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Re: Re: Mathematica skill level snippet(s)

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  • Subject: [mg104818] Re: [mg104745] Re: Mathematica skill level snippet(s)
  • From: John Fultz <jfultz at>
  • Date: Tue, 10 Nov 2009 06:04:18 -0500 (EST)
  • Reply-to: jfultz at

On Sun, 8 Nov 2009 06:49:11 -0500 (EST), Nasser M. Abbasi wrote:
> "AES" <siegman at> wrote in message
> news:hd3n4j$a2k$1 at
>> [Side question:  How many total words and symbols are there in the
>> **full** Mathematica vocabulary?  If you made a glossary of **every**
>> single documented term (symbol name, function, option, operator,
>> non-alphameric symbol, etc, etc in Mathematica 7), how many terms would
>> be in it?]
>> [I'm guessing maybe 3000 or 4000?  Or even more?]
> For version 7, Length[Names[=93System`*=94]] results in 3429
> I made a list for few version in my Mathematica versions table, click on
> the
> links in the last column to see the symbols.
> My theory is this: A Mathematica expert is someone have used more than 50%
> of these symbols. I am still working on my 5%  :)
> --Nasser

It's probably considerably less than 50%, actually.  Mathematica has really
quite a number of functions which are either fairly domain-specific or syntactic 
sugar (i.e. a function which accomplishes something the language can already do 
without much difficulty, but allows for simpler expression).  And, of course, 
these functions are far from equal in, for example, the
complexity of IdentityMatrix to Import (the latter of which I'm *still* looking 
up in the docs all the time for various tidbits).

I'm really just guessing here, but I suspect my own usage of these kernel 
symbols is below 25%.  Dan Lichtblau's is probably higher than mine, but I doubt 
he's at 50% either.

The fact that we make such productive use of Mathematica nonetheless, I think, 
is a mark in its favor.  You really can come in with a certain domain knowledge, 
plus a core body of functionality (mostly related to pattern and list 
processing) and be incredibly productive.

Stephen Wolfram wrote a blog post which included a ListPlot of the function
count from Mathematica's inception to version 7.

The plot is about a third of the way through the post.  Note the number here is 
significantly below your number because you're counting all System` symbols,
whereas he was counting System` *functions*.

John Fultz
jfultz at
User Interface Group
Wolfram Research, Inc.

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