Use this tag for questions concerning history of mathematics, historical primacies of results, and evolution of terminology, symbols, and notations. Consider if History of Science and Mathematics Stack Exchange is a better place to ask your question.

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Why do we have 360 degrees in a circle and why we need radians? [duplicate]

I have two related questions: 1- Why do we have 360 degrees in a circle? 2- I have seen in most of the mathematical concepts, angle is expressed in radians not in degrees. Why was radian ...
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Is the Dirac measure named after P.A.M. Dirac?

Does anyone know if the notion of a Dirac measure was named after P.A.M. Dirac? If yes, did he actually introduce it, or is it because integration w.r.t. a Dirac measure does what the so-called Dirac ...
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544 views

Sperner's theorem on antichains - where does it come from?

Sperner proved in 1927 (the paper was published in 1928) his theorem stating that the maximal size of an antichain of subsets of $[n]$ is $\binom{n}{n/2}$. In the introduction to his paper, he ...
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Mendelson's $\mathit{Mathematical\ Logic}$ and the missing Appendix on the consistency of PA

In the first edition of Elliott Mendelson's classic Introduction to Mathematical Logic (1964) there is an appendix, giving a version of Schütte's (1951) variation on Gentzen's proof of the consistency ...
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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 ...
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Is there any branch of Mathematics which has no applications in any other field or in real world?

Is there any branch of Mathematics which has no applications in any other field or in real world ? for instance , maybe : number theory ? mathematical logic ? is there something like this ?
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Symbol for function composition [duplicate]

Possible Duplicate: History of $f \circ g$ Choice of symbols can be an indicator of intellectual allegiance. Consider how, back in the day (and before LaTeX regularised things so much!), the ...
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5answers
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How did Newton invent calculus before the construction of the real numbers?

As far as I know, the reals were not rigorously constructed during his time (i.e via equivalence classes of Cauchy sequences, or Dedekind cuts), so how did Newton even define differentiation or ...
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1answer
85 views

What type of famous equation except diophantine equation such that no algorithm can exist to determine whether there is a solution?

What type of famous equation except diophantine equation such that no algorithm can exist to determine whether there is a solution? I know that if these equation have a solution, then it could be ...
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134 views

Using other fields of math to simplify a proof.

One of the first non-trivial results given in most courses on algebraic topology is the proof of the Fundamental Theorem of Algebra using topological methods. This is on page 11 of J.P. May's A ...
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1answer
353 views

Serge Lang and categories

I was told that (Serge) Lang has never fallen in love with categories, to use a polite euphemism. Other people claim that, in some occasion, he has even declared his lack of interest in the subject in ...
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1answer
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Origin of the Breadth-First Search algorithm

I'd like to know about the history of the breadth-first search algorithm. Can anyone point me to its inventor? It appears that the depth-first search algorithm is attributed to a man named Charles ...
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294 views

Books on the history of foundations of mathematics?

Can you point me to some books on the history of the foundations of mathematics? At the moment I'm searching for something light because of my lack of mathematical maturity and also the fact that I'm ...
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3answers
609 views

Homogeneous Differential Equations Inspiration

Homogeneous first order differential equations can be solved by substituting $y/x = v$. I was wondering what is the inspiration for this. I am trying to understand the thinking behind this ...
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33answers
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Can you provide me historical examples of pure mathematics becoming “useful”?

I'm trying to think/know about something but I don't know if my basis premise is plausible, here we go. Sometimes when I'm talking with people about pure mathematics, they usually dismiss it because ...
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Results that came out of nowhere.

Most big results in mathematics are built on years and years of groundwork by the author and other mathematicians, such as Wiles' proof of FLT or the classification of finite simple groups. ...
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2answers
239 views

Who conjectured that there are only finitely many biplanes, and why?

This question on MathOverflow motivates me to ask what the reasoning is behind the conjecture that there are only finitely many biplanes. More generally, it has been conjectured that for fixed $\...
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2answers
608 views

Is the Galois group associated to a random polynomial solvable with probability 0?

Choose a random polynomial $P\in\mathbb{Z}[x]$ of degree $n$ and coefficients $\leq n$ and $\geq-n$. Let $r_1,\ldots,r_n$ be the roots of $P$ and consider $$G=\operatorname{Gal}(\mathbb{Q}(r_1,\...
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Why, historically, do we multiply matrices as we do?

Multiplication of matrices — taking the dot product of the $i$th row of the first matrix and the $j$th column of the second to yield the $ij$th entry of the product — is not a very ...
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Which notable mathematicans have tried solving the Riemann hypothesis?

I have read that the Riemann hypothesis is the most important open question in mathematics and has been open since 1859. I am wondering which famous mathematicians have actually tried to solve it and ...
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Does there exist a copy of Euclid's Elements with modern notation and no figures?

I am working through Euclid's Elements for fun, but I find the propositions difficult to understand without referencing the provided figures. Unfortunately, the figures usually give away the proofs, ...
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1answer
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Liouville's proof of the existence of transcendental numbers

The existence of transcendental numbers can be shown easily by considering the cardinality of the set of solutions to polynomials with integer cofficents and the cardinality of the real numbers. It ...
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170 views

Is there a way to determine how many solution does “ The hundred Fowls problems” have looking at the coefficients?

I was looking at the different versions of the hundred fowls problems. I came across the problem posed by Chinese mathematicians posed in 5th century,and then Indians in 9th, 10th centuries. Alcuin of ...
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4answers
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Why $\sqrt{\frac {\sum(x-\mu)^2} {N}}$ instead of $\frac {\sum{\Bigl|x-\mu\Bigr|}} {N}$? [duplicate]

Possible Duplicate: Motivation behind standard deviation? In statistics very often you see something of the sort: $$ \textrm{quantity}=\sqrt{\frac {\sum(x-\mu)^2} {N}} $$ to measure things ...
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2answers
170 views

Plato's Disc of Gold

In the book Mathematical Cranks, Underwood Dudley describes the following problem on page 36: Dear Archimedes, Your problem is solved but:-- About twenty years ago he lived on Crete and was ...
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1answer
330 views

Square root principle value convention

Why is the principal square root of a complex number defined as $\sqrt z = \sqrt r e^{-i \varphi / 2}$ for $\varphi \in (-\pi, \pi]$ ? Wouldn't it be more natural to let $\varphi \in [0, 2\pi)$ as it ...
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1answer
199 views

Who is responsible for the analytical/topological proof of FTA?

The fundamental theorem of algebra asserts: Theorem Let $P$ be a polynomial of degree $\geq 1$ in $\Bbb C$. Then there exists a $z_1\in\Bbb C$ such that $P(z_1)=0$. The proof sketch goes as ...
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2answers
300 views

What was Klein working on when he “replaces his Riemann surface by a metallic surface”?

I am reading The Value of Science by Poincare, and the following paragraph from Chapter I seems rather interesting: Look at Professor Klein: he is studying one of the most abstract questions of ...
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Paul Erdos's Two-Line Functional Analysis Proof

Legends hold that once upon a time, some mathematicians were rather pleased about a 30-ish page result in functional analysis. Paul Erdos, upon learning of the problem, spent ten or so minutes ...
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2answers
681 views

Who proved the Master Theorem?

In all of the classes I've had on algorithms, and the books I've seen that talk about the master theorem, none of them mention where it came from, which is pretty odd. Certainly, it didn't just kind ...
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0answers
91 views

History of imperative in hypotheses

In mathematical hypotheses it is traditional to use the imperative instead of a declarative sentence. What is the origin of this tradition? Does it go back to ancient Greek mathematics? Or maybe ...
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2answers
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How many classification of mathematical topics exists?

I found only one Mathematics Subject Classification, are there more?
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How do mathematicians think about the existence of numbers?

Question: How do mathematicians think about the existence of numbers? And how did Newton, Euler, and other famous mathematicians thought about this concept? I know that existence of numbers is a big ...
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A quote from Arnold

Arnold said the following in a talk on teaching: Jacobi noted, as mathematics' most fascinating property, that in it one and the same function controls both the presentations of a whole number as ...
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2answers
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How did people calculate numerical values of transcendental and trigonometric functions?

I know that back in the Stone Age, people used tables on this thing called paper to look up values for functions like $\sin$ and $\ln$. But how did the guys who wrote the tables calculate those values?...
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3answers
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Where did these symbols come from?

Where did these symbols come from? Like Pi, Fee and this weird E/sideways M and the triangle.
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1answer
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Why are vector spaces sometimes called linear spaces?

I have never come across the term 'linear space' as a synonym for 'vector space' and it seems from the book I am using (Linear Algebra by Kostrikin and Manin) that the term linear space is more ...
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Who first called the Grothendieck's schéma scheme?

Grothendieck called "schemes" schémas in French. I find it strange we call them schemes. In fact, Grothendieck called them (pre-) schemas(this is an English word) in his talk(in English) at Proceeding ...
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1answer
99 views

Examples of concepts, definitions or areas of study that were later abandoned

I've been recently thinking about what I've learned in mathematics, and I realised that in contrast to physics (or the other sciences), I tend to take the concepts and definitions for granted in that ...
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2answers
189 views

Semantic parsing of a sentence from “The mathematical analysis of logic” By Goerge Boole, 1847

Having the pleasure of reading some original text, I was wondering if someone can translate two small statements on the second half of page 11 from http://archive.org/stream/mathematicalanal00booluoft#...
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1answer
186 views

Who first explicitly noted that second-order logic is unaxiomatizable?

As every student now knows, second-order logical consequence is unaxiomatizable. (At least when we read the second-order quantifiers in the natural way, as running over all possible properties on the ...
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7answers
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Films about math: a question about math education and motivation for learning math [closed]

I'm interested in movies about or related with mathematics or physics, I mean not documentaries which I also consider movies, but artistic or mainstream films about math. Now I have the following in ...
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1answer
596 views

When was the term “mathematics” first used?

By the second century, in the Almagest, Ptolemy provides a modern conception of "mathematics" as a "science": 'Mathematics' ... is an attribute of all existing things, without exception, both ...
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1answer
216 views

Earliest proof of completeness for axiomatization of Boolean Algebra

Suppose we define Boolean algebra as the system of algebraic rules (logical equivalences) obeyed by AND, OR, NOT with AND, OR, NOT defined by the usual truth tables. We also have variables, which can ...
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1answer
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Why do some people state that 'Zero is not a number'?

Every now and then I read about people who wonder whether zero is a number. It never occurred to me to question this, so I checked the Wikipedia page which, when talking about the Rules of Brahmagupta ...
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1answer
484 views

Early proofs of Leibniz's formula

Wikipedia attributes Leibniz's formula to Madhava of Sangamagrama, James Gregory and Gottfried Leibniz. But what were their proofs?
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Good examples for mathemathical problems/statements that are easely solvable/provable in one theory and hard to solve/prove in another

Let $P$ be a mathematical statement or a mathematical problem. I am looking for a couple of nice examples for $P$ that satisfy the following criteria: Given two (or more) mathematical points of view ...
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1answer
356 views

Early history of lower bounds on the prime counting function

Let $\pi (x)$ be the number of prime numbers less than or equal to $x$. Euclid's proof of the infinitude of primes gives a horrible lower bound of the type $ \pi (x)>> \sqrt{\log{x}} $. ...
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277 views

Who first discovered that the torus supports a flat structure?

Who first recognized that there exists a homogenous metric on the closed genus 1 orientable surface?
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1answer
172 views

Original Proof of Riesz-Thorin

Wikipedia says that Riesz proved the Riesz-Thorin theorem in 1926 without using any complex methods. Does anyone know where the original proof can be found? http://en.wikipedia.org/wiki/Riesz%E2%80%...