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

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5
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1answer
97 views

How to properly mention names and surnames when writing introductions

I am writing a historical introduction to my master's thesis. Therefore I am mentioning a lot of people and I don't want to write their full name and surname each time. However, I cannot write their ...
0
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1answer
208 views

Beginnings of Greek Mathematics

For another proof of the pythagorean theorem, consider right triangle ABC (with right angle at C) whose legs have length a and b and whose hypotenuse has length c. On the extension of side BC pick a ...
8
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4answers
500 views

Can we prove that odd and even numbers alternate without using induction?

It is a simple exercise to prove using mathematical induction that if a natural number n > 1 is not divisible by 2, then n can be written as m + m + 1 for some natural number m. (Depending on your ...
9
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1answer
329 views

Origin of Littlewood's idea about sign changes of $Li(x) - \pi(x)$

Background (skip if you like). Skewes and Littlewood are closely identified with the idea that $Li(x)- \pi(x)$ changes sign infinitely often, but Littlewood closed a gap in the work of Schmidt, who ...
61
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20answers
3k views

What are some examples of mathematics that had unintended useful applications much later?

I would like to know some examples of interesting (to the layman or young student), easy-to-describe examples of mathematics that has had profound unanticipated useful applications in the real world. ...
2
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1answer
74 views

Where can I get all mathematician's birth day and death day?

Did anyone do some some similar statistic thing? wiki's page is too few. mathematician in wiki For example, I want to know which day/ month that most mathematicians be born or died.
3
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1answer
159 views

Calculation involving $\int_2^x \frac{dx}{\log x}$

Background (skip to the gray if you prefer). In Legendre's 1798 work on number theory he conjectured that $\pi(x)\sim \frac{x}{\log x - A}$ in which he proposed that $A = 1.08366.$ Gauss disputed the ...
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0answers
78 views

Which link is there between Calculus and Quadrature?

I'm trying to find the origin of the integration process. To do that I'm studying "De Analysi" by Newton. I would like to know the process that lead Newton to the Rule I $\ref{Rule I}$ below, and if ...
10
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2answers
251 views

How was the first log table put together?

Henry Briggs compiled the first table of base-$10$ logarithms in 1617, with the help of John Napier. My question is: how did he calculate these logarithms? How were logarithms calculated back then? ...
-1
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1answer
165 views

Ancient babylonian geometry

An old Babylonian tablet calls for finding the area of an isosceles trapezoid whose sides are 30 units long and whose bases are 14 and 50.
1
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3answers
256 views

Ancient Babylonian problem: solve the system $x + y = 50$, $x^2 + y^2 + (x - y)^2 = 1400$

$x + y = 50, x^2 + y^2 + (x - y)^2 = 1400$. [Hint: Subtract the square of the first equation from twice the second equation to get a quadratic in $x - y$.] I have gotten it reduced to $x^2 + y^2 ...
0
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1answer
364 views

Who are the greatest mathematicians of the last years? Don't give a ranking, comment on recent achievements that led to new areas in mathematics. [closed]

Let me begin by saying that I agree that the question should be addressed carefully, I intend this as a pedagogical exercise. Every musician has its favorite musicians of all time, even if he agrees ...
4
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0answers
201 views

How much are mathematics driven by applications?

At some point this provocative question came to my mind: Are mathematics mostly driven by applications? I am taking into account some of the comments made to my original question so I want to ...
3
votes
2answers
179 views

De Moivre's formula

I'm starting to study complex numbers, obviously we've work with De Moivre's formula. I was courious about the origin of it and i look for the original paper, I found it in the Philosophicis ...
4
votes
1answer
75 views

Who was the first to solve the linear first order ODE?

Who was first to solve equations of the form $y' + p(t)y = g(t)$? The method of the integration factor is mildly tricky to students at first, so I imagine there must have been some time spent to come ...
11
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1answer
191 views

What is “inner” about the inner product?

The inner product I am asking about is the one that generalizes the dot product for an arbitrary inner product space. Why is it called an "inner" product? Is there an outer product? Who named it ...
7
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2answers
150 views

Historical meaning and usage of determinant

Can anyone please explain how, why, and where determinants were developed/formalized? What was their historical usage? Why were they initially formulated and what were they used for (and later ...
3
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1answer
78 views

Expressing integers as a sum of squares

There have been many results about the number of squares needed to represent a positive integer. Lagrange's four-square theorem tells us that $4$ squares suffice for any integer and there have been ...
3
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0answers
87 views

Classification of Groups

Arthur Cayley classified all groups of order $4$ and $6$ in 1854, and groups of order $8$ in 1858. What about groups of order $2,3,5,7$?. These are prime numbers, and the most basic theorem in group ...
4
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0answers
74 views

The number of solutions of $ax^4 - by^4 \equiv 1$ (mod $p$) for a prime of the form $p = 4n + 1$

Weil writes in his paper "The number of solutions of equations in finite fields" that Gauss finds the number of solutions of $ax^4 - by^4 \equiv 1$ (mod $p$) for a prime of the form $p = 4n + 1$ in ...
18
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1answer
403 views

Why did Gauss think the reciprocity law so important in number theory?

Gauss's Disquitiones Arithmeticae centers around the quadratic reciprocity law. It seems that he developed the genus theory of integral binary quadratic forms to find a natural proof of the quadratic ...
6
votes
3answers
304 views

How was $e$ first calculated?

I understand how $\pi$ is calculated, but I am interested in references that explain when and how the natural exponent $e$ was developed. What mathematical principles are behind the value of $e$?
5
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1answer
65 views

Origin of the term “planar graph”

I would like to know who coined the term planar graph? I was able to trace the term back to a paper "Non-Separable and Planar Graphs" by Hassler Whitney, Proc. Natl. Acad. Sci USA. 1931 February; ...
7
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4answers
214 views

Is there an established notation, either modern or historical, for any unit of measure which is then further subdivided into 360 degrees or parts?

This question about notation is simple as dirt, but would be useful for me regardless, because of some work that I'm doing in music theory. Basically, while there's a notation for subdividing the ...
5
votes
1answer
133 views

History of mathematics in engineering

I am starting out to teach a course in calculus for (first semester) engineering students. I woild like some soure book (or other kind of sources) for "history of engineering mathematics". Searching ...
6
votes
1answer
114 views

Who introduced the term “norm” into mathematics?

I've always been curious about the motivation behind the use of the word norm, as used in linear algebra and functional analysis, for a function that assigns a positive number to a vector. Who ...
4
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1answer
179 views

List of proofs of non-trivial theorems which were unnoticed to be wrong for at least a few years

For example, the Weber's proof of Kronecker–Weber theorem. I would like to know such proofs. It seems to be important for me to remember that a widely accepted proof might be wrong.
6
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1answer
114 views

Permutations that preserve all algebraic relations between the roots of a polynomial

When trying to answer the question of whether a given equation can be solved with radicals, historically people have paid lots of attention to permutations that preserve all algebraic relations ...
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1answer
79 views

Why are regular $p$-groups called “regular?”

In the concept of regular $p$-Groups, what does "regularity" stand for? What is "regular" in such groups? I would like to know idea behind defining these groups, and naming these groups "regular." ...
12
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2answers
597 views

What is the mathematical intuition behind àl-jàbrà?

The term algebra comes from the arabic term àl-jàbrà that means "to force", "to restore". Over centuries mathematicians, in east and west, celebrate by this term mathematical disciplines. What is ...
4
votes
3answers
373 views

On the origins of the (Weierstrass) Tangent half-angle substitution

The Weierstrass substitution is great for transforming complex trig integrals into simpler rational functions. Wikipedia suggests that it wasn't invented by Weierstrass, since Euler was already ...
5
votes
6answers
537 views

Why don't we use base 6 or 11?

Another question on this site asks why we have chosen our number system to be decimal base 10. There are others asking basically the same thing as well. I'm not really satisfied with any of the ...
9
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2answers
417 views

Where, specifically, did Principia Mathematica fail?

I'm very fascinated by the book Principia Mathematica. From what I've learned so far, Principia Mathematica set out to be, essentially, the bible of mathematics and logic, from which all mathematical ...
5
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2answers
177 views

On the original Riemann-Roch theorem

I think Riemann first stated and proved a part of the Rieman-Roch theorem on a compact Riemann surface. And later Roch supplemented it. I wonder what the original statements of the R-R theorem by ...
1
vote
1answer
63 views

who found that translation in N space is the same as shearing in N+1 space?

According to the wikipedia, Although a translation is a non-linear transformation in a 2-D or 3-D Euclidean space described by Cartesian coordinates, it becomes, in a 3-D or 4-D projective ...
27
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4answers
6k views

Are We Teaching Pre-Calc Wrong?

It took some 1,250 years to move from the integral of a quadratic to that of a fourth degree polynomial. When we jump too fast to the magical algorithm, when we fail to acknowledge the effort that ...
28
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7answers
884 views

Why are topological spaces interesting to study?

In introductory real analysis, I dealt only with $\mathbb{R}^n$. Then I saw that limits can be defined in more abstract spaces than $\mathbb{R}^n$, namely the metric spaces. This abstraction seemed ...
7
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1answer
935 views

How were Hyperbolic functions derived/discovered?

Trig functions are simple ratios, but what does Cosh, Sinh and Tanh compute? How are they related to euler's number anyway?
6
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1answer
191 views

Where did Descartes write, “With me everything turns into mathematics.”

I have been trying to source a famous quote of Descartes, "Omnia apud me mathematica fiunt." or "With me everything turns into mathematics." I cannot find a source for this. The English e-books I ...
3
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5answers
523 views

Have people tried to find the area under a curve by means other than integration?

It seems pretty frustrating that some definite integrals can only be evaluated numerically, so have people tried to find another method of finding the area under a curve that isn't numerical? I'm ...
7
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0answers
120 views

Origin of $\mapsto$ notation

Who invented the brilliant $\mapsto$ notation for describing a function's action on a point, as in $x \mapsto x^2$? This is in some sense a counterpart to Who came up with the arrow notation $x ...
5
votes
1answer
138 views

Did Brook Taylor develop his formula also in many variables by himself?

I was wondering whether Brook Taylor was also familiar with analysis in many variables at that time. I found no information about it online. Greetings Eu2718
12
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3answers
207 views

Why “integralis” over “summatorius”?

It is written that Johann Bernoulli suggested to Leibniz that he (Leibniz) change the name of his calculus from "calculus summatorius" to "calculus integralis", but I cannot find their correspondence ...
3
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1answer
93 views

History Question on Continued Fractions

I worked out the periodicity of some infinite continued fractions last night by hand. (Don't ask me why)For example, $\sqrt{13}= [3,1,1,1,1,6,1,1,1,1,6,\ldots]$. Last night I worked out the first ...
5
votes
2answers
341 views

The origin/use of “derivative” and “differentiate”

Apologies if there is a duplicate somewhere; I couldn't find one. The use of the root "deriv" in the context of differentiation seems odd: we have differentiation, differentials, differentiable, ...
4
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2answers
457 views

History of Functions

I am interested in the history of functions. Why did Euler introduce them? When and why did they become central to mathematics? I know the second question has something to do with the famous ...
7
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1answer
157 views

On the pronunciation of the second derivative

I have been looking at Lancelot Hogben's Mathematics for the Million (first published in 1936). In the chapter on calculus he says that the second derivative $\displaystyle \frac{d^2y}{dx^2}$ is ...
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0answers
145 views

Historical Question about Schur-Zassenhaus Theorem

I couldn't find any historical information about Schur-Zassenhaus theorem in many books or even papers which mention this theorem. I think, Schur proved that if $G$ is a finite group and if $N$ is ...
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4answers
1k views

Is mathematical history written by the victors?

The question is the title of a recent piece in the Notices of the American Mathematical Society, by twelve authors (of which I am one). The contention is that traditional history of mathematics is ...
2
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1answer
112 views

What is the equality of ratios?

Equality among ratios. what is it called? is Proportion the answer?