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

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Cross products and determinants in $\mathbb{R}^3$

I know that the absolute value of determinant of three vectors in $\mathbb{R}^3$ is the volume of the parallelepiped determined by the three vectors. The volume can be computed by basic calculation ...
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1answer
98 views

In Whitehead & Russell's PM, what makes anything true or false?

It seems that truth and falsehood are fundamental to meanings and types. A proposition is defined as anything that is true or that is false. PM defines truth as "consisting in the fact that there is ...
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1answer
107 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
72 views

Lagrange's original proof of Remainder Theorem?

Where can I find Lagrange's original proof of the Remainder Theorem?
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1answer
54 views

Discovering the mathematical nature of Nature - Galileo's inclined plane experiment

In 1638 Galileo published Two New Sciences, in which he described his inclined plane experiment. He discovered that the acceleration of gravity was uniform, and could be modeled mathematically by the ...
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1answer
56 views

Diophantus problem

I was given following problem as an example of early mathematics with the solutions. But it seems i can't understand from where they are getting the 35z^2 = 5 from in the solutions. Could someone ...
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2answers
213 views

Shape made by Beltrami

Beltrami made (out of thin paper or stiff cloth) a model of a surface of constant negative Gauss curvature. The original might have resembled a large saddle shaped Pringles chip, and frills might have ...
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1answer
62 views

Who first described commutative algebraic theories explicitly?

Lately, I've been thinking that the concept of a commutative algebraic theory is really, really important. So I'm curious; who had the honor of first discovering this concept? In particular, I'd like ...
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1answer
58 views

Prove that if $x$ is a real number, and $x-\lfloor x\rfloor \ge 1/2$, then $\lfloor 2x\rfloor=2\lfloor x\rfloor +1$

Prove that if $x$ is a real number, and $x-\lfloor x\rfloor \ge \frac{1}{2}$, then $\lfloor 2x\rfloor=2\lfloor x\rfloor +1$ I'm so confused because i don't completely understand the rules for floor ...
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1answer
2k views

Definition: finite type vs finitely generated

The mathematical term "finite type" appears more and more in the modern articles nowadays. But it is still hard to be found in the standard textbooks. I learned the definition of it from Stacks ...
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1answer
294 views

Beginnings of Greek Mathematics

For another proof of the pythagorean theorem, consider right triangle ABC (with right angle at C) whose legs have length a and b and whose hypotenuse has length c. On the extension of side BC pick a ...
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2answers
76 views

Is there a book or a list online where Fermat's conjectures are compiled?

I heard/ read somewhere that "Fermat's last theorem" is named as such because it is "Fermat's last conjecture to be disposed of." This got me interested in knowing what Fermat's other conjectures are. ...
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3answers
351 views

How did it happen that base 10 went on to be the most popular? [duplicate]

Possible Duplicate: why have we chosen our number system to be decimal (base 10) 0,1,2,3,.......9! What are the reasons fow which this system is the most popular? Why not any other base? It ...
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2answers
246 views

Why was Newton concerned with finding tangents?

While trying to teach myself calculus, I stumbled upon a BBC documentary called The Birth of Calculus. In the documentary, the narrator explains that Newton and other contemporary mathematicians were ...
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2answers
48 views

how to factor terms?

as i'm reading a paper a paper "An Underdetermined Linear System for GPS" By Dan Kalman and solving an equation ,and as i'm not good in math i missed there ,in factoring of the following equation: ...
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1answer
184 views

Where does the % symbol originate from? [duplicate]

Possible Duplicate: What is mathematical basis for the percent symbol (%)? Where does the % symbol originate from?
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1answer
920 views

History of solving linear equations with matrices

I'm solving linear equations with matrices right now and I wonder, how did it start. Who, how, why came to idea that such kind of equations could be solved with matrices? What was first: matrix or ...
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1answer
185 views

When - during the study and development of- - and how were complex numbers introduced in the study of [real-valued] power series (expansions)?

Follow-up to: Mathematical reason for the validity of the equation: $S=1+x^2S$ and General question on relation between infinite series and complex numbers (This question seems broad at this stage, ...
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0answers
38 views

What are the levels of math? [closed]

I'm in geometry and I want to know what are the next levels of it. I was in algebra and then geometry. So does that mean. Algebra 2 comes after the geometry?
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1answer
71 views

Can we build mathematics without studying it?

This is one question that I can never get the answer of, because I am too young at this moment. My question is that can a common person like me, not a genius, just a normal person, build mathematics ...
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0answers
25 views

Konig's theorem and perfect graphs

I want to understand why perfect graphs are so named and why are they relevant. Consider the following statement from wikipedia's article on Konig's theorem. A graph is perfect if and only if its ...
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0answers
18 views

Rooms and Passages Domains

I'm currently looking into Dirichlet Laplacian and Neumann Laplacian boundary conditions on the rectangle and came across the Rooms and Passages domains, I was just wondering if anyone knew why ...
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0answers
24 views

Explanation of the term rings [duplicate]

why do we call rings rings ? Is it random name or is it because of some structural property?
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17 views

Prime Counting: In truncation rule #2 mentioned in an AMS.org article, I'm unclear how “special leaves” work?

I'm reading through an AMS.org article on prime counting. The article covers the history of prime counting and focuses on improvements to the Meissel-Lehmer method. It is the improvement on page ...
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0answers
29 views

Did Ackermann produce a finitary consistency proof of second-order $PRA$?

In Wilhelm Ackermann's Doctoral Thesis (it is claimed, by Richard Zach, for one, in his paper "The Practice of Finitism: Epsilon Calculus and Consistency Proofs in Hilbert's Program", arXiv: ...
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0answers
23 views

What is the origin of the distinction between assignable and inassignable number?

Leibniz described his infinitesimals as being inassignable numbers in a number of texts, e.g., in his Cum Produisset that was analyzed in detail by H. Bos in a seminal text dating from the 1970s. The ...
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32 views

Why do we define a limit/continuous function/vector space etc. the way we do?

I am looking for any material dealing with the evolution of what now are standard mathematical definitions. One example what I am looking for: Let $(a_n)_{n\in\mathbb N}$ be a sequence with ...
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60 views

Proportion and disproportion in the Pythagorean theorem.

Is there any accepted explanation about why the square areas of the Pythagorean theorem are proportionated if the referential lengths of the legs and the hypothenuse are disproportionated? I think ...
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0answers
57 views

On the History of the Concept of Module

I am interested in knowing a little bit more about the history of the concept of module. As far as I know, there are two primary meanings of the word in mathematics, namely, modules as derived from ...
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0answers
12 views

On Symmetric Bilinear Forms by Milnor and Husemoller

Note: I am not sure the question is worth to be asked. But I have always been curious about this... The usual practice in mathematics is to put the names of authors in alphabetic order. However, ...
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0answers
22 views

Power Set, Theory of Linear Algebra, and Axiomatic Systems

So for homework, my History of Math professor gave us these three questions: Explain why the power set of a set S (collection of all subsets) has the same cardinality as the set [all functions from ...
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47 views

Was Ramsey mistaken in thinking that the same proposition can be both elementary and non-elementary in form?

According to Ramsey's Foundations of Mathematics, chapter III, suppose $'a', 'b', ..., 'z'$ were all the individuals, then $\phi{a}.\phi(b)...\phi(z)$ expresses the same proposition as $(x)\phi(x)$ ...
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36 views

The genesis of vectors

In a recent post that I've visited, the user is asking about what is the between a vector field and a scalar field. There are good answers, and I could answer using the example that $\mathbb{R}$ (as ...
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0answers
22 views

In the problem of dividing a line in extreme and mean ratios, how do I show that 1 and x are incommensurable?

In other words, the line is divided at x such that 1/x = x/(1 - x). The problem hints at using the Euclidean algorithm to prove that 1 and x are incommensurable. Also need to show that the proportion ...
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20 views

Did Euler talk about Eulerian circuits?

The Wikipedia article on Eulerian paths states: Euler proved that a necessary condition for the existence of Eulerian circuits is that all vertices in the graph have an even degree, and stated ...
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0answers
48 views

Weak Law of Large Numbers - Bernoulli's proof

Question concerning Bernoulli's demonstration of Bernoulli's Weak Law of Large Numbers. Although, I get the general sense of the third lemma, I don't really get the formulation of it, more ...
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0answers
23 views

Different ideal vs. dual lattice

I found this statement in a text trying to explain what the different ideal by Dedekind is: "The main idea needed to construct the different ideal is to do something in number fields that is ...
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0answers
28 views

Developable surfaces in $\mathbb{R}^4$

It is known that there are developable surfaces in $\mathbb{R}^4$ which are not ruled: the famous example is of Hilbert and Cohn-Vossen in their book "Geometry and the Imagination" (p. 342). The ...
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1answer
45 views

Dedekind's “different”: sources, definition, original name

I am interested in getting the original information regarding Dedekind's idea of the "different" (regarding ideals). Particularly, I am interested in: 1- Knowing the original German name he used for ...
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0answers
40 views

Clarification of a quote on Riemann-Roch Theorem

I find this quote in Martin Krieger, Doing Mathematics: Convention, Subject, Calculation, Analogy, New Jersey, World Scientific Publishing, 2003, p. 223. "Hilbert then shows how one of Dedekind's ...
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0answers
40 views

Who thought applying real value definite integral to contour integral firstly?

Who thought applying real value definite integral to contour integral firstly? Example $$ \int_{0}^{\infty} \frac{\sin{(x)}}{x} dx $$ $$ \int_{0}^{2\pi} \log{(\sin{(x)})} dx $$
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0answers
53 views

Grothendiek and singular points

My question relates to the following thread I opened some weeks ago: A question regarding Grothendieck , topos and (adelic??) points Specifically, consider this paragraph: At 1:14:30 and after, ...
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2answers
49 views

Orthogonality properties in Newton's calculus.

In a lecture notes, there is written: Isaac Newton uses orthogonality properties to establish the principles of calculus. The definitions of derivative and integral for this author is based on ...
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0answers
84 views

Demonstrative geometry around the world and its significance.

This is not exactly a mathematical question. I am from Pakistan; and over here students are taught a subject 'demonstrative geometry' (as a part of mathematics) from secondary level education. ...
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59 views

Difference between infinitesimal motion and finite motion

I was reading an article about back ground of Killing's work by Thomas Hawkins from Historia mathematica 1980.In it Hawkin's says that,Killing was trying to generalise all types of space ...
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0answers
16 views

On the history of sigma-ideals

Could anyone provide me with some insight regarding the history of sigma-ideals, i.e., who coined them, first publications on the matter, main authors thereafter and so on? Thanks in advance.
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46 views

On the origins of Homological algebra

In Martin Krieger's book "Doing Mathematics: Convention Subject, Calculation, Analogy" (2003) I find the following statement (apparently, a quote from somone else) : "Homological algebra starts from ...
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26 views

Origins of the Cesaro Operator

I am wondering when the Cesaro Operator was first studied. I can find an article from 1965 but I'm wondering if there are any previous ones.
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26 views

how to get same line from gradient?

I have image like this how to get $x_4,y_4$ ? from gradient it like same line $y_1,x_1$ and $y_0,x_0$
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Who coined ideals in Set Theory?

One of the meanings of the word "ideal" in maths refers to Set Theory. Even though handbooks say that concept can be translated to Order Theory or to Algebra effortelssly, I am interested in: 1) ...