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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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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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Was the property of symmetry under permutation of Vieta's formulas known/explicitly stated before the papers of Waring,Lagrange and Vandermonde?

I am more particularly interested if there were some preceding research on the permutations of variables in polynomials before the early 1770s and if "similar functions" were defined by some other ...
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62 views

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
60 views

How was the system of $degrees$ devised? [on hold]

We are all familiar with the equivalence relationship between radians and degrees, $$1^c =\big(\frac{180}{\pi}\big)^o$$ I was wondering what else degrees are equivalent to. What is the basis of ...
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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
67 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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92 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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Divide Interval I=[0,1] into small sub-intervals such that length of sub-pieces is of length 1/2,1/3,1/4,1/5,… ,1/n [closed]

Please, answer this question as soon as possible, how to divide the interval of $I=[0,1]$ into small sub-intervals such that length of sub-pieces is of the lengths 1/2, 1/3, 1/4, 1/5, ... ., 1/n. ...
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2answers
36 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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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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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
22 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
76 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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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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24 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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142 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
907 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
35 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) ...
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1answer
127 views

How did Gauss find the units of the cubic field $Q[n^{1/3}]$?

Recently I read jstor article "Gauss and the Early Development of Algebraic Numbers", which gives a good description of the genesis of Gauss's ideas regarding the foundations of algebraic number ...
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2answers
105 views

Courant (1943) and History of Finite Element Method

I am interested in the history of Finite Element Methods and Methods of Weighted Residuals (MWR), especially reduced quadrature and collocation methods. I have a paper coming out called “Orthogonal ...
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1answer
105 views

Is there criticism in literature of Euclid's fifth common notion (“The whole is greater than the part”)?

In Book I of Euclid's Elements, the fifth common notion says "The whole is greater than the part". For Euclid, magnitudes are objects that can be compared, added, and subtracted, provided they are of ...
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48 views

A person who has not joined IMO, can contribute to mathematics in the future? [duplicate]

The following question is a question that confuses my mind long since. I'm sorry if it looks nonsense. If mathematicians who had made important discoveries in mathematics such as Bernhard Riemann, ...
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1answer
70 views

“Module” versus “Abelian Group” of the Integers, German Language usage circa 1962

In the highly respectable BBFSK Vol I B2 we are told that the integers form a module with respect to addition. Where by module they mean a set together with an operation (+) defined in it satisfying ...
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1answer
121 views

Are problems in “Arithmetica” of Diophantus all solved now?

It's well-known that Diophantus had written ”Diophantus“ which contains many problems about solving arithmetic equations. I wonder whether all of them has been solved using modern techniques, as some ...
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1answer
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Have there been any computer proofs that were found to contain bugs post-publication?

I'm curious if there are any known examples of proofs using a computer which after being published, (in a journal or otherwise) turned out to have bugs in the software which invalidated the proof. I'm ...
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1answer
49 views

Where did the mean estimator come from?

What was the motivation behind the definition of the mean estimator : $$\hat{\mu}=\frac{1}{N}\sum_{i=1}^N X_{i}$$ Did we come up with this very form through trial and error ? I do know that it's ...
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4answers
150 views

Where does $\in$ come from and where is it defined?

Kind of a weird question but where does the $\in$ symbol come from exactly and where do we imbue this symbol with any kind of meaning? As far as I can tell it isn't a symbol that is part of the ...
2
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1answer
61 views

In Mathematics is there a discrete logarithm function?

I find it difficult to understand this part in this book. Because, as far as I know, there is no unique function or formula for discrete logarithms. I cann't understand what this formula does. Is ...
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35 views

Examples showing how George Boole's notation differs to modern notation.

I'm writing a project about George Boole, and was wondering if there was any significant examples showing the change in notation. Any help would be welcome, thank you.
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2answers
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Motivation of the Logarithm

Suppose that someone wants to calculate approximately the product of 101,123,958,959,055 and 342,234,234,234,236 without using a computer. Since these numbers are so long, completely carrying out ...
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1answer
168 views

What fonts or typefaces were commonly used in old (pre-1950) mathematics literature?

I recall reading some books in my university library which were published in the 1920s and 1930s, and am wondering about their fonts. They looked very nice, and I would like to find some. It seems ...
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1answer
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Name for “the kernel lemma”?

Lately I've been fascinated by the result that one might state slightly informally Lemma. (In the context of linear algebra over a field.) If $p$ and $q$ are relatively prime polynomials and $...
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Is there any method known in the Mathematical Statistics that proves that the prime numbers are not randomly distributed?

I am asking for my curiosity. Maybe everyone knows the answer to that question. I do not know. I don't have a maths education. Is there any method known in the Mathematical Statistics that proves ...
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0answers
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What is the timeline of the sets of real, rational, integer, and natural numbers?

Historically, did mathematicians: 1) construct the set of real numbers using rationals, integers, and naturals? Or 2) did they already know the set of reals existed and partitioned it into ...
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5answers
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How do we mathematically define the meaning of the word “undecidable”?

I need to understand the meaning of this mathematical concept: "undecided/undecidable". I know what it means in the English dictionary. But, I don't know what it means mathematically. If You ...
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0answers
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History of the Barzilai-Borwein method

I seem to recall hearing the story that the Barzilai-Borwein method (a first-order optimization method with superlinear convergence) was discovered by accident, involving some indexing error in some ...
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27 views

The Hahn-Kolmogorov Extension Theorem

How did Hahn and Kolmogorov prove the Hahn-Kolmogorov Extension Theorem? Did they contruct the extension in a similar way to what Carathéodory did?
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an evolutive graph of the number

the idea that "wanting to do something new" sometimes led to "the need for a new kind of number" is clearly stated in both Morris Kline's book and in several videos in this playlist, both about ...
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1answer
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What are the arguments of the mathematicians who objected against the ontological proof Gödel offered?

Q: What are the arguments of the mathematicians who objected against the ontological argument/proof Gödel offered? $$ \begin{array}{rl} \text{Ax. 1.} & \left\{P(\varphi) \wedge \Box \; \forall ...
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1answer
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Origin of infix notation

Wondering where the infix notation of things like 1 + 2 came from, when roughly it came about, and if it was before/after prefix or postfix notation. I know the ...
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56 views

Why are categories and monads called that way?

The words "category" and "monad" existed already in philosophy. The usage of the terms in category theory seems to be slightly influenced by the philosophical meaning, but actually the concepts are by ...
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0answers
79 views

Which one is the correct/standard mathematical notation?

I want to learn that, which one is the correct/standart mathematical notation? $f:\mathbb{R}\rightarrow \mathbb{R^{+}}$ or $f:\mathbb{R}\rightarrow (0,\infty)?$ What is the standard mathematical ...
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1answer
77 views

Why is “antiderivative” also known as “primitive”?

If I had to guess, I would say that calling the antiderivative as primitive is of French origin. Is one term more popular than the other?
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1answer
269 views

History of definitions for an ellipse?

Recently I've been learning about ellipses. It seems as though there are four (from what I've learned of so far) different ways to define ellipses, all which seem to be connected in kind of obscure ...
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Is finitary method for Hilbert and modern logic - Turing computability?

It is known that Hilbert proposed in the state of crisis of foundations of mathematics that we create formal theories which we analyze using "proof theory" or "metamathematics". He then also said that ...
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Who, when, and why invented the symmetric derivative?

When computing an approximate derivative of a function on a computer, engineers use the symmetric derivative for reduced error. Who came up with the symmetric derivative? Who proved it? When? Why was ...
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1answer
92 views

Hilbert Program: Consistency vs Soundness

I have been wondering why exactly Hilbert asked for a decidable, complete, and consistent set of axioms for mathematics, rather than a decidable, complete, and sound set of axioms. Consistency being: ...
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2answers
344 views

Hilbert program: Does Consistency and Completeness imply Decidability?

I have a question regarding the Hilbert Program. Below I will express my current understanding of it $($... if I get something wrong, please correct me!$)$ ... followed by my question. Roughly put, ...
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1answer
95 views

Why do we call it Bayes' theorem?

I'm not a historian, nor would I claim to be one, but I've seen a lot of people say that it was Laplace who formalized the theorem: $$P(A|B)=\frac{P(B|A)P(A)}{P(B)}$$ Why don't we call it "Laplace'...