I'm no encyclopædist - I do not usually have the temperament to do extensive research to create an encyclopædic article - but it is natural for me to proofread as I read, so most of my edits will likely be relatively minor fixups.
I have long felt that the Internet should be making it possible to learn any aspect of human knowledge that exists - from any starting point, to any depth. While Wikipedia cannot assume the entire burden of making that possible, it clearly has a major role to play and I look forward to helping it do so.
Some things I hope to do as time, energy and knowledge permit.
Learn some more about finite fields and group theory. Go back to the AKS Primality Test paper Prime is in P and finish following the proof. Further extend the AKS Primality Test article, to include the full algorithm (in a manner comprehensible to programmers) and the full proof. Find, read and grok the more recent papers that improved on the algorithm. Add articles (where not already present) to describe the improved algorithms. Add a summary article on AKS-style tests to bind them all.
Alea iacta est
Information is scattered between Julius Caesar, Crossing the Rubicon and List of Latin phrases, and Wiktionary is entirely deficient: 'alea', 'iacta' -> 'iactus' -> 'iacere', and the full phrase 'alea iacta est'
List of prime numbers
Now the list is alphabetised, restore as cross-references those types that were previously related by proximity.
Somewhere, show that , and extend Fibonacci prime to use this to clarify the divisibility assertion.
Missing math articles
Work through some more of Wikipedia:Missing science topics/Maths1.
Add to the types of clue, and improve some examples. Extend or create a new page for thematic cryptics along the lines of The Listener crosswords (though once you start describing these it is difficult to imagine where you might stop). Expand or split off discussion of The Listener Crossword from The Listener (British magazine). Mention notable compilers, The Magpie (and defunct predecessors).
The various things I've already forgotten because I didn't write them down