Math Symbol Frequencies • Hacker News Board

Re: Math Symbol Frequencies

#11

Post by dleeftink » Sun, Jun 08, 2025, 3:02 AM UTC

A related report from way back, that counts expressions instead of symbols[0]. The counting procedure used in OP's referenced table might benefit from first extracting expressions, and then counting individual symbol frequencies.

[0]: Watt, S. M. A Preliminary Report on the Set of Symbols Occurring in Engineering Mathematics Texts. In Proceedings of MICA 2008: Milestones in Computer Algebra 2008.

Re: Math Symbol Frequencies

#12

Post by xelxebar » Sun, Jun 08, 2025, 3:03 AM UTC

VonTum wrote: post #2

I had a bit of a chuckle that apparently 5 out of 50000 opening "(" parentheses weren't closed, but then I saw that 2 out of 12000 "]" brackets weren't opened! What criminal is using these standalone?

Probably not this, but J uses lonely brackets and braces as standalone operators: https://code.jsoftware.com/wiki/NuVoc.

Re: Math Symbol Frequencies

#13

Post by dleeftink » Sun, Jun 08, 2025, 3:05 AM UTC

mkl wrote: post #6

layer8 wrote: post #4

It seems weird that ∋ would be the sixth-most frequent symbol, while ∈ doesn't figure at all.

Agreed. Even stranger to me is @ as the fourth most common operator, supposedly more common than +. The whole thing seems dubious.

The table byline says: "The @ symbol is used to encode mathematical formulas for the computer. It is not visible to the user."

Re: Math Symbol Frequencies

#14

Post by devrandoom » Sun, Jun 08, 2025, 3:42 AM UTC

VonTum wrote: post #2

I had a bit of a chuckle that apparently 5 out of 50000 opening "(" parentheses weren't closed, but then I saw that 2 out of 12000 "]" brackets weren't opened! What criminal is using these standalone?

I hope you irony of your comment isn't lost.

Re: Math Symbol Frequencies

#15

Post by yorwba » Sun, Jun 08, 2025, 4:33 AM UTC

mkl wrote: post #6

layer8 wrote: post #4

It seems weird that ∋ would be the sixth-most frequent symbol, while ∈ doesn't figure at all.

Agreed. Even stranger to me is @ as the fourth most common operator, supposedly more common than +. The whole thing seems dubious.

Its number of occurrences is 103,090. In the master's thesis identified as the original source https://cs.uwaterloo.ca/~smwatt/home/students/theses/CSo2005... the Unicode value of the operator occurring 103,090 times is given as 2061, and the thesis helpfully explains that

Unicode 2061, 2062 and 2063 are invisible operators. TeX does not have any of these invisible operators. These invisible operators result from the TEX to MathML conversion.

– 2061 – Function application

– 2062 – Invisible times

– 2063 – Invisible separator

And Wikipedia says that function application may be represented as

U+2061 FUNCTION APPLICATION (⁡, ⁡) — a contiguity operator indicating application of a function; that is an invisible zero width character intended to distinguish concatenation meaning function application from concatenation meaning multiplication. https://en.wikipedia.org/wiki/Function_application#Represent...

I'm not sure though how an automated conversion process would be able to distinguish between these.

Re: Math Symbol Frequencies

#16

Post by smcin » Sun, Jun 08, 2025, 7:29 AM UTC

gfaure wrote: post #5

VonTum wrote: post #2

I had a bit of a chuckle that apparently 5 out of 50000 opening "(" parentheses weren't closed, but then I saw that 2 out of 12000 "]" brackets weren't opened! What criminal is using these standalone?

There is the normal notation for half-open ranges, which would lead to unbalanced brackets.

Ah. Good point.

Re: Math Symbol Frequencies

#17

Post by jxjnskkzxxhx » Sun, Jun 08, 2025, 1:25 PM UTC

VonTum wrote: post #2

I had a bit of a chuckle that apparently 5 out of 50000 opening "(" parentheses weren't closed, but then I saw that 2 out of 12000 "]" brackets weren't opened! What criminal is using these standalone?

I mean.... You just used those standalone.

Re: Math Symbol Frequencies

#18

Post by omoikane » Sun, Jun 08, 2025, 4:18 PM UTC

I wonder if these tables are telling us that it's more conventional to write "a a". Is there a style guide for writing equations?

Re: Math Symbol Frequencies

#19

Post by seanhunter » Sun, Jun 08, 2025, 4:39 PM UTC

layer8 wrote: post #4

It seems weird that ∋ would be the sixth-most frequent symbol, while ∈ doesn't figure at all.

There definitely is some sort of methodological problem. It thinks \otimes is more than 4 times more frequent than the plain good old fashioned integral sign. There’s absolutely no way that is the case.

Re: Math Symbol Frequencies

#20

Post by jostylr » Sun, Jun 08, 2025, 7:38 PM UTC

omoikane wrote: post #18

I wonder if these tables are telling us that it's more conventional to write "a a". Is there a style guide for writing equations?

Could be. We tend to think of a number line going in that order, that is, the lower numbers are to the left. What is interesting is that being > 0 is often a condition, such as epsilon > 0. Though that is often paired with something like 0 < |x-a| < epsilon. I have often wondered about an alternate mathematics in which the inequality sign was always pointed in the same direction and whether that would ease the difficulty students have with inequalities.