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

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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) ...
3
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1answer
59 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 ...
4
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0answers
45 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 ...
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0answers
32 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 ...
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0answers
35 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 ...
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10answers
416 views

What are the theorems in mathematics which can be proved using completely different ideas?

I would like to know about theorems which can give different proofs using completely different techniques. For example: When I read from the book Proof from the Book, I saw there were ...
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2answers
54 views

books about relation between Mathematics and reality and life? [on hold]

Which books I should read to understand better Mathematics? Intuition books to understand better Maths. The books show clearly the relation between Mathematics and reality and life.
6
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1answer
293 views

Ramanujan and sum of four cubes

This is more a question on History than proof itself. About a decade ago, a college professor and a Math coach told us about this beautiful theorem: Every multiple of 6 can be written as a sum of ...
5
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0answers
62 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. ...
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0answers
53 views

What happened to the publications of 19th and 18th century? [on hold]

My question is about the time when there were no access to the internet to submit them. So is it possible that we have lost numerous important researches of that epoch?
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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 ...
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1answer
38 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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4answers
148 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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0answers
23 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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0answers
131 views

how mental math is helpful to learn math? is it any scope for research or to improve new vedic math tricks? [closed]

Many peoples said vedic math is not math. its only collection of tricks but i have question that can we improve this tricks? is it any one try to improve that kind of tricks? if yes! what result they ...
0
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1answer
34 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. ...
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6answers
7k views

Why is a full turn of the circle 360°? Why not any other number?

I was just wondering why we have 90° degrees for a perpendicular angle. Why not 100° or any other number? What is the significance of 90° for the perpendicular or 360° for a circle? I didn't ever ...
2
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1answer
69 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 ...
1
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1answer
69 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 ...
3
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1answer
64 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} ...
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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
70 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
29 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
76 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
335 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 ...
53
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17answers
15k views

Anecdotes about famous mathematicians or physicists

I'm not sure whether this question suits this website, however, I don't know where else I could ask it. It is no mathematical problem or something similar, still I hope it won't be closed. A few ...
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5answers
423 views

When can ZFC be said to have been “born”?

The "History" section of the Wikipedia article on ZFC isn't particularly helpful. The only thing I understood from it is that ZFC appeared after 1922. In what book or paper was ZFC first explicitly ...
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0answers
37 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
127 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: $\underline{\text{Question}}:$ ...
89
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28answers
7k views

What are some examples of notation that really improved mathematics? [closed]

I've always felt that the concise, suggestive nature of the written language of mathematics is one of the reasons it can be so powerful. Off the top of my head I can think of a few notational ...
22
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3answers
897 views

Who came up with the $\varepsilon$-$\delta$ definitions and the axioms in Real Analysis?

I've seen a lot of definitions of notions like boundary points, accumulation points, continuity, etc, and axioms for the set of the real numbers. But I have a hard time accepting these as "true" ...
1
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0answers
40 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
76 views

Value of an elliptic integral of the first kind

The elliptic integral of the first kind $$ \int_0^{\pi/2}{\frac{du}{\sqrt{1-k^2\sin^2{u}}}} $$ cannot be expressed in terms of standard functions. But in the following context from The Pendulum by ...
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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 ...
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3answers
118 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. ...
8
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1answer
287 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?
3
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2answers
80 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 ...
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0answers
77 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] $ ...
4
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2answers
303 views

Could someone give me an example of an algebraic variety and explain what it is

I've read the wikipedia article but I don't know what an affine plane is and the definition/example did not seem clear. What I know is that in the 1880s mathematicians like Hilbert, Kronecker, Lasky ...
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1answer
36 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
73 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 ...
72
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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 ...
5
votes
1answer
146 views

Why are logarithms of trigonometric functions useful?

I have noticed that in many trigonometric tables the logarithm of the trigonometric values are given. Why this is given and not the actual values of the trigonometric functions? For example, instead ...
6
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9answers
1k views

what is the definition of Mathematics ? [closed]

we all study mathematics , and all of us learn mathematical methods to solve problems , we learn how to prove , how to think mathematically but the question is, what is mathematics ? how can we ...
0
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1answer
35 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 & ...
0
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1answer
74 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 ...
78
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16answers
8k views

Why did mathematicians take Russell's paradox seriously?

Though I've understood the logic behind's Russell's paradox for long enough, I have to admit I've never really understood why mathematicians and mathematical historians thought it so important. Most ...
24
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6answers
2k views

Where did mathematicians learn how to do truth tables?

I'm trying to find out who invented truth-tables. Here is what I have so far. Leibniz 'invented' binary arithmetic, or at least is the first one recognized to have codified and explained a base 2 ...
108
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10answers
6k views

Why do people use “it is easy to prove”?

Math is not generally what I am doing, but I have to read some literature and articles in dynamic systems and complexity theory. What I noticed is that authors tend to use (quite frequently) the ...
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3answers
1k views

When the trig functions moved from the right triangle to the unit circle?

I have to write a paper about the unit circle and I'm trying to uncover some of its origins. Also, when the trig functions were expanded to angles greater than 90° and what was the rationale behind ...