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

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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
37 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
72 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
73 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
174 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
81 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
79 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
97 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
367 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 ...
1
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0answers
53 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
138 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
47 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
138 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
83 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
119 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
297 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
41 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
87 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
36 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
75 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
149 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 ...
3
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2answers
77 views

Why do we think of group compositions as multiplication?

This has bothered me for some time: The composition in a group is usually denoted $xy$ or $x\cdot y$. Powers (note the word) are denoted by $x^n$, inverses by $x^{-1}$, and the neutral element by $1$. ...
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2answers
121 views

What comes after seconds?

Angles can be measured in different ways. For example, one can measure angles in degrees/minutes/seconds. So $1^\circ$ is divded into $60$ min. and $1$ min is divided into $60$ sec. That way a tenth ...
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0answers
67 views

How much math was “Broken” by Russell's Paradox?

As you know, the phrase "the set of all sets that don't contain themselves" caused a paradox that "broke" (made trivial) Naive set theory. How much mathematics had to be redone because of this? Most ...
5
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1answer
160 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 ...
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2answers
38 views

What are these numbers in a logarithmic table?

Below is an image from a table of logarithms. As an example, one sees that $\log(661.3) = 2.82\color{red}{040}$. In this logarithmic table there are some numbers to the right. My question is: What is ...
95
votes
15answers
9k views

Has lack of mathematical rigour killed anybody before? [closed]

One of my friends was asking me about tertiary level mathematics as opposed to high school mathematics, and naturally the topic of rigour came up. To provide him with a brief glimpse as to the ...
1
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1answer
28 views

Derivation of the discriminant of a cubic polynomial by algebraic manipulation.

The problem was asked before: Using Vieta's theorem for cubic equations to derive the cubic discriminant . I tried to solve it by purely algebraic manipulation but was faced with an explosion of ...
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5answers
88 views

What does the solution of a PDE represent?

So I took a course in PDE's this semester and now the semester is over and I'm still having issue with what exactly we solved for. I mean it in this sense, in your usual first or second calculus ...
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1answer
105 views

What is the difference (or relationship) between geometric length and arithmetic numbers?

In Abbott's Understanding Analysis there was a phrase like, "Ancient Greeks did not understand the difference (or relationship) between geometric length and arithmetic numbers." What is this ...
2
votes
1answer
20 views

Noether comment to Dedekind and Weber's work

I am trying to consult Emmy Noether's “Erläuterungen zur vorstehenden Abhandlung”, some sort of epilogue or comment to Richard Dedekind and Heinrich Weber's “Theorie der algebraischen Funktionen einer ...
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3answers
56 views

History and early development of Mathematics

Please provide references (books, articles, websites) that describe the conceptual development of calculus, complex numbers, group theory and matrix. I am curious about how the Mathematicians ...
0
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1answer
37 views

On Dedekind's prime ideals

Prime ideals were an essential tool for Dedekind to save or restore unique factorization. Is it fair to say that the shift from Kummer's ideal numbers to Dedekind's ideals (with prime ideals, and so ...
5
votes
1answer
250 views

What does “hom” stand for in hom-sets and hom-functors?

With given category $\mathcal{C}$ and its objects $A$ and $B$, a hom-set $\hom_\mathcal{C}(A, B)$ is the collection of all morphisms from $A$ to $B$. There is also a related notion of hom-functor ...
3
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1answer
67 views

A question regarding Kummer [closed]

As you know, Ernst Kummer noticed that examples such as $$6 = 2\cdot 3 \text{ or } 6 = 3 \cdot 2 \text{ and, crucially } 6 = (1 + \sqrt{-5}) (1 -\sqrt{-5}) $$ proved the failure of unique ...
3
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0answers
60 views

Why didn't Bernoulli and Euler use an integral comparison to estimate the solution to the Basel problem?

I was reading the history of the Basel problem in William Duhnam's book, Euler - The Master of Us All. The book tells how Jakob Bernouili did some clever manipulation to show that the sum of $1/n^2 ...
2
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1answer
57 views

Original paper by Gauss on gaussian integers

Could anyone provide me with the title and date of Gauss's paper where he first introduces gaussian integers and proves their unique factorization? If you could also provide me with his exact proof ...
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0answers
22 views

Maltsev on Algebraic Systems

As far as I know, it was A.I Maltsev who fist coined the term "Algebraic systems" in a paper from 1953. Then Birkoff, MacLane and others extended its usage and appplications. My question is a simple ...
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0answers
38 views

Notations for interior product

There are two symbols in the Unicode "Supplementary Mathematical Operators" range whose names intrigue me 2A3C: INTERIOR PRODUCT: ⨼ (like $\lnot$ upside down) 2A3D: RIGHTHAND INTERIOR PRODUCT: ⨽ ...
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2answers
74 views

Why is the letter “F” used for the curvature 2-form?

Given a differentiable manifold $X$, a vector bundle $E\to X$ and a connection $A$ on $E$. The curvature $2$-form of the connection is a $2$-form with values on the endomorphisms of $E$ defined as ...
7
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1answer
92 views

(Co)homology theory and electrical circuit

I have read that one of the origins of the theory of (co)homology is the study of electrical circuits by Poincare. I'd like to know more about that. Could someone sugest any reference on this subject? ...
4
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0answers
75 views

In the mean value theorem, we are guaranteed $c$ such that $f'(c) = (f(b)-f(a))/(b-a)$. Does $c$ have a name?

The Mean Value Theorem says approximately that for differentiable $f$, there is a $c \in (a,b)$ such that $$ f'(c) = \frac{f(b)-f(a)}{b - a}. $$ I presume that the number $f'(c)$ is the mean value. My ...
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1answer
48 views

On Gaussian Primes

Some primes in the ring of integers (17, for example) cease to behave as such in the ring of gaussian integers, while others (7, for instance) keep being prime there as well. The former are of the ...
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0answers
61 views

When did Liouville come up with the first transcendental numbers?

There are some conflicting sources regarding this. It is a matter of fact that Liouville defined what it was for a number to be approximated to degree $n$ by rational numbers. He then effectively ...
3
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1answer
51 views

who coined the prime ideals?

I know that Ernst Kummer first made used of "ideal complex numbers", and, hinging on that, Dedekind later introduced his "ideals" in Vorlesungen über Zahlentheorie. But, who coined the term "prime ...