“What’s trigonometry?” some pureblood at the World Cup asks him. “It’s a variant of arithmancy,” says Harry, who’s become somewhat adept at bullshitting translations between magical and muggle things when the incentive was avoiding Aunt Marge’s wrath.
Nobody’s ever heard of trigonometry except for one elderly pureblood witch, who had heard it mentioned once back in school by a classmate who went on to become a famous name in advanced and extremely theoretical arithmancy.
Everybody loses no time in agreeing that trigonometry must be this tremendously advanced arithmancy specialization and Dudley Dursley must be an absolute arithmancy prodigy to the point where even the arithmancy buffs don’t want to risk making themselves look stupid by asking him about his research.
OBVIOUSLY Dudley goes to some extremely foreign wizarding school with an advanced research program available. There can’t be many of them with an advanced “trigonometry” program like that, so nobody asks which school it is because what if there’s only one of them and they look stupid for not knowing about it?
Besides, Harry Potter, the Boy Who Lived, is giving him the time of day like he’s someone really important, so, yeah.
Oh, yeah, he’s definitely the type of absent-minded brilliance that forgets his wand regularly, head in the clouds with all those theorems.
Dudley actually takes up computer programming at Smeltings. He tried it out because he likes video games, and then sort of fell in love with the process, the building something up out of lines of code, the thrill of success when it works. The awestruck reactions of wizards who see a couple of his notebooks when he sits there scribbling out code on a spiralbound notebook with a ballpoint pen is almost tangible.
The ballpoints and the notebooks take some suspicion for their muggleness until Harry points out that you don’t need to pay attention to how much ink is left and when you need to dip it, so it’s perfect for somebody who might want to scribble out whole pages of that stuff without noticing whether they’ve run out of ink, and the notebooks have pages so you could remember where something is. Pretty soon quill-tipped ballpoints are all the rage and spiralbound parchment stacks are being sold in all the stores.
Somebody asks Dudley about his family history. “Oh, they’ve all been like me,” he says, “as far back as anybody remembers” and he means not-a-wizard, but everybody thinks the opposite.
His father is blustery and yells and prone to explosive bursts of anger, he says, and his mother is obsessed with cleanliness and etiquette, and everyone is perfectly happy to never suggest they’d like to meet them.
Once Dudley figures out that everyone thinks he’s a wizard, he and Harry have a solid laugh over it and Harry teaches Dudley what he’d need to know to continue the deception. Fred and George are brought into the equation and provide him with lots of cool tricks and such so that he can appear to do some small bits of magic now and again.
He eventually marries Daphne Greengrass, who knows about his muggleness at that point and loves the idea of getting one over on her overly bloodpurist parents without them ever knowing about it. Harry and Sirius quietly gift them Number Twelve, Grimmauld Place, and the assumption that Dudley has the sort of money that buys a historic Pureblood property as a starter home goes round and round.
Dudley ends up on the Board of Governors, and later Minister for Magic, and in their old age Petunia and Vernon suffer the mingled pride and fury that their son is a Government Minister and they can’t brag about it.
