Questions tagged [math-history]

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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Did Leibniz use the Feynman trick to solve difficult integrals?

Okay, I know that the technique Feynman popularized is an application of the Leibniz rule, and Leibniz preceded Feynman by many years. But did Leibniz actually solve integrals that way?
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Is the term "category" in Category theory entirely different from the category in topological spaces?

$(X, \tau) $ be a topological space. $A\subset X$ is said to be first category (meager) if it can be expressed as a countable union of nowhere dense sets. Otherwise we call the set $A$ second ...
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Showing Euclid's Proposition 30 ("Lines parallel to the same line are parallel to each other") is equivalent to the 5th Postulate.

I am trying to show that the 30th Euclid's proposition, "Straight lines parallel to the same straight line are also parallel to one another." is equivalent to the 5th Postulate: "If ...
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What real analysis wants to convey and how it developed? [closed]

Most of us have studied real analysis as undergrad. But i cannot understand the main convincing point to study real analysis and how to summerise it. I know this question is little tricky and everyone ...
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What is the specific term for an Isosceles triangle where the legs are longer/shorter than the base?

I'm shocked that I couldn't find an answer to this anywhere, but I have a situation where I have to categorize isosceles triangles by whether their legs are (individually) longer or shorter than their ...
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3 votes
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Learning Math from Old Hard Books

Does any one have a syllabus for how math was taught in UK in the 1800s? For example, a curriculum from the time that made use of the following book (as an example), Toddhunters Treatise on ...
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Why people usually use the term "perfectly normal Hausdorff space" instead of "perfectly normal Fréchet (T1) space"?

If a normal T2 space is a normal T1 space and a perfectly normal T2 space is a perfectly normal T1 space, then I would assume people will be more likely to use the latter term because T1 is weaker ...
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Is there a somewhat official or usually accepted classification of math subjects?

We have algebra, topology, calculus... but we all know that these are very vague and very general way to classify math. I came up with this question when I first saw ArXiV`s paper's categories and ...
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How algebraic expressions were simplified before the ‘Order of Operations’ was established?

I have two questions concerning the order of operations. The first relates to the history of mathematics, and the second relates to a computational example that I would be interested in solving ...
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Developments of Riemannian geometry in recent decades.

I have very little knowledge about Ricci flow and Riemannian Geometry. I can't understand the evolution from the traditional Riemannian geometry to Ricci flow (or geometrical analysis ). Obviously, ...
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Modern axiomatically rigorous version of Euclid's Elements

I have been wanting to read Euclid's Elements (Oliver Byrne's version) for a few months, but I have recently learned that a number of the proofs in Euclids Elements are not very rigorous, and that the ...
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Historical Mistake of Assuming Measurability

I am recently reading about Fourier transforms and convolutions. It was a surprise to me that it takes quite several paragraphs to prove the measurability of innocent looking $f(x-y)$ (reference: ...
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"summand" is to "sum" $\left(\sum\right)$ as ___ is to "product" $\left(\prod\right)$

(Not a duplicate of If "multiples" is to "product", "_____" is to "sum") When working with sums or series, I often refer to $a_n$ in the summation $\sum\...
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Where did Lagrange prove that if $p\equiv 3\bmod{4}$ and $q=2p+1$ are primes, then $q$ divides $2^p-1$?

It is said that Lagrange proved in 1775 that if $p\equiv 3\bmod{4}$ and $q=2p+1$ are primes, then $q$ divides $2^p-1$ but I have not been able to find the source, where he did this. Can you help me? ...
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Cosine of the sum of two angles from the half angle formulas

My goal is not necessarily to give the simplest derivation possible. I've been trying to rescue the half angle formulas from oblivion and give them the status they deserve by showing its many ...
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3 votes
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Why vector bundles are defined differently in algebraic geometry and topology?

Over schemes, we can define locally free sheaves; vector bundles associated to a quasi-coherent sheaf (Stacks Project). These notions seem to be dual to each other. It is easy to see on $\mathrm{...
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What is meant, exactly, by nonrepeating when talking about irrational numbers?

My question is referring to the exact definition mathematicians use when describing the decimal expansions of irrational numbers as "nonterminating and nonrepeating." Now, I understand, at ...
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1 answer
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What are arithmetical logarithms?

According to the YouTube video "Evariste Galois a documentary" by MsrEvaristeGalois, when the young Evariste Galois was taking his entrance exam for the Ecole Polytechnique, his examinateurs ...
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Geometric interpretation of complex numbers and relation with cartesian plane

I was reading about how for the imaginary numbers now called complex numbers Gauss found a geometrical interpretation and were "legalized" in math. So basically $i$ is a rotation through $90^...
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Why is multiplicative disjunction called "par" in linear logic?

In linear logic multiplicative disjunction is often called par. This terminology goes back at least to Girard's seminal text Linear logic. I vaguely remember that I read that "par" is an ...
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reference request about Genaille-Lucas rulers (or rods)

I'm unable to find any reference to algorithms to perform divison in the case when the divisor has more than one digits with Genaille rods (see e.g.https://en.wikipedia.org/wiki/Genaille%E2%80%...
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Probability of outcomes in numerology (history)

I was reading some books about the history of mathematics and there is always a chapter on Pythagoreans and their mysticism. One thing I did not know was that there was and still a process called ...
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What is the best book on Biography of George Boole?

I'm searching for a good book which describes the life of George Boole… His family life, career, ideas etc… Which one could you recommend ? Thank you
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Intuitions behind Frobenius' generalization of characters to nonabelian finite group given the historical context

I'm reading about the history of character theory of finite group, especially about the invention of character theory by Frobenius. According to most of the related papers (e.g. Pioneers of ...
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Why does compound interest exist?

Background My understanding is that compound interest arises in the following way: The bank offers its clients some interest rate $r$ on an account with principal $P$ that yields $rP$ after some time $...
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1 vote
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Why is the notation $\text{Hom}_C(A,B)$ used to denote morphisms? [duplicate]

In category theory, the set of morphisms between two objects A and B of a category C is denoted $\text{Hom}_C(A,B)$. Historically or practically, why is this notation used? Of course, Hom likely ...
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How "Fundamental" is the "Fundamental Theorem of Linear Programming"?

I was reading about the "Fundamental Theorem of Linear Programming" Wikipedia - this theorem states that the maximum or the minimum of a linear program occurs at the corner regions. I tried ...
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2 votes
2 answers
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Understanding the "long division" notation used in Heath's commentary on Euclid Book 7 Proposition 2

Heath's commentary on proposition 2 of book 7 of the Elements uses some notation I'm not familiar with, as shown in the image below. I wonder if someone could show the "long division" in a ...
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26 votes
1 answer
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Theorem which inspired Dennis Sullivan to switch to maths

The recent Abel prize winner Dennis Sullivan switched from Chemical Engineering to majoring in Maths after hearing a talk about an illuminating particular theorem. From here: The epiphany for me was ...
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12 votes
1 answer
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Is there a historical connection between $\sigma$-algebra and topology?

Through learn about probability theory and topology, I feel that definition of $\sigma$-field(algebra) and topology are similar. From this, I also know about they are not same each other. Furthermore, ...
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Motivation for definition of linearity

I recently started studying linear algebra, and I learnt that the definition of linear function is different than that of elementary algebra. T is linear if: T(a + b) = T(a) + T(b) T(cv) = c T(v) is ...
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1 vote
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Looking for math history books that I'm not sure exist

I've browsed many math history books, but I've never read too deep into any single one. I always find myself reading the about the same facts and same people over and over -- the set of topics doesn't ...
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Historic origin of symbol $\mapsto$ to define a function [duplicate]

Everything is in the title. We were wondering this evening with my girlfriend about the origin of the symbol $\mapsto$ (distinct from symbol $\to$) to define a function, and how students didn't know ...
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What is the grouding for Commensurability?

I understand that before Hippasus of Metapontum proved that the square root of 2 is an irrational number, it was commonly assumed that, given two line segments, it would be possible to find a third ...
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Physical theories and Mathematics

I study pure mathematics. In pure mathematics, we begin from some axioms and obtain theorems. I am also interested in studying physics. I have two questions about the relationship between physical ...
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1 vote
1 answer
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Determinant identity for symmetric 4x4 matrix with zero diagonal

Does anybody know a reference or attribution for this identity? $$ \det \begin{pmatrix} 0 & {a_{12}}^2 & {a_{13}}^2 & {a_{14}}^2 \\ {a_{12}}^2 & 0 & {a_{...
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diagram of squares; name

In mathematical recreation quizzes, there are some diagrams of squares this kind of division continues again and again. Is there any name for this square?
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4 votes
1 answer
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How to approach the problem of summation of Eisenstein series on shifted lattices?

This question is an attempt to complete the issues discussed in a previous question of mine (How did Gauss sum Eisenstein series?), since my updated question did not recieve any attention. In my ...
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Origin of Büchi arithmetic

What is the origin of Büchi arithmetic? Wikipedia only says it is named in his honour. "A Survival Guide to Presburger arithmetic" mentions in section 6.1 what was the motivation for the ...
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History of the Poincaré-Bendixson theorem

Years ago I heard my teacher say that the motivation that Poincaré had to arrive at the famous Poincaré-Bendixson theorem was that a King would give a prize to whoever solves the problem of the ...
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Why people invent discrete mathematics like propositional logic, logical equivalences, predicate logic, etc?

I'm now learning discrete mathematics. I wonder why they invent discrete mathematics. For example, a english sentence "some lion drink coffee" can be translated into statement using ...
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Vector product: What came first? The method, or the need for the result?

I'm reviewing vector products, and I was always just taught here's how we calculate the vector product, and here's a list of properties that it satisfies (orthogonal to the plane spanned by the ...
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How to get roots with galley division?

After spending considerable amount of time to find an intuitive explanation, I've decided to come here and ask a question. Aside of long division, there exist other methods of division. One of such ...
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3 votes
2 answers
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Is conditional probability axiomatic? [closed]

Is the conditional probability $P(A|B) = P(A \cap B)/P(B), P(B) \ne 0$ an axiom in the Kolmogorov scheme or is it derived from the other axioms?
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Help me to find good references about this equation. [closed]

What are some recommended references disucssing Gauss's Hypergeometric Equation? Specifically, I would like references discussing: the origin of the equation, how to obtain it, the solution by the ...
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2 votes
1 answer
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Why was O. Gabber not an author of the 1983's Faisceaux Pervers?

Essentially the title. I noticed that in the 2018 re-printed version of Faisceaux Pervers, O. Gabber is an author (making the work BBDG) as opposed to the classic Faisceaux Pervers (BBD) of 1983 in ...
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Book reference about abacuses (abaci)

I'm searching one or more books about abaci. On one side I'm interested in the history of the abacus while on the other side I'm searching for books explaining algorithms used to perform the four ...
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2 votes
2 answers
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Book references about continued fractions

I'm searching for one or more books about continued fractions which covers these aspects: An introductory level book about continued fractions. A divulgative book about continued fractions with some ...
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Is there a name for non-reflexive "equivalence" relation?

An equivalence relation $a \sim b$ is a binary relation which is symmetric, transitive, and reflexive. What if I give up on reflexiveness? I mean, in the set where the binary operation $\sim$ is ...
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Some Greeks' enumerative problem

Greeks already formulated many "counting problems", which have been reinterpreted in modern Enumerative Geometry. A classical example is Apollonius' problem (counting how many circles are ...
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