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

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Have Information Theoretic results been used in other branches of mathematics?

consider this a soft-question. Information Theory is fairly young branch of mathematics (60 years). I am interested in question, whether there have been any information theoretic results that had ...
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3answers
131 views

Examples of open problems solved through short proof

Are there good examples of reasonable open problems in mathematics that had an 'obvious' solution via application of a theorem already known/not yet found in mathematics but could have been found with ...
2
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1answer
118 views

An endless loop in a program that search for mathematical theorems and proofs − a milestone? [closed]

I don't know if there exist computer programs working on its own, trying to find and prove theorems, delivering proofs and go on searching for new theorems. But if (when) there are such programs, ...
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2answers
103 views

What is the most appropriate book for teaching, not the content but skills of mathematics

Hello Everyone I am a high school student currently doing Extension 1 Mathematics at my school. I am currently looking for a high quality mathematics book. Although I am not looking for a book, like ...
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2answers
131 views

Value of $\pi$ by Aryabhata

Aryabhata gave accurate approximate value of $\pi$. He wrote in Aryabhatiya following: add 4 to 100, multiply by 8 and then add 62,000. The result is approximately the circumference of circle of ...
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0answers
49 views

Lagrangian and Hamiltonian Mechanics

I am interested in how Lagrangian and Hamiltonian mechanics and then symplectic geometry was developed starting from Newtonian mechanics. We can start by assuming that Newtonian mechanics tells us ...
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1answer
54 views

Necessary and sufficient condition for a number to be regular

Background: A number is said to be (sexagesimally) regular if its reciprocal has a finite sexagesimal expansion (that is, a finite expansion when expressed as a radix fraction for base 60). With the ...
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0answers
29 views

Looking for an English translation of Descartes's mathematical works

Good day to everyone! I am looking for an English translation of Descartes' mathematical works (particularly in elementary number theory). Would someone be kind enough as to point me to an ...
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3answers
112 views

geometry developments during the Islamic Golden Age (7-13 century)

Can anybody refer me to publications on geometry during the Islamic Golden Age? My interest is especially on Arab geometry an non-Euclidean geometry. But searching for sources was a saddening ...
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0answers
60 views

Chi-square or chi-squared?

The $\chi^2$ test/distribution is referred to as either "chi-square" (more frequently) or else "chi-squared" (less frequently). What is the history behind the name? Footnote 2 in this paper by Peter ...
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3answers
414 views

What is the oldest math source that we know of?

What is the oldest math source that we know of? Or to put it differently, what is the first math that was ever done?
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0answers
97 views

Did Landau prove that there is a prime on $(x,(1+1/5)x)?$

Was Landau the first to prove that there is a prime on $(x,\frac{6}{5}x )?$ In his Handbuch $^1$ discussing the limit $$\lim_{n\to\infty} (\pi((1+\epsilon)x)-\pi(x))=\infty $$ he seems to say that ...
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0answers
230 views

What is the most cited mathematical paper?

Just out of curiosity: What is the paper with the largest number of citations in all of mathematics? I think it is Shannon's A Mathematical Theory of ...
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1answer
111 views

Euler Vs. Diderot

I'm reading The Music of the Primes by Marcus Du Sautoy and I came across a page with the following excerpt about Leonhard Euler: "The role of the court mathematician is perfectly illustrated by a ...
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0answers
90 views

Who First Considered This Generalization of the Fibonacci Numbers?

I am looking for the author who originally researched a generalization of the Fibonacci numbers, which Koshy, in Chapter 7 his book Fibonacci and Lucas Numbers with Application refers to as the ...
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2answers
145 views

Understanding the concepts of division and fractions

$\require{cancel}$ I'm having some issues regarding division so I will start by asking how this concept was developed throughout the ages: What was the first civilization to introduce the idea of ...
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0answers
310 views

To what extent were mathematicians in previous centuries aware of the lack of rigour in their methods?

By modern standards, much of pre-modern mathematics isn't rigorous. Famous examples include Euler's solution to the Basel problem or literally anything involving sets before Cantor and Russel came ...
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1answer
98 views

Algebra on a Louvre tablet

Problem: On a Louvre tablet of about 300 B.C. are four problems concerning rectangles of unit area and given semiperimeter. Let the sides and semiperimeter be $x,y$ and $a$. Then we have ...
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0answers
490 views

2015-related question: why are Lucas-Carmichael numbers named after Lucas?

Summary 2015 is a so called Lucas-Carmichael number. I believe (for reasons that I will explain below) that the 'Carmichael' in the name is a reference to ordinary Carmichael numbers and not to the ...
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1answer
94 views

How was 78557 originally suspected to be a Sierpinski number?

A Sierpinski number is an odd number $k$ such that $k2^n+1$ takes only composite values. In 1962, Selfridge proved that $78557$ is a Sierpinski number. It remains the smallest known such number. How ...
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12answers
3k views

What are some theorems that currently only have computer-assisted proofs?

What are some theorems that currently only have computer-assisted proofs? For example, there's the four colour theorem. I am very curious about this and would like to generate a list.
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2answers
151 views

Infinite series for the arctangent from the tangent of half-angle formula

From Hodge's biography of Turing: He had found the infinite series for the "inverse tangent function", starting from the trigonometrical formula for $\tan\left(\frac{1}{2}x\right)$.* The ...
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4answers
1k views

Why is “mathematical induction” called “mathematical”?

One of my whims is that I never write "mathematical induction" but just "induction". We are doing maths, so what is the point about precising? We don't say "Let $f$ be a mathematical function from the ...
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2answers
194 views

What are some mathematical problems which have been forgotten?

As mathematicians continue to study mathematics, often times they run into a problem which takes a considerable amount of effort to solve. For instance, trying to factor polynomials has lead to a ...
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2answers
56 views

Why does the radius come before the angle?

Based on my understanding, when delineating two variables (for a coordinate system or otherwise) convention is to label the 'independent variable' first, then the 'dependent variable'. So for a ...
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1answer
269 views

Why did Fermat care about characterizing primes on the form $p=x^{2}+ny^{2}$?

Im currently trying to figure out the genesis of quadratic reprocity by using Cox and Lemmermeyers books. I also got a copy of some works of Fermat but it is in German. It seems like there is some ...
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1answer
75 views

who discovered the orthocenter of a triangle?

I tried to answer Is there a name for this result in planar geometry? and wanted to go back to the first mention of the orthocenter (or even the altitude of a triangle, but i did draw a complete ...
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3answers
622 views

How did the Ancient Greeks know that the circle method of finding square roots was mathematically valid? How do we know that?

The Ancients used this method. (or at least James Grime said in a numberphile video) To construct the square root of a number, draw an interval of length $a+1$, and then draw a semi-circle with the ...
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2answers
216 views

Why do we write $a^n$ instead of $^n\!a$ for exponentiation?

For subtraction I can understand why $2-3 = 2+(-3)$ since we read from left to right, but I don't see why this need apply to exponentiation. What benefit is there to writing the base before the ...
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2answers
236 views

Source of Hardy-Littlewood's 2nd Conjecture

In what paper do Hardy and Littlewood first mention, specifically, their 2nd conjecture? It is not mentioned specifically in Partitio Numerorum III. This conjecture is usually expressed as ...
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5answers
250 views

Why do we first introduce the open set definition for continuity instead of the neighborhood definition?

After (nearly) completing my course in topology, something weird just stuck out to me which I hadn't considered before. When first discussing continuity, we often use the following definition: Let ...
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1answer
83 views

Who introduced the term indefinite integral and the notation $\int f(x)dx$?

I find the notation $\int f(x)dx$ for the indefinite integral of $f(x)$ on some interval $I$ is both suggestive and confusing. On the one hand, this notation is very suggestive when we calculate ...
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1answer
63 views

Lagrange's original proof of Remainder Theorem?

Where can I find Lagrange's original proof of the Remainder Theorem?
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2answers
47 views

St.Petersburg Paradox and Bernoulli's quote

I was reading about St.Petersburg paradox, and understood the proof that $\frac{S_n}{n\log n} \overset{P}{\rightarrow}1$. The textbook then quotes Bernoulli: "There ought not to exist any even ...
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1answer
306 views

When was it realized that complex numbers can't lie on a number line?

When I first learned about representation of a complex number by a point in a $2D$ plane, I wondered: what if it's redundant? What if a line is sufficient? Apparently, it's not, but I still wonder: ...
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7answers
5k views

Genius mathematicians who never published anything

Amongst philosophers, Socrates is an example of a genius with a great influence on human history who never wrote anything. Almost all facts which are known about his revolutionary ideas are written by ...
3
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1answer
84 views

What exactly is the 'tension' between arithmetic and geometry?

We all know Pythagorean theorem, $a^2+b^2 = c^2 $ Im reading John Stillwell, Mathematics and its history at the moment, and during the greek antiquity they had some trouble by interpretating ...
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1answer
126 views

When was contemporary logical notation established

When contemporary fundamental logical notation was established? I mean basic symbols as used nowadays $\iff\implies\land\lor\lnot\forall\exists\vdash\models$.
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97 views

History of the term “anodyne” in homotopy theory

There is a notion of an anodyne morphism (usually of simplicial sets). This type of morphisms is used, for instance, to establish basic properties of quasicategories. But the name is quite mysterious. ...
3
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1answer
86 views

Original Papers on Singular Homology/Cohomology.

I am currently reading Singular Homology Theory and Cohomology on my own mainly from Hatcher's "Algebriac Topology" and "Topology and Geometry" by Bredon. Quite often it happens that it takes a lot of ...
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11answers
4k views

Why are integers subset of reals?

In most programming languages, integer and real (or float, rational, whatever) types are usually disjoint; 2 is not the same as 2.0 (although most languages do an automatic conversion when necessary). ...
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1answer
64 views

Who are the two men credited with inventing logarithms?

This is a bonus question on a pre-calculus quiz I've been tasked with grading. Napier is clearly one of the answers. Who should I accept for the second inventor? In particular, should Newton be ...
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0answers
66 views

Development of measure and probability theory

I am interested in a reference (article, maybe a book chapter) on the development of mathematical probability theory - that is, mostly starting from the beginning of the 20th century. It is surprising ...
10
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1answer
272 views

Does anyone know about Ramanujan's method of solving the quartic? [closed]

I have read (probably) in Kanigel's book The Man Who Knew Infinity that S. Ramanujan devised his own method of solving the Quartic Equation after he learnt to solve the Cubic Equation. Does anyone ...
2
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0answers
70 views

What did homogeneous coordinates allow 19th century mathematicians to do?

I read about Mobius developing Barycentric and homogeneous coordinates, and I read about homogeneous coordinates and what they are and I'm totally on board with taking a line from the origin and ...
2
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2answers
170 views

The Big Picture of Commutative Ring

For final assignment on my Abstract Algebra class $-$ which is about Commutative Rings with Unity covering roughly Modules, Field of Fractions of an Integral Domain, Integrality and Fields, Prime ...
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0answers
45 views

Why are there so many different symbols to represent the Heaviside (unit step) function

In signal processing, the unit step function is typically written as $u(t)$. In other references though I have seen it represented as $H(t)$ and even $\theta(t)$. The unit impulse is fairly ...
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52 views

In which years in the prefaces to mathematical books thanks to secretaries for typing text books have disappeared?

In which years in the prefaces to mathematical books thanks to secretaries for typing text books have disappeared? Just interesting. When latex won?
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1answer
276 views

Meaning of the word “conjugate” across mathematics?

Clearly, the word conjugate or conjugation is used for a myriad of different concepts across mathematics and even in science (see the Wikipedia page). Its meaning can range from the fraction used to ...
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0answers
37 views

International Awards for Roger Apery?

Roger Apery stunned the math community when he proved that $\zeta(3)$ is irrational, in a truly elementary fashion. I wonder if he received any international awards specifically for this achievement. ...