2
votes
3answers
61 views

Why the name “umbilic”?

Umbilic points are points on a surface at which the principle curvatures of the surface are equal. "Umbilic(al)" refers to the navel/belly button. But why do we call these points so? What about the ...
3
votes
0answers
100 views

Why do Mathematicians use $u$ and $v$ as variables?

I'm sure this has happened to you as well: you are reading some hand-written work, the variables used are $u$ and $v$, and at some point the handwriting becomes unclear and you cannot distinguish the ...
10
votes
1answer
141 views

Why is $e$ the Identity?

Some authors use $e$ to be the identity element of a group instead of $1$. What is the origin of this notation? Was this before or after we used $e$ to represent the base of the natural logarithm? ...
11
votes
4answers
135 views

The origin of the function $f(x)$ notation

What are the historical origins of the $f(x)$ notation used for functions? That is when did people start to use this notation instead of just thinking in terms of two different variables one being ...
9
votes
5answers
441 views

What are reasons why some symbols in mathematical logic are not standardized?

Why is so hard to find a standardisation regarding symbolism and/or terminology in Mathematical Logic ? We see again and again students asking if e.g. $\rightarrow$ and $\implies$ means the same ...
3
votes
2answers
70 views

Notation and the name choice for meet and join (in order theory)

I have two simple questions: From where do the names meet and join come from? I don't see any intuition between those names in context of order theory. From where does the notation come? I have to ...
1
vote
1answer
77 views

From $\mathsf{O}$ to $\mathsf{I}$ via $\infty$

The following is not true mathematics, but a little imaginary story about mathematical symbols. I wonder if there is - in parts - a true (etymological) story behind it. Once there was a symbol ...
2
votes
1answer
143 views

Why do we write $f : X \rightarrow Y$ as opposed to $f \in X \rightarrow Y$.

I've always been taught to write $f : X \rightarrow Y$ as opposed to $f \in X \rightarrow Y$. This seems weird though, since $X \rightarrow Y$ can be viewed as the set of all functions with source $X$ ...
3
votes
2answers
137 views

Notation: Why do we learn to write the higher powers in an equation first?

I have always written equations in the form $y=ax^2+bx+c$ but after entering an equation into Wolfram Alpha I noticed that the answer was displayed in the form $y=c+bx+ax^2$. I know that there is no ...
73
votes
24answers
6k views

What are some examples of notation that really improved mathematics?

I've always felt that the concise, suggestive nature of the written language of mathematics is one of the reasons it can be so powerful. Off the top of my head I can think of a few notational ...
0
votes
0answers
42 views

Alternate convention in matrix multiplication?

I'm going through Halmos's Finite-Dimensional Vectorspaces. I noticed an oddity in a proof where the indexes seemed to be swapped when multiplying a matrix by a vector. I went back about 30 pages to ...
7
votes
4answers
214 views

Is there an established notation, either modern or historical, for any unit of measure which is then further subdivided into 360 degrees or parts?

This question about notation is simple as dirt, but would be useful for me regardless, because of some work that I'm doing in music theory. Basically, while there's a notation for subdividing the ...
7
votes
0answers
120 views

Origin of $\mapsto$ notation

Who invented the brilliant $\mapsto$ notation for describing a function's action on a point, as in $x \mapsto x^2$? This is in some sense a counterpart to Who came up with the arrow notation $x ...
7
votes
1answer
157 views

On the pronunciation of the second derivative

I have been looking at Lancelot Hogben's Mathematics for the Million (first published in 1936). In the chapter on calculus he says that the second derivative $\displaystyle \frac{d^2y}{dx^2}$ is ...
3
votes
1answer
83 views

Numerator and denominator separated by hyphen

This is a question about historical notation practices. A colleague recently sent me a scan of a portion of a 1935 paper: P. R. Bassett. "Passenger Comfort in Air Transportation", Journal of the ...
8
votes
2answers
340 views

Notation for intervals

I have frequently encountered both $\langle a,b \rangle$ and $[a,b]$ as notation for closed intervals. I have mostly encountered $(a,b)$ for open intervals, but I have also seen $]a,b[$. I recall ...
1
vote
1answer
81 views

backwards membership notation set theory

This is more of a notational/historical question. I had a course last quarter where the professor would write things like $A \in x$ for $A$ a subset of some bigger space $X$ and $x$ an element of $X$. ...
4
votes
1answer
66 views

Is the Knuth arrowup notation defined for non-natural exponents?

I recently found out about Knuth's arrowup notation. Wikipedia, among other websites, only shows a definition for $a \uparrow^n b$ where $n \in \Bbb{N}_0, a \in \Bbb{R}, b \in \Bbb{N}$ as following: ...
3
votes
3answers
311 views

What do these old symbols from set theory mean? (Large E, $\cdot$ and $+$ for sets, and $\ \bar{\!\bar X}\,non\!\geqslant\frak n$)

So, I'm trying to prove the theorems in this paper by Tarski: On Well-ordered Subsets of any Set, Fundamenta Mathematicae, vol.32 (1939), pp.176-183 but it is from 1939, and I don't recognize a few ...
2
votes
2answers
66 views

Why is $S/R$ a ring extension?

If $S$ is a ring and $R \subset S$ is a subring it's common to write that $S/R$ is an extension of rings. I frequently find myself writing this and read it quite often in textbooks and lecture notes. ...
8
votes
1answer
681 views

What is the name of the $\in$ symbol and where does it come from?

It looks like a lower-case epsilon, but the Wikipedia page on epsilon states that they are not the same. Does this symbol have a typographic identification outside of mathematics? Where did the ...
0
votes
0answers
19 views

Notation used for H in Hyperbolid geomtry metric

This is suppose to be understood as $H_2^2$ Taken from the full equation : from lecture 3 of Cosmology on youtube by Leonard Suskind Can anyone please give some information on the notation ( ...
4
votes
0answers
40 views

Symbol for function composition [duplicate]

Possible Duplicate: History of $f \circ g$ Choice of symbols can be an indicator of intellectual allegiance. Consider how, back in the day (and before LaTeX regularised things so much!), ...
4
votes
3answers
499 views

Where did these symbols come from?

Where did these symbols come from? Like Pi, Fee and this weird E/sideways M and the triangle.
10
votes
2answers
369 views

What do Greek Mathematicians use when they use our equivalent Greek letters in formulas and equations?

Like for example, it's common to use the Greek letter $\theta$ to represent an angle right? So what would a Greek person doing math use to represent an angle? Would they also use $\theta$? Or is there ...
0
votes
1answer
78 views

Two $\psi$ functions

This is either a notation/history question or a point of confusion. In (for example) Ramanujan's proof of Bertrand's postulate, he uses the following notation: $\log [x]!$ means $\log ([x]!),$ in ...
5
votes
1answer
189 views

History of Lie algebra notation (in Fraktur)?

Does anyone know how it has become the standard to express Lie algebras in fraktur? I'd also like to know how it's established for each era and region, not only the origin. It doesn't seem that ...
9
votes
1answer
174 views

Articles on ideas in the history of mathematics notation?

I'm teaching a course this term on the history of scripts (writing systems) and rather than talking interminably about Semitic and Chinese and their spawn, I'd like to give students a more varied ...
2
votes
3answers
228 views

Is there a reasoning behind the depiction of the numbers as they are $\{1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9\}$?

Is there a reasoning behind the depiction of the numbers as they are: $$\{1,2,3,4,5,6,7,8,9\}$$ Is there any other form of depiction for $6$ and $9$ other than $VI$ and $IX$?
10
votes
2answers
1k views

Which symbol should be used for an empty set?

Currently, a discussion started on the German Wikipedia article for Empty Set (the German discussion), whether $\emptyset$ or $\varnothing$ should be used or is more common as a symbol for an empty ...
59
votes
5answers
2k views

Why does mathematical convention deal so ineptly with multisets?

Many statements of mathematics are phrased most naturally in terms of multisets. For example: Every positive integer can be uniquely expressed as the product of a multiset of primes. But this ...
5
votes
1answer
520 views

Who came up with the arrow notation $x \rightarrow y$?

I read that the arrow notation $x \rightarrow y$ was invented in the 20th century. Who introduced it? Each map needs both an explicit domain and an explicit codomain (not just a domain, as in ...
4
votes
2answers
200 views

Analytic versus Analytical Sets

Browsing MathOverflow I came across a question about analytical sets. Through the discussion following a comment made by our very own Asaf, I learned that bold face $\mathbf{\Sigma^1_1}$ and light ...
7
votes
0answers
475 views

How do Greek mathematicians name variables? [closed]

I've always wondered how people in Greek name variables that other people use greek letters e.g. $\theta$. They use latin?
6
votes
4answers
1k views

History of $f \circ g$

$f \circ g$ is usually interpreted as $f(g(x))$ although, as Google shows, $g(f(x))$ is used frequently too. My question: Does anybody know who was the first mathematician to use this symbol and what ...
6
votes
1answer
312 views

Was the definition of $\mathrm{erf}$ changed at some point?

I have seen two competing definitions of the error function. When I was an undergrad, Spiegel's Mathematical Handbook of formulas and tables (mine is the 1968 edition) was the definitive authority, ...
1
vote
1answer
453 views

This multiple integral notation, has it got a name? $\int dx \int dy \, f(y,x)$

I've encountered, on Wikipedia (examples below), an integration notation which seems to be prefix-style: the integral sign is immediately followed by the $\mathrm dx$ (or $\mathrm dy$, or what have ...
4
votes
0answers
219 views

Divisibility notation history

I'm writing a paper project for school about divisibility, so I'd like to include a bit of history about that subject. I'm mostly interested in notation of $|$ sign used in past, but everything else ...
9
votes
1answer
333 views

What is the “etymology” of the notation “:=”?

I've noticed that sometimes people use ":=" to set variables, like "With $f(x):=x^{2}$, we have $f(1) = 1$." This is also the variable definition operation in Mathematica. My question is, did ...
4
votes
0answers
206 views

Where does the 'divides' sign come from?

When $a$ divides $b$ we say $a | b$. Where does the $|$ sign come from? This is not homework, just personal interest in the history of mathematical language.
4
votes
2answers
153 views

Trig reciprocal function nomenclature?

The fact that the reciprocal of $\sin\theta$ is $\csc\theta$, and the reciprocal of $\cos\theta$ is $\sec\theta$ messed with my head for the longest time when I was taking trig. Why are the functions ...
8
votes
2answers
609 views

Why is “h” used for entropy?

Why is the letter "h" (or "H") used to denote entropy in information theory, ergodic theory, and physics (and possibly other places)? Edit: I'm looking for an explanation of the original use of "H". ...
10
votes
3answers
680 views

What was the notation for functions before Euler?

According to the Wikipedia article, [Euler] introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical ...
0
votes
1answer
112 views

Where does the % symbol originate from? [duplicate]

Possible Duplicate: What is mathematical basis for the percent symbol (%)? Where does the % symbol originate from?
9
votes
3answers
606 views

Who introduced the notation $x^2$?

In the book 'Problem Solving and Number Theory' I read The law of quadratic reciprocity was discovered for the first time, in a complex form, by L. Euler who published it in his paper ...
2
votes
0answers
651 views

History of mathematical symbols, especially the symbol for right angle

Yesterday a child asked me, why (historically) a right angle is denoted by an arc and a dot like in this picture: I dont't know it, but I am interested in it too, so I post this question to this ...
2
votes
1answer
308 views

Why are variables lowercased?

While contemplating the existence of math, I came across an interesting problem: Why are variables often lowercased? There may not be a reason, but if there is, I would like to find out. Maybe it's ...
1
vote
2answers
276 views

What is the origin of the prefix logic notation used in WFF 'N PROOF?

The classic "modern logic" game of WFF 'N PROOF uses a set of symbols to represent logical relations that I've seen used nowhere else: $C$ for then; $A$ for or; $K$ for and; $E$ for if and only if; ...
5
votes
1answer
464 views

Is the Unicode designed assuming the Continuum Hypothesis?

The Unicode chart for "letterlike symbols" states that א 2135 ALEF SYMBOL = first transfinite cardinal (countable) ב 2136 BET SYMBOL = second transfinite cardinal (the continuum) I ...
22
votes
4answers
1k views

Who invented $\vee$ and $\wedge$, $\forall$ and $\exists$?

I can rather easily imagine that some mathematician/logician had the idea to symbolize "it E xists" by $\exists$ - a reversed E - and after that some other (imitative) mathematician/logician had the ...