As those who know me can attest, I rarely read fanfiction. I've written an awful lot of it (a million words or so with Kathleen in our Saint Seiya/Samurai Troopers/DBZ universe, and more elsewhere), but it's really very infrequent that I find a fanfiction story that is worth my time to read, and most of it is deep in the past, such as Ryan Matthew's Dirty Pair fics or Bishoujo Senshi Sailor Ranma (multiple authors).
Harry Potter fandom, by its sheer volume, could be expected to produce a few real gems. Naked Quidditch (https://www.fanfiction.net/s/3689325/1/The-Original-Naked-Quidditch-Match) is something of a classic, and certainly very funny. The fandom has also produced what may well be the most popularly read fanfic ever, Harry Potter and the Methods of Rationality (http://hpmor.com/).
But none of the fics I've ever read have struck me so powerfully as The Arithmancer and its sequel Lady Archimedes (start here: https://www.fanfiction.net/s/10070079/1/The-Arithmancer ) by "White Squirrel", and, indeed, few books of any sort, fan or published fiction, have worked so well for me. I was directed to it by a side comment in a discussion on (IIRC) James Nicoll's journal, and ended up badly hooked once I started.
There are a few parallels between The Arithmancer and Harry Potter and the Methods of Rationality (henceforth abbreviated as HP&tMOR). In both cases a major character of the original books uses rational, scientific approaches to evaluate magic and this causes changes large and small in the events of the various books. In HP&tMOR, of course, it's Harry Potter, whose Aunt Petunia married an intelligent and rational man rather than the abominable Vernon Dursley, and who is thus raised with a scientific point of view (and much better treated than in the original, of course!).
In The Arithmancer, it is Hermione Granger we follow; The core conceit of The Arithmancer is that while Hermione is undoubtedly generally brilliant, she has a particular facility for mathematics which turns out to apply to magic, and its speciality of Arithmancy in particular. Hermione, child of Muggle parents, receives her letter from Hogwarts and – once she and her parents are convinced this is no trick – is extremely enthusiastic to start her studies at an honest-to-god school of magic.
The first thing that stands out about this fic is that all of the characters we meet are recognizable. One of the hardest challenges of writing in someone else's universe is that you don't write the way they do, and that makes it almost trivially easy to screw up the characters. White Squirrel nails the characters, and even expands on them in ways that make many of them more interesting (and often likeable) people.
Part of this, of course, is that she's writing from another point of view, giving us how Hermione sees the people, how she feels about them, and so on, and since pretty much anyone who's going to read The Arithmancer will have read the original Harry Potter series, her observations build upon and supplement what we know in the series. But a lot of it is that she pays more attention to the characters – and as time goes on, she pays a lot of attention to characters we only saw sketched out, like Cedric Diggory, Professor Vector, and others, in the original.
This is a massive fanfic. The Arithmancer covers the first four years, and Lady Archimedes follows on to complete the set – though it is not yet complete, somewhere in the Sixth Year at this point. The length may be daunting, but it grabbed my attention so much that it took only a relatively few days before I'd raced through the entire thing.
One of the key challenges of writing a fic of this nature – where you bring in knowledge to the universe that the original author either did not know, or didn't consider important to the story (and Rowling would be correct – she was able to tell her story without worrying about these things) – is that you may break the story in any of a number of ways. True, that "break" may actually be part of your plan, but if it's not handled well, it will make the story painful to read; for instance, if your introduced new knowledge suddenly allows 11 year olds to defeat Voldemort and all his foes trivially, you make the older people look like idiots. Or, alternatively, you make your one bright protagonist into the worst sort of Mary Sue, solving all problems with her awesomeness and leaving all the other characters in the dust, or at best following her as a cheerleading squad.
White Squirrel deftly avoids these pitfalls. Yes, Hermione slowly develops unique, and sometimes terrifying, applications of magic, but the way in which magic works keeps her progress to a reasonable pace, throws interesting obstacles in her way, and involves many other people. She develops relationships with multiple characters that throw light both on their character, and hers, and the relationships she establishes are important to the plot.
One of the most brilliantly artful features of The Arithmancer and its sequel is this: Hermione is made the main character (and a strong and interesting one she is), and she has major and important effects on the story and characters… and yet the general outline of events in the plot remains largely untouched, and some of the most important personal events and contacts are not wiped out. She still ends up befriending both Harry and Ron, in a similar fashion to the original, but with a far more believable sequence of events leading to it. Voldemort's major plots still are carried off, without either sidelining Hermione or taking away some of Harry's important aspects.
The latter's really well done: Hermione gets victories, and changes events significantly, but The Boy Who Lived isn't reduced to a secondary character. Instead, the solution to various events – such as the confrontation with the Basilisk in the Chamber of Secrets – gives both of them important things to do.
The plot starts to change, inexorably, in later books, but not enough to keep us from instantly knowing which book we're in, or the overall shape of the challenges to be confronted by our heroes. And despite Hermione's sometimes quite mindboggling inventions in magic, the two great figures of the series – Dumbledore and Voldemort – are not lessened by her presence; indeed, when we finally see the conflict between them in the Ministry of Magic, Hermione personally registers the vast difference between her new skill and tricks and the sheer power and virtuosity of the most powerful wizards in the world.
It is impossible to read this without some comparison to HP&tMOR, and – putting it bluntly – the comparison does not go well for HP&tMOR. Both The Arithmancer and HP&tMOR are fics that concentrate on something that the author knows and is interested in (mathematics for the one, and rational thought for the other), but their approaches, especially to characters, are quite divergent. HP&tMOR's version of Harry is something of a jerk, and despite his vaunted intellect often misses things that a reader (or at least this reader) finds obvious. He's more private and less trusting, meaning much less interaction with the other characters in ways that will garner sympathy. He may have improved after, say, Chapter 25 or so (I think that's as far as I read) but it would take a lot of redemption to change my opinion. In addition, HP&tMOR is a more... didactic fic; Eliezer Yudkowsky has been up-front about part of the purpose of the fic being to convey the methods of rational thought to readers, and this affects it somewhat negatively when considered solely as a story.
By contrast, the Hermione and Harry of The Arithmancer are recognizably the same people, and grow up in ways that even Rowling didn't carry off well. We also see them examining their world critically and addressing issues that always bothered me as an adult (for instance, Snape's utterly intolerable behavior in classes, Harry's mistreatment at the hands of his relatives, and the reactions of Hermione's parents to the terrifying threats she keeps encountering). This is a version of the Potterverse that makes more sense in both a logical and an emotional way. It couldn't exist without the originals, but in many ways it is better than the original.
This includes character relationships. Some of the relationships of the original book remain the same – most notably the three-man-band of Harry, Hermione, and Ron, at least for a large part of the series – but others change, and not just relationships between the kids but between adults and the children as well.
We get to see a real mentoring relationship between an adult wizard and a student of promise – something that Rowling occasionally touched on but never really went into. Professor Vector was barely mentioned in the books, but here the Arithmancy professor (a former Slytherin!) plays a huge part and is lovingly detailed and characterized.
We see Hermione in a real daughter–parent relationship with her parents, and how the constant cycle of peril affects their view of the magical world and of Hogwarts in particular (both Hermione and her parents try to get her OUT of Hogwarts to avoid the apparently inevitable deadly danger that shows up every year).
Hermione, as she gets older, actually confronts Dumbledore about certain poor decisions… and he recognizes her right to do so, as Dumbledore is nothing if not honest with himself (due to his own poor choices earlier in life). Despite this and other occasional opposition to authority, White Squirrel's depiction of Hermione and the teachers remains true to their nature; this was one area that HM&tMOR bothered me with, having Harry essentially pressure/bully McGonagall within the first day or two of meeting her, with some rather sophomoric manipulation that the McGonagall of the original books would have shut down cold. The Arithmancer keeps the characters we know, with their good and bad points, and all relationships are based on those characters.
J.K. Rowling admitted, after the series was done, that the Hermione-Ron pairing really didn't work so well, and that Harry-Hermione was an obviously better choice from a more disinterested point of view. In The Arithmancer, Hermione and Harry are very close friends – a friendship more clearly drawn and interesting than in the original – but White Squirrel chooses not to go down that path as a romance. Instead, she takes a surprising turn which, in context of the universe of the fic, makes perfect sense, and pairs her with George Weasley – one of the few people who's bright enough to at least try to keep up with her in the magical realm, and not at all bothered by her sometimes dangerous experimentation.
Speaking of characters… it takes no little skill to make one of the most repulsive characters in fantasy literature more repulsive, but White Squirrel achieves it through his more detailed and unflinching depiction of Dolores Jane Umbridge. Vile though she was in the original Harry Potter and the Order of the Phoenix, Umbridge is at least twice as bad in The Arithmancer/Lady Archimedes. Rarely have I wanted to see a character humiliated so badly.
Now, while I have indeed been pretty much unreservedly gushing, this doesn't mean the story is without flaws. There are occasional misuses of words that make me twitch, and other common flaws in posted fics (though, thankfully, vastly less present in this than in most).
Despite these, leaving aside the copyright/trademark issues, The Arithmancer would be perfectly publishable material, with only one real sin: there's a fair amount of rather jarring viewpoint-switching in the story, and it's not properly signaled by scene or chapter changes. While most of the story is from Hermione's point of view, there are many points where White Squirrel clearly wants to let the reader know the thoughts of another character and just jumps blithely into their head, even if it's just a paragraph or two, and then back to Hermione, without warning in either direction.
Even this, however, is only a relatively minor blemish; obviously it didn't stop me from gobbling down the entire series as fast as I could make time for it. Its TRUE flaw is that IT ISN'T FINISHED AND GOD I WANT TO SEE HOW IT ENDS…
Naturally, highly recommended!