
116 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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30 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 ...
8
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0answers
162 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 ...
0
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0answers
12 views

On the history of sigma-ideals

Could anyone provide me with some insight regarding the history of sigma-ideals, i.e., who coined them, first publications on the matter, main authors thereafter and so on? Thanks in advance.
1
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1answer
57 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 ...
2
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2answers
122 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 ...
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0answers
36 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.
0
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2answers
107 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 ...
0
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0answers
40 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
22 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.
6
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190 views

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

Crossposted on HSM (http://hsm.stackexchange.com/questions/2435/did-guinness-book-of-records-screw-this-up) See Guinness Book of Records ...
6
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0answers
76 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 ...
1
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1answer
54 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 ...
0
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0answers
68 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 ...
0
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0answers
19 views

how to get same line from gradient?

I have image like this how to get $x_4,y_4$ ? from gradient it like same line $y_1,x_1$ and $y_0,x_0$
0
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0answers
49 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) ...
4
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0answers
60 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
36 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
59 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 ...
5
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0answers
100 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. ...
3
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1answer
68 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
14 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 ...
1
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1answer
40 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 ...
2
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0answers
29 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 ...
0
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1answer
38 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. ...
2
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1answer
76 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 ...
3
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1answer
79 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} ...
7
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4answers
187 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, ...
1
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1answer
86 views

Non-standard model of arithmetic and Gödel's theorem [closed]

This is a cross-post of a question asked on History of Science and Mathematics Stack Exchange. I've read Skolem's paper on his non-standard models of the arithmetic ("Über die ...
1
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1answer
46 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
83 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
34 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 ...
3
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1answer
117 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 ...
11
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4answers
381 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 ...
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0answers
58 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
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1answer
141 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
52 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 ...
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0answers
34 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 ...
-3
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3answers
155 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. ...
3
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2answers
88 views

Why do we need to rationalize fractions? [duplicate]

Teachers often take off points from students who write 1/sqrt(2) instead of sqrt(2)/2. Why do we need to write it as sqrt(2) / 2 ? Where did that convention come from? Do we need to even do it? Why do ...
7
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0answers
128 views

Riesz's 1909 proof of the Riesz Representation Theorem

Frigyes Riesz originally proved the Riesz Representation Theorem on $ C[0,1] $ -- here is his 1909 paper in English (original French). He builds a real valued function $ \text{A} $ on $ [0,1] $ ...
8
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1answer
307 views

Bourbaki and set inclusion

Which notation ($\subset$ or $\subseteq$) was preferred by Bourbaki for set inclusion (not proper)? A side question: Was the notation for subset one of the many notations invented by Bourbaki?
1
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1answer
42 views

Kronecker's 1870 paper on finite Abelian Groups??

Could anyone please provide me with the exact bibliographic reference for Kronecker's 1870 work on finite Abelian groups? If you could provide me with his exact formulation (or even with a acanned ...
4
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1answer
107 views

How can I maintain notes while self studying Maths?

Thank you for stopping by this thread. I'm an engineering student rekindling an interest in Maths. I just love studying Maths in my free time (and sometimes it trespasses into my non free time). I ...
0
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1answer
39 views

order of operations in different cultures?

Are there any cultures or countries around the world that use a different convention for order of operations than the BEDMAS convention? i.e.: Parentheses Exponents & Roots Multiplication & ...
71
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6answers
7k views

Mathematically, why was the Enigma machine so hard to crack?

Mathematically, why was the Enigma machine so hard to crack? In laymen terms, what was it exactly that made cracking the Enigma machine such a formidable task? Everything I have seen about the ...
1
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1answer
55 views

informal semantics regarding CH and AC

why is the assertion $\aleph_1=2^{\aleph_0}$ referred to as a hypothesis, whereas $$\forall \alpha( S_\alpha \ne \varnothing) \Rightarrow \prod_\alpha S_\alpha \ne \varnothing$$ is called an axiom? ...
0
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1answer
76 views

Which one of the following logical propositions is to be preferred?

I'm trying to update the symbolism of Giuseppe Peano's "Arithmetices Principia", to make the translation freely available. Might I ask you, which of the following might be a correct mathematical ...
5
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1answer
156 views

How fast was the Turing's machine for breaking the enigma code?

We know that, recently, personal computers make around $10^9$ calculations per second, and I'm just curious about how many calculations was able to compute the machine invented by Turing for breaking ...