Questions tagged [algebra]

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What motivated the idea of the Tschirnhaus transformation of polynomial equations?

As I studied Cardano's formula for the cubic, Tschirnhaus transformation came up as a very important step. The more I studied it the more attractive and interesting it seemed. So I am curious about ...
pokssin's user avatar
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1 vote
1 answer
124 views

List of textbooks on Abstract Algebra in the order of time

I am knowing Abstract Algebra things; I am searching aims of Abstract Algebra and origins of parts of Abstract Algebra. I thought original initial textbooks have explicit links to aims and origins of ...
Sensebe's user avatar
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5 votes
1 answer
240 views

Who discovered the rational root theorem?

As the title says, I would like to know who discovered the rational root theorem. The Encyclopaedia Britannica states that “The 17th-century French philosopher and mathematician René Descartes is ...
José Carlos Santos's user avatar
2 votes
2 answers
221 views

What was known about Chebyshev polynomials in 1900?

Around 1900, was it widely known that the Chebyshev polynomial $T_n(X)$ satisfies the identity $$ T_n(X) \circ \frac{X+X^{-1}}{2} = \frac{X^n+X^{-n}}2?$$ And also, would one expect top-notch ...
Michael Zieve's user avatar
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1 answer
1k views

Leonhard Euler's Mathematical Proof of God [closed]

There is a famous legend inspired by Euler's arguments with secular philosophers over religion, which is set during Euler's second stint at the St. Petersburg Academy. The French philosopher Denis ...
Agent Smith's user avatar
1 vote
0 answers
110 views

I'm wondering how the Egyptians figured out the false position method in solving their equations?

I'm wondering how the Egyptians figured out the false position method in solving their equations? Is there a good source that can tell me how they thought through this?
Markvz's user avatar
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2 votes
1 answer
352 views

Why is $Ax^2+Bx+C=0$ called standard form of Quadratic Equation? And who declared it the standard form?

$Ax^2+Bx+C=0 $ is mentioned as standard form of quadratic equation in every textbook or encyclopaedia, but what's so special about it that its called standard form of quadratic equation. Also, I am ...
Ermac's user avatar
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1 vote
0 answers
161 views

Classification of "Epitaph of Diophantus" problem

The well-known riddle of the Epitaph of Diophantus, attributed to Metrodorus, is one of the style of simple problem in algebra whose pattern when expressed in contemporary algebraic notation is: $$x = ...
Prime Mover's user avatar
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6 votes
1 answer
341 views

What is the origin of "root" as a solution to an equation?

I was curious to know more on the history of the term "root", in the sense of "a value that results in a true statement, when substituted into an equation" (e.g., the roots of $2x^...
Rax Adaam's user avatar
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0 answers
95 views

Did anyone ever propose an analytic definition of zero divisors, including nilpotents, as opposed to algebraic definition?

I wonder, can we meaningfully define zero divisors based on analytic rather than algebraic approach? For instance, if we extend the real numbers with divergent integrals and series, and evaluate the ...
Anixx's user avatar
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1 answer
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Egypt pefsu problem

Looking at the pefsu problem of the Moscow Mathematical Papyrus here I don't understand why the algorithm takes $1/2$ of the calculated grain measure to produce beer. Why aren't the $5$ heqats ...
Michael Munta's user avatar
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0 answers
203 views

Abel's "solution" of the quintic

Before Abel embarked to proving the insolubility of the quintic with radicals, he thought he had found a solution and sent his work in a letter to the Danish mathematician Carl Ferdinand Degen in 1821....
dimachaerus's user avatar
1 vote
1 answer
123 views

Did anyone ever propose a hypercomplex numbers system with more than one anisotropic axis?

The real number axis is asymmetric against zero: for instance, multiplication of two negative or two positive numbers will produce a positive number, a square root of a negative number is not real, ...
Anixx's user avatar
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0 votes
1 answer
82 views

Did anyone ever try to determine or propose the algebraic role of Euler-Mascheroni constant?

Both the constant $\pi$ and the constant $e$ have clear algebraic roles in complex numbers and in differential calculus. But did anyone ever propose an algebraic role for Euler-Mascheroni constant $\...
Anixx's user avatar
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13 votes
3 answers
5k views

Why are quaternions more popular than tessarines despite being non-commutative?

Is this simply because of marketing, hype, etc? The bicomplex numbers (especially tessarines) look just great being commutative and all. Images source:https://citeseerx.ist.psu.edu/viewdoc/download?...
Anixx's user avatar
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2 votes
1 answer
283 views

Has the idea that the result of division of positive number by negative number should be negative ever been controversial?

If we divide a positive number by another positive number, the result becomes greater as the divisor becomes smaller. If we continue this logic, division by a negative number should be greater than ...
Anixx's user avatar
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1 vote
0 answers
103 views

Why are linear forms called "forms"?

My question is about linear forms, quadratic forms, n-linear forms, differential forms and so on. The first term of these names seem clear to me, but I cannot make a link between these mathematical ...
Myvh's user avatar
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4 votes
1 answer
541 views

Who invented multiplying by the conjugate to rationalize denominators and when?

1860 Manual of Algebra describes a method which is now taught in upper secondary schools worldwide: To rationalize the denominators of fractions which consist of binomial quadratic surds, use the ...
ain92's user avatar
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5 votes
1 answer
458 views

What was Gauss's method for solving the "trinomial equation"?

In the second part of his fourth proof of the fundamental theorem of the algebra (published in 1849 [1]), entitled "A contribution to the theory of algebraic equations", Gauss gives a new ...
user2554's user avatar
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2 votes
1 answer
175 views

The origins of differential homological algebra

Differential homological algebra in its initial formulation is due to Eilenberg and Moore, who first published the homological version of the Eilenberg–Moore spectral sequence in 1965 (and the ...
jdc's user avatar
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Research about Stafford Beer's claim about a method for solving simultaneous equations unknowingly via a game by kids?

I found this claim in the book "How many grapes went into the wine", in the Artorga section: In 1956 I devised a game for solving simultaneous linear equations in two variables. The theory ...
GodTaxist's user avatar
1 vote
0 answers
79 views

Is there any paper on how Viete may have came up with his algebraic notation?

Is there any indication that Viete read Bombelli or Stifel before he discovered his algebraic notation?
GEP's user avatar
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5 votes
2 answers
507 views

Who pioneered the study of the sedenions?

I found lots of background information about the discovery of both imaginary and complex numbers, and enough information about the first two types of hypercomplex numbers; quaternions and octonions (...
Mr. J. Larios's user avatar
1 vote
1 answer
479 views

Can any one person be credited with "inventing" algebra?

I have been told by a computer scientist that most people in that field believe that algebra was invented (along with algorithms) by the 9th century mathematician Muhammad ibn Musa al-Khwarizmi. (I ...
sph's user avatar
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4 votes
0 answers
145 views

Ala-El-Din Muhammed El Ferjumedhi

I'm looking for more details of a 14th century mathematician Ala-El-Din Muhammad El Ferjumedhi. I'm translating a popular book on the history of mathematics, and there is one figure that shows a ...
Stephan Matthiesen's user avatar
5 votes
1 answer
245 views

How did Bombelli transform $\sqrt[3]{2\pm11\sqrt{-1}}$ into $2\pm\sqrt{-1}$?

The story of Bombelli solving the equation $x^3=15x+4$ in L'Algebra and introducing $\sqrt{-1}$ is well known. The equation, having obvious root $x=4$, is solved using Cardano's formula: $$ x=\sqrt[3]{...
Adrien's user avatar
  • 171
10 votes
2 answers
339 views

Did Descartes leave solving the quintic as an exercise to his readers?

In this document by Jim Brown it is claimed (on Section 3, pg 5) that: [Descartes] believed that all polynomials of degree $>4$ could be solved with the same methods as had been applied to the ...
ZKG's user avatar
  • 211
13 votes
2 answers
22k views

How long has the order of priority of arithmetical operations been widely taught in high schools?

Browsing Facebook, I often come across posts like this, to test peoples' understanding of order of operations. This inevitably prompts a deluge of answers that either misunderstand the concept or ...
Joel Roberts's user avatar
5 votes
0 answers
177 views

Origin of the expression “Fundamental theorem of Algebra”

Who was the first person to use the expression “Fundamental theorem of Algebra”? It is well-known that Gauss called it “Fundamental theorem of algebraic equations”. Grattan-Guiness, in his The Rainbow ...
José Carlos Santos's user avatar
5 votes
1 answer
1k views

What algebra problem did Serge Lang give to calculus students?

Joel Spolsky tells this story: Serge Lang, a math professor at Yale, used to give his Calculus students a fairly simple algebra problem on the first day of classes, one which almost everyone could ...
J.G.'s user avatar
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6 votes
2 answers
980 views

How did the modern understanding of Galois theory come about?

The "modern" understanding of the Galois group of a polynomial is as automorphisms of the splitting field of the polynomial which keep the base field fixed. These concepts were unknown to Galois, who ...
Nat Kuhn's user avatar
  • 213
3 votes
2 answers
353 views

Was further research done about the invention of Algebra?

In his book “A History of Mathematics”, Carl Boyer mentions that both AlKhwarizmi and Abd ElHamid Ibn Turk wrote their books on Algebra (“Aljabr w Almuqabla” and “Logical Necessities” respectively) at ...
Islam Hassan's user avatar
4 votes
1 answer
181 views

In history of algebra, who was the first to add one equation to another equation?

In history of algebra, who was the first to add one equation to another equation? Someone gave me the name of an Italian mathematician of Renaissance period, but I lost the email. I wish to make it a ...
user97019's user avatar
1 vote
0 answers
79 views

How was invented quadratic equation? [duplicate]

How actually people invented the quadratic equation? What practical problem did they solve? There are some info about this exist in internet, but it is very abstract - I cant find the concrete task ...
AeroSun's user avatar
  • 111
6 votes
2 answers
390 views

When it was discovered that cubic equations always have roots?

Every cubic equation (with real coefficients) has a real root. Who was the first person who proved this? Is it already contained in Bombelli's Algebra?
José Carlos Santos's user avatar
1 vote
0 answers
233 views

When did usage of the word polynomial become standard?

When did (cognates of) the word polynomial become standard in mathematical writing for expressions like $x^2 -x + 1$ and $ax^2 + bxy + cy^2$? In the 3rd edition of an 1822 English translation by Rev. ...
Stan's user avatar
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