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

learn more… | top users | synonyms (1)

1
vote
0answers
39 views

History: continuously differentiable groups over the real numbers

Continuously differentiable groups over the real numbers are all isomorphic to addition, as is well-known, but who proved it and when?
1
vote
0answers
135 views

Etymology of algebra (as k-algebra)?

Why algebra (over a field) is called "algebra?" (My random guess is that it's a back-formation of some algebras, chopping adjectives from say Lie algebra or Clifford algebra, etc.) And when was that ...
1
vote
0answers
156 views

History of calculus-based optimization

I would like to know: - who started with calculus-based optimization problems and when it was, - if there is a book focusing on history of ellipses/ conic sections - if someone ever tried to ...
1
vote
0answers
249 views

Who found this example of continuous nowhere differentiable function?

In many books from mathematical analysis (for example in Rudin) is presented the following example of continuous nowhere differentiable function: $$f(x)=\sum_{n=1}^\infty (\frac{3}{4})^n g(4^n x) ...
1
vote
0answers
156 views

History of operator precendence

I have seen a lot of debates over operator precedence but what is the history of operator precedence and how it evolved over time? Why multiplication precedes addition; Is it just to be definitive? ...
1
vote
0answers
96 views

Historical relation between computer science and the theory of dynamical systems

I wonder if there is any historical relation between the fields of Dynamical systems (and related fields such as Optimal control) and (theoretical) Computer science. The reason for which I ask this ...
1
vote
0answers
130 views

Reference: Wittgenstein teaching mathematics

Can anyone give me any reference concerning L.Wittgenstein teaching school kids mathematics? I have been wondering what kind of mathematics he taught and how he lectured the material.
1
vote
0answers
114 views

Opinions attributed to Gauss

In this article, Armand Borel writes the following: [...] In fact, during the next quarter century, we experienced a tremendous development of pure mathematics, bringing solutions of one ...
1
vote
0answers
159 views

What was Cayley's formula for the number of invariants? (Lost Formula!?)

I need to find Cayley's formula for the number of linearly independent invariants of homogenous polynomials. This is a combinatorial formula. He is believed to have discovered it in 1854. ...
1
vote
1answer
186 views

Expanding squares and simplification of equations

as i'm reading a paper "An Underdetermined Linear System for GPS" By Dan Kalman i understand the paper but when i traced the equations there's something i don't understand ,may be my mathematics is ...
1
vote
0answers
121 views

When was the term 'ramification' first used in math literature?

In my studies so far, I have had the word 'ramification' come up in Algebraic Number Theory and Complex Analysis. The Wikipedia article tells me that 'ramification' is also used in some other fields. ...
1
vote
1answer
55 views

How Leibniz invented the Binary System?

Do you know which reasoning and observations made Leibniz invent the Binary system ? Some say that he was inspired by Chinese mathematicians do we have any record of how he came with this idea ?
0
votes
3answers
221 views

Why do mathematicians use $\oplus$ instead of $+$?

What is the historical reason for using $\oplus$ instead of $+$ to denote operations that are generally thought of as addition? Similarly, why is $\otimes$ used instead of $\times$ (or just $\cdot$) ...
0
votes
4answers
918 views

What is the definition of a positive integer?

I am reading the book "The Number-System of Algebra (2nd edition)". At the starting of page-4 the author writes: A positive integer is a symbol for the number of things in a group of distinct ...
0
votes
1answer
454 views

Resurrection of my Tamagawa numbers Question, to understand the Formulation of BSD

My previous question was closed very badly for asking the broad and deep things, so I now understand the consequences of asking such questions, so I refrain from asking such questions, so this is not ...
0
votes
2answers
132 views

What is the poetry of mathematics? [closed]

In computer science it's often noted, said or agreed on that algorithms are the poetry of computer science. What is considered the poetry of mathematics? Is it statistics? If there is something agreed ...
0
votes
2answers
145 views

How to calculate 3x7 by using logarithm?

This is a story about Newton I read once when I was a child. Now that book is lost and I can only tell you what I remember. When Newton was young, he had been already famous in curiosity and ...
0
votes
2answers
635 views

Is it to the students' advantage to learn the language of infinitesimals? [closed]

A colleague of mine asked an interesting question reproduced below with his permission. It is reasonable to ask whether it is to the students' advantage to learn the language of infinitesimals - ...
0
votes
2answers
158 views

Does axiom of foundation/regularity protect against Russell-like paradoxes?

In ZF set theory the axiom of regularity (also called axiom of foundation) says that: In all nonempty sets x there is an element y such that x∩y=∅ As I been told that the intention of the axiom ...
0
votes
2answers
110 views

Why do some sources call calculus, “the calculus”?

No need to cite specific sources since I think it's a fairly common thing to see. What's up with that? Thank you Edit: I've seen it in several places. Here's where I'm currently looking at it at: ...
0
votes
2answers
65 views

a maximum of 128 independent rules

Can anyone tell me what these 128 rules are in the following paragraph? Are they the rules dominating Conway's automaton or other kind of rules like the whole universe rules that could be summarized ...
0
votes
2answers
87 views

What is the meaning of calculating sine of a number?

When we calculate sine/cos/tan etc. of a number what exactly are we doing in terms of elementary mathematical concept, please try to explain in an intuitive and theoretical manner and as much as ...
0
votes
1answer
175 views

Johann Bernoulli did not fully understand logarithms?

This wikipedia article makes the claim: "Bernoulli's correspondence with Euler (who also knew the above equation) shows that Bernoulli did not fully understand logarithms." This is found under ...
0
votes
1answer
131 views

Is there a analysis conjecture proven to be unprovable or a proof is non-existence?

Is there a analysis conjecture proven to be unprovable or a proof is non-existence? So, is it once a math history milestone
0
votes
1answer
52 views

What is the origin of the name Hermitian and Unitary matrix?

A matrix $H$ is Hermitian if $H ^\dagger = H$. A matrix $U$ is Unitary if $U^\dagger=U^{-1}$. My question is: Why do we name matrices of such properties Hermitian and Unitary? These names are ...
0
votes
1answer
75 views

Technical meaning of “profinite circle”

In a private exchange with a professional mathematician, I found the following statement: the "small etale topos" of a finite field is a "profinite circle", and thus looks like circle. Could anyone ...
0
votes
2answers
229 views

Why there is no “Nobel Prize” in mathematics however it is one of the most important fields in sciences in the side of research?

Mathematics is really a field of inventions and research where we find interesting problems some of which we can solve and others which remain open. I'm sorry to ask this question because I see it ...
0
votes
2answers
373 views

What comes after seconds?

Angles can be measured in different ways. For example, one can measure angles in degrees/minutes/seconds. So $1^\circ$ is divded into $60$ min. and $1$ min is divided into $60$ sec. That way a tenth ...
0
votes
2answers
330 views

The word “times” for multiplication…? [closed]

The word "times" for multiplication operation which is quite touching to the concept of time (feeling time this way 0*1=0). When was introduced that term? Did any other language have the kind of term ...
0
votes
1answer
55 views

Name for LDC: Lebesgue?

Is there also a name associated to the Lebesgue dominated convergence theorem like Beppo-Levi or Fatou? Would Lebesgue be reasonable? Who did originally prove it?
0
votes
1answer
89 views

Reference on Infinite Dimensional Manifold

I am studying manifold. For comprehension, I read the site http://en.wikipedia.org/wiki/Manifold, and there is some information about infinite dimensional manifold. Now I have two questions or ...
0
votes
2answers
140 views

General questions about theorems and laws

I have doubts about the construction of mathematical elements. There are proofs, that are proven using other theorems (corollaries) and/or axioms or definitions, such as Fermat's Last Theorem, the ...
0
votes
3answers
249 views

Resource request: history of and interconnections between math and physics

Reading this article I became curious to learn more of (- study more thoroughly and *seriously*$^{\star}$-) the topic. Is / are there some good references - either papers, books and/or other ...
0
votes
1answer
112 views

omar khayyam work on ODE (ordinary differential equation)

I wanted to know if Omar Khayyam did work on ODE and if there is any connection between that and the cubic equations.
0
votes
1answer
162 views

Alternative, consistent frameworks of mathematics with isomorphic mappings to physical phenomenon

A friend of mine who is quite an aggressive Nominalist told me the other day: "Mathematics and numbers are arbitrary; they can accurately predict physical systems in real life only because they are ...
0
votes
1answer
33 views

What is the example called, where someone was wrongly convinced of a sequence function because of naive induction.

I remember I have seen a classical example of a mistake, where someone was convinced that a sequence defined somehow had a close form, which did in turn work until some very high $n$. I think the ...
0
votes
1answer
30 views

On applications of Alexander's Theorem

I would like to know a bit about applications of the Alexander Theorem from Knot and Braid Theory. I would be very interested in learning about possible applications for the description of everyday ...
0
votes
1answer
75 views

Seemingly contradictory results [duplicate]

The following infinite sums produce remarkable results. $1+2+3+4+...=-\frac{1}{12}$ $1-2+3-4 +...=\frac{1}{4}$ So how are these results compatible with the statement; that integers are closed ...
0
votes
1answer
48 views

Why do we use a single 'dash' for difference : $-$ and a double 'dash' for sum: $+$? [closed]

Why do we use a single 'dash' for difference : $-$ and a double 'dash' for sum: $+$? Just a shower thought: Who came up with this notation? It kind of makes it look like the difference is simpler ...
0
votes
1answer
47 views

Spanish translation for the term operad?

I would like to know which is the correct term in Spanish for operad(s)? https://en.wikipedia.org/wiki/Operad_theory I cannot be operador, since that is reserved for operators. I do not see anything ...
0
votes
1answer
77 views

Who (which) was the mathematician “Abel” who countered Cauchy's “proof?” [closed]

...as in this quotation: "Cauchy's approach to rigour didn't save him from errors, however. He 'proved' incorrectly that the limit of a convergent series of continuous functions is continuous. Abel ...
0
votes
1answer
20 views

A question in understanding some part of paper of Frobenius

I am learning German, and reading German paper of Frobenius (click here). It is "Verallgemeinerung des Sylow'schen Satzes / G. Frobenius" I didn't understand few things, and I didn't find the answer ...
0
votes
3answers
80 views

History and early development of Mathematics

Please provide references (books, articles, websites links, video links) that describe the conceptual development of calculus, complex numbers, group theory, matrix and linear algebra. I am curious to ...
0
votes
2answers
45 views

Functions applied from the right

In some of the older books by Nathan Jacobson (like Lie Algebras and Lectures in Abstract Algebra), a convention is used that is quite uncommon at least today: Functions are applied from the right. ...
0
votes
1answer
65 views

Sophie Germain primes

Why did Germain come up with her Germain primes? I am intrigued to know why Sophie came across these primes. Do they have any applications?
0
votes
1answer
186 views

Understanding the difference between relations and functions.

$R=\{(1,2),(1,3)\}$ is a relation but not function. The logic for this is that if the first element of every ordered pair must remain different, then it is said to be function. Otherwise, it's just ...
0
votes
1answer
108 views

History of five lemma

I am interested in the history of five lemma. Who was first to prove it and What was the purpose of proving it ? http://en.wikipedia.org/wiki/Five_lemma
0
votes
3answers
68 views

Should the notion of continuity, usually ascribed to Cauchy, be ascribed to Leibniz?

In his text, Deleuze and the History of Mathematics, Simon Duffy writes: Leibniz also thought the following to be a requirement to continuity: "When the difference between two instances in a ...
0
votes
2answers
249 views

Roberval's Method and Tangent Construction involving parabola $y^2=4ax$

Problem: Let $u$ denote the distance of a moving a point $P$ on the parabola $y^{2}=4px$ from the directrix $x=-p$ and from the focus $\left(p,0\right)$. If the point moves in such a way that ...
0
votes
1answer
85 views

What type of famous equation except diophantine equation such that no algorithm can exist to determine whether there is a solution?

What type of famous equation except diophantine equation such that no algorithm can exist to determine whether there is a solution? I know that if these equation have a solution, then it could be ...