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 ...
- 1,740
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 ...
- 5,869
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 ...
- 80k
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....
- 3,582
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 ...
- 3,760
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 ...
- 80k
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, ...
- 80k
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 ...
- 1,901
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 ...
- 80k
8
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 ...
- 80k
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 ...
- 80k
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 ...
- 80k
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 ...
- 1,486
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 ...
- 1,971
7
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,
$x+y=a$, and
$x-y=b$...
- 15.2k
7
votes
Accepted
History of extension problem of abelian groups
A detailed account of the early history of group extensions is given in chapter 9 of Nicholson's 1993 PhD thesis (freely available from Oxford's research archive). Later, cohomological, developments ...
- 80k
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. "...
- 80k
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 ...
- 2,462
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. ...
- 80k
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 ...
- 80k
6
votes
Accepted
Were European algebraists aware of the work of Al-Khwarizmi?
People like del Ferro, Cardano, Tartaglia, Viète, and Fermat are from the 16-17th century. Al-Khwarizmi is from the 9th century. People like Fibonacci (13th century) had already translated what they ...
- 5,381
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 ...
- 7,279
5
votes
Origin of the Term "Entire Function" (ganze Funktion, fonction entière, etc.)
The older English term is "integral function".
The origin of this usage becomes clear when you compare with the term "meromorphic function" (ratio of two entire functions). This ...
- 51.1k
4
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 ...
- 5,976
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 ...
- 101
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 ...
- 31
3
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) “...
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.
- 51.1k
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 ...
- 51.1k
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#...
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