42 votes

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

Commutativity is over-rated: in fact, it holds back bicomplex numbers: It prevents your number system characterising non-commuting operations, e.g. rotations in $3$-dimensional space, Hamilton's ...
J.G.'s user avatar
  • 1,720
27 votes

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

Your description "total uselessness of quaternions" in a comment above is poorly chosen, and reflects more on your interests than on the real state of knowledge of mathematics. The Hamilton ...
KCd's user avatar
  • 5,597
16 votes
Accepted

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

This question comes up often, but there is no up to date scholarly study of it that I know of. The most comprehensive recent accounts (and they are rather brief) seem to be Jeff Miller's Earliest Uses ...
Conifold's user avatar
  • 76k
12 votes
Accepted

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

Much has been written about various roadblocks to the acceptance of negative numbers, and I have a folder containing photocopies of a few such papers, but I don't have time now to look for that folder....
Dave L Renfro's user avatar
11 votes

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

Hamilton expected that the quaternions would be of physical interest. In this, he was right. But he was too early. He had discovered them in 1843, it was almost a century later, in 1928, when Dirac ...
Mozibur Ullah's user avatar
10 votes
Accepted

What algebra problem did Serge Lang give to calculus students?

In 1969 Lang wrote an article for the Columbia Daily Spectator, Don't Blame Us if You Flunk Math (Volume III, Number 4, December 8, 1969). The phrasing of the subline illustrates how much the times ...
Conifold's user avatar
  • 76k
9 votes
Accepted

How did the modern understanding of Galois theory come about?

The systematic modern terminology and presentation of the Galois theory is due to Artin, a part of his joint project with Emmy Noether to reformulate the "concrete" older algebra in abstract terms, ...
Conifold's user avatar
  • 76k
9 votes
Accepted

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

It is in the third book of La Géometrie: I could also add rules for equations of the fifth, sixth, and higher degrees, but I prefer to consider them all together and to state the following ...
Michael E2's user avatar
  • 1,861
8 votes
Accepted

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

Bombelli did not have a general method for such transformation, nor does it exist. Doing so is equivalent to solving the irreducible case of the cubic, which is impossible in (real) radicals. It is ...
Conifold's user avatar
  • 76k
8 votes
Accepted

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

I think there are two separate issues here: the origin of "root" and of the custom to arrange polynomial equations in descending powers equated to zero. The latter was initiated by Stifel ...
Conifold's user avatar
  • 76k
8 votes
Accepted

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

Attempting to find substitutions that would generalize Cardano's and Ferrari's solutions to the cubic and quartic was a popular enterprise in the 17-18th centuries. Gregory, Leibniz, Euler, Bezout and ...
Conifold's user avatar
  • 76k
7 votes
Accepted

Who discovered the rational root theorem?

When in doubt, go to the source. There is a nice facsimile edition of Descartes's La Géométrie with English translation, freely available on Internet Archive. Descartes does not spell out the trick as ...
Conifold's user avatar
  • 76k
7 votes
Accepted

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

I think I can shed some sort of light on the other methods in use for solving trinomials (and general polynomials) from Lambert (1758) to Langrange (1770) and Euler (1776), as well as the (more ...
Sam Gallagher's user avatar
7 votes

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

but for how long has PEMDAS been widely taught in high school mathematics classes? I assume this will differ for different parts of the world, so please include what countries or regions you can speak ...
jkien's user avatar
  • 1,901
6 votes

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

For sure, the technique was used by Leonhard Euler (15 April 1707 – 18 September 1783). See : Elements of Algebra (English transl., 1822), page 208: Since the two equations are, $x+y=a$, ...
Mauro ALLEGRANZA's user avatar
6 votes
Accepted

When it was discovered that cubic equations always have roots?

There is a problem with how the question is phrased, which is unfortunately common. Modern concepts pull together many different threads which come apart when projected into the past far enough. "...
Conifold's user avatar
  • 76k
6 votes

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

It is easy to find fault with Descartes and Leibniz spent his life doing it (see Belaval Y., Lz critique de Desc., P.1960). Descartes knew that some problems of higher degrees are reductible and ...
sand1's user avatar
  • 2,387
6 votes

Who pioneered the study of the sedenions?

There are (at least) two different types of numbers called "sedenions". The first ones were introduced by Muses in 1980, who called them $16$-ions, and renamed into "sedenions" by Carmody in 1988. ...
Conifold's user avatar
  • 76k
6 votes

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

As with many "who was first" questions there is no straightforward answer. This is what May described as priority chasing coming to grief in Historiographic vices: "The hope of finding ...
Conifold's user avatar
  • 76k
5 votes

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

D. T., "Methodus auferendi omnes terminos intermedios ex data æquatione." Acta Eruditorum (1683), pp. 204-207. The 'D' may stand for doctor, because the author's full name was Ehrenfried ...
njuffa's user avatar
  • 6,516
4 votes
Accepted

Who pioneered the study of the sedenions?

On Bibliography of Quaternions and Allied Mathematics by Alexander Macfarlane I found this: On page 72; James Byrnie Shaw 1896 Sedenions (title). American Assoc. Proc., 45, 26. I couldn't find this ...
Mr. J. Larios's user avatar
3 votes

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

The answer is yes: J. Lagarias, Euler's constant: Euler's work and modern developments, BAMS, 50 (2013), no. 4, 527–628.
Alexandre Eremenko's user avatar
3 votes
Accepted

Was further research done about the invention of Algebra?

Nothing new was discovered after Boyer published his textbook. In 2014, Victor J.Katz and Karen Parshall published their book Taming the Unknown: A history of algebra from antiquity to the early ...
José Carlos Santos's user avatar
3 votes

How did the modern understanding of Galois theory come about?

My impression is that Artin's role in the development of Galois theory is usually greatly overrated. Kiernan's article jumps from 1900 to Artin in the late 1930s. Certainly a "modern" Galois theory ...
anon's user avatar
  • 31
2 votes

Was further research done about the invention of Algebra?

Perhaps the following papers may help clarifying the issue: Hoyrup, Jens : i) “The Formation of Islamic Mathematics”: Sources and Conditions. Preprints og Reprints 1987 Nr 1. (available online) ii) “...
Driss Lamrabet's user avatar
2 votes

What was known about Chebyshev polynomials in 1900?

Chebyshev polynomials really appear in various connections since 16th century, see, for example https://arxiv.org/abs/2203.10955 But they were not named after Chebyshev until the early 20 century. So ...
Alexandre Eremenko's user avatar
2 votes

List of textbooks on Abstract Algebra in the order of time

Notation: BK = Book BK#1892 The theory of substitution and its applications to algebra. Rev. by the author and translated with his permission by F.N. Cole 1892 (Book was mentioned in preface of BK#...
1 vote

Egypt pefsu problem

The short answer, it seems, is that the type of beer referenced in the problem ("1/2 1/4 malt-date beer") is a weaker beer, and thus only uses 1/2 as much grain as "regular" beer. ...
Brant's user avatar
  • 155
1 vote

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

This won't be much of a "historical" answer (although my external links probably have interesting history in them), but hopefully it'll be mathematically useful, at least if construed as a ...
J.G.'s user avatar
  • 1,720
1 vote

What was known about Chebyshev polynomials in 1900?

One might ask the same question about Lucas and his Lucas sequence $V_n := \alpha^n + \beta^n$ where $P:=\alpha+\beta$ and $Q:=\alpha\beta.$ The difference in the Dickson and Lucas cases seems to be ...
Somos's user avatar
  • 275

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