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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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structure-preserving: a history?

I am familiar with the occurrence of structure-preserving morphisms in Category Theory, but I would love to know more about the history of the concept, where it started and so on? I suspect it might ...
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1answer
28 views

Is the term *monotone* used fairly consistently to mean non-decreasing or non-increasing but not strictly?

In BBFSK, (~1960, Germany) at least in the section I am currently reading, the authors use the term monotone increasing (decreasing) to mean what I often see called strictly increasing (decreasing). ...
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0answers
58 views

How was logarithm discovered? [migrated]

How was the concept of $\ln(x)$ found before the man knows that it is the area under hyperbola or it is related to the power of $e$ (base of logarithm). How did Napier compute the value of $e$ or $\ln(...
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2answers
87 views

Bourbaki: Universal Quantification Interpretation

I'm trying to understand Bourbaki's definition of universal quantification. The definition is on Page 36 in Theory of Sets as follows: $(\exists x R) \equiv (\tau_{x} \mid x) R$ $(\forall x R) \...
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0answers
23 views

Cylindrical coordinates: history [closed]

Cylindrical coordinates $x=r \cos \theta$, $y=r\sin\theta$, $z=w$ seem to be a simple generalization of polar coordinates. When did they appear first? Also, who came up with the name?
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0answers
31 views

The origin of the term “Frobenius norm”

How did the name Frobenius get attached to "Frobenius norm" of a matrix? I could not find any work of his that uses the norm.
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2answers
45 views

A given perimeter length that is circular encloses the maximum area - which are the (analytic) proofs? [duplicate]

I'm guessing Newton, because of his integrals. But what proofs have been established, and which is the most mathematically intuitive one? I was looking for the tag "circumference", supplied the newer ...
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1answer
250 views

Origins of 'We' Pronoun in Mathematics

In proofs/books/papers on mathematics the pronoun "we" is usually used. For example: In order to derive the quadratic formula we first complete the square. Or: ... we can deduce this ...
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48 views

How did Newton discover the binomial theorem? [closed]

How did Newton discover the binomial theorem? I searched this on many sites but I did not got any answer. Can you please help me out?
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1answer
36 views

Minimal Transitive Closure

Any binary relation over any set (finite or infinite) must has a transitive closure. Moreover, every binary relation must has a minimal transitive closure. Who proved this well-known result in ...
4
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2answers
43 views

How did they make slide rules?

If I'm understanding this correctly, before programmable computers were invented, the only way to do complex calculations was to use a slide rule. But hold on — to construct a slide rule, you need to ...
4
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1answer
66 views

Is this elementary, nilpotent-free approach to automatic differentiation strong enough for real analysis? How similar is it to Newton's system?

This is a sequel to this question: Is the theory of dual numbers strong enough to develop real analysis, and does it resemble Newton's historical method for doing calculus? The ring of "dual ...
4
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1answer
158 views

Ars longa, vita brevis.

There's little use studying mathematics without actually doing mathematics. There is a plethora of exercises in any textbook worth its salt. I suppose those with some business in looking up something ...
44
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2answers
5k views

Why are the trig functions versine, haversine, exsecant, etc, rarely used in modern mathematics?

I was browsing through a Wikipedia article about the trigonometric identities, when I came across something that caught my attention, namely forgotten trigonometric functions. The versine (arguably ...
2
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0answers
47 views

Origin of the name of 'Handshaking Lemma'

The earliest use of the term 'Handshaking Lemma' that I can find on Google Books is from page 24 of Match - Volumes 6-8 published by Institut für Strahlenchemie im Max-Planck-Institut für ...
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3answers
73 views

Famous fractions: Can any “special” numbers be approximated by simple ratios like $3.14\ldots$ as $22/7$?

The ratio $22/7$ dates back to antiquity as an approximation of $3.14\ldots$. I'm wondering whether there are any other "famous" numbers with a similar situation. That is, something like $e$ or $\phi$ ...
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0answers
43 views

Chinese character as mathematical symbol

Titchmarsh mentioned on p.25 of Mathematics for the General Reader (1959) that There are some kinds of algebra which are so complicated that they use up the whole alphabet, both capital and small ...
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3answers
48 views

Is there an intentional correlation between Latin letter esh and various summation syntax?

So when browsing Unicode characters, I stumbled upon one mysterious case, esh. The upper case Ʃ looks very similar to sigma Σ which is used for summation notation ∑. The lower case ʃ is also ...
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0answers
189 views

Who was the first to use $\bigwedge$ and $\bigvee$ as universal and existential quantifiers?

It's not surprised that somebody uses $\bigwedge$ and $\bigvee$ as universal and existential quantifiers since $$ \bigwedge_{x\in A}\,\varphi(x)\Leftrightarrow \varphi(a_0)\wedge\varphi(a_1)\wedge\...
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0answers
72 views

Why is the derivative called derivative? [duplicate]

What is the historical reason for this term? Derivative represents slope function of curve. I am not getting why this term make sense?
3
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0answers
51 views

How did Steiner prove his famous formula?

In convex integral geometry and geometric measure theory, Steiner's formula is the name of the following elegant result: Let $B_n$ be the unit ball in $\mathbf R^n$. If $S$ is a nonempty bounded ...
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3answers
3k views

Was there ever an axiom rendered a theorem?

In the history of mathematics, are there notable examples of theorems which have been first considered axioms? Alternatively, was there any statement first considered an axiom that later has been ...
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2answers
3k views

Why, historically, did Gödel think CH was false?

Gödel was the first to show that ~CH was not provable from ZFC. However, he also thought CH was false in his view of the "Platonic" reality of set theory. It seems this view was also somewhat common ...
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2answers
414 views

A geometry theory without irrational numbers?

Is there any theory or theorem of geometry -- whether used in practice or not -- which denies or forbids the use of irrational numbers? If not, were there any notable attempts at it? Disclaimer: I ...
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2answers
30 views

Common meaning of conjugation

If you look for conjugation in wikipedia, you find around 15 different mathematical meanings for this concept. Is there something in common to all those meanings?
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0answers
45 views

Were there any results that were true in old axioms, but are false in modern axioms, and are not obvious paradoxes?

Recently I learned that it can't be proved that mathematical axioms are consistent. And furthermore, in 1900s math was based on an inconsistent system of axioms. So, are there any results, that were ...
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2answers
112 views

Some questions about different axiomatic systems for neighbourhoods

I was thinking a few days ago about the development of topology, especially how you arrive at the concept of a topology $\tau$. I knew that a lot of initial ideas came from Hausdorff who defined a ...
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1answer
93 views

"What is the specific mathematical reason behind the origin of the Collatz Conjecture that makes it difficult to solve it? [closed]

Is there a known so specific mathematical reason that makes it difficult to solve the Collatz Conjecture? Clearer: What is the specific mathematical reason behind the origin of the Collatz ...
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2answers
102 views

Why do we apply functions the “wrong way around”, i.e. why do we write $f(x)$ instead of $(x)f$?

In English, we read and write from left to right, but for some reason we apply functions in the opposite order. Consider the following procedure: Take an element $x$, apply a function $f$ to it and ...
2
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1answer
44 views

First Classification of Finite Subgroups of $SO(3)$

One can find a classification of all isomorphism types of finite subgroups of $SO(3)$ on, say, GroupProps: https://groupprops.subwiki.org/wiki/Classification_of_finite_subgroups_of_SO(3,R). However, I ...
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0answers
9 views

where do sensitivity, specificity, recall and precision terms come from?

Binomial classification accuracy metrics is filled with lot of definitions as sensitivity, specificity, recall, precision. Sometimes I have felt confused with the terms and I would appreciate if ...
4
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2answers
125 views

First papers of famous mathematicians

Is there any specific resource that would allow me to find the first papers/articles published by famous mathematicians? For example, I would like to read what the first paper published by Von Neumann,...
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2answers
767 views

Is infinite sequence of irrational numbers digits mathematically observable?

I have a little question. In fact, is too short. Is infinite sequence of irrational numbers digits mathematically observable? I would like to explain it by example because the question seems ...
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1answer
48 views

History of various definitions of topology

This question is not actually a serious mathematical one. I have been reading Point Set Topology for a while, and turns out that there are various possible ways to define a topology. Most popular one ...
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0answers
28 views

Gauss' Proof of Lagrange Four-Square Theorem?

I read recently that Gauss provided a proof of Lagrange's Four-Square Theorem using his ideas about equivalence classes of quadratic forms (i.e. linear substitution of variables) somehow applied to $w^...
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0answers
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Inconsistent axioms

As far as I know, no inconsistency is known to descend from the Zermelo-Fraenkel (ZFC) axioms. Question: historically, has a surprising inconsistency been found to descend from any comparably simple, ...
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1answer
98 views

Kepler's books: Mysterium Cosmographicum, Astronomia Nova, and Harmonices Mundi

I have started doing some research on Kepler and I have come across these three books that he wrote: Mysterium Cosmographicum, Astronomia Nova, and Harmonices Mundi. I was wondering if anyone is ...
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1answer
87 views

If a ray r emanating from an exterior point of triangle ABC intersects side AB at any point between A and B, then r also intersects side AC or side BC [duplicate]

Prove Proposition 3.9: If a ray r emanating from an exterior point of triangle $ABC$ intersects side $AB$ at any point between $A$ and $B$, then $r$ also intersects side $AC$ or side $BC$. Can ...
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0answers
100 views

Two definitions of $\pi$

I have the feeling that ancient mathematicians (like Greek or Chinese), trying to find good approximations of $\pi$ used two definitions: If $A$ is the area of a disk and $r$ is its radius, $\pi=A/r^...
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2answers
40 views

Inventor of Topological groups

I had difficulty in finding the person who introduced the term "topological groups". I just want to know who introduced the term topological groups.
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60 views

Notation $\gamma$ for Euler's constant $\gamma$.

Question. In which book or article George Boole used the notation $\gamma$ for Euler's constant? Background. Today, Euler's constant is usually denoted by $\gamma$. In 1993 it was found out that the ...
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0answers
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Difference between Roberval and Newton about differentiation.

I was reading about the first contributes that will bring the Birth of Calculus with Newton and Leibniz, and in particular the initial problem of finding the tangent of a curve in each point. Roberval ...
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0answers
60 views

Why do we use $\Omega$ to Represent a Subset of $\mathbb{R}^n$

From Wade's "Introduction to Analysis": NOTE: Because French mathematicians (e.g., Borel, Jordan, and Lebesgue) did fundamental work on the connection between analysis and set theory, and ensemble ...
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1answer
28 views

Definition of Slope of Tangent to a Curve Using Limits

I am restudying Calculus on my own, and I am a little bit stuck on the definition of the slope of a tangent line to a point on a curve. I understand the definition somewhat, but I got to wondering ...
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0answers
91 views

Who was the first female mathematics professor? [closed]

Some sources cite that Maria Agnesi was the first female mathematics professor (e.g. https://study.com/academy/lesson/maria-gaetana-agnesi-contributions-to-math-accomplishments.html, where they say ...
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22 views

history of analogy between number field and function fields

it is well known that an analogy exist between number fields and function fields and you can translate ideas and problems about one of them to another. there are many problems in number theory ...
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36 views

Why do we have the present order of operations, and how do hyperoperations fit in?

Something that's been bugging me for a fairly decent while is the order of operations - not so much using it, however, as to understanding where it comes from. Typically we're introduced to it in the ...
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145 views

How did mathematicans prove things before ZFC or Peano

I do not get it. How was a+b=b+a or a (b +c) = ab + ac proved by ancient mathematicians before set theory or Peano axioms? If you cannot logically prove the laws of arithmetic without Peano or set ...
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2answers
929 views

Has a conjecture ever originally been decided by constructing the proof with mathematical logic?

So, one of the things that mathematical logic does is study theorems as abstract objects. There also many theorems about mathematical logic, and these theorems can have connections to other fields. ...
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1answer
38 views

What was the Hamilton's initial problem that led to him inventing quaternion?

I read wiki topic about history of Quaternion, and it confuses me on why, according to Hamilton, there's a problem with multiplication of triple (i.e. 1+i+j), and somehow the quadruple (or Quaternion) ...