Magic had been the most important thing lost in the purges three hundred years ago.  Out of fear, humanity had discarded one of their greatest gifts, remorseless in destroying anyone who dared to practice magic, or even showed signs of possessing the ability.  Magical creatures were hunted to extinction- species like phoenixes and unicorns existed now only as specimens preserved in museums, creatures of legend as much as reality.  Of course, people doubted that they were all gone, even in this enlightened age, as humanity began to understand the true meaning of all they had lost, the potential that their ancestors had strangled with their own hands. 
But it was right for them to doubt.  The affinity for magic was coded deep into their kind, and it was only a matter of time, a matter of chance, before it would resurface.
With so much time having passed since magic was commonplace, Matilda's parents didn't recognise the signs.  Tilly remembered staring at the campfire on her first camping trip with her family, imagining how the flames would dance and waver, how they would almost seem to follow the instructions she gave them in her thoughts.  She told no one, rationalised it as coincidence and nothing more.

Kids didn't pretend to be mages.  The loss was too deep even for that- magic was the sort of thing spoken of in reverent tones and careful words, or not mentioned at all. 
Once she began to truly suspect something strange was happening, Tilly did not go to her parents and say "I think I'm magic."  She said "I think I'm losing my mind," and her parents, concerned, booked her in with the school counsellor.  Their dear Tilly was not the kind of teenager who made things up, and if she felt as if she was somehow overhearing the thoughts of her teachers and classmates, well, something surely had to be wrong. 

The counsellor, a kindly older woman by the name of Margaret, asked Tilly to demonstrate this... unusual talent, and she successfully guessed what number Margaret was thinking of ten times in a row.
"Let's try one more time," Margaret suggested. 
"I know you're trying to trick me into getting it wrong.  You're thinking of the letter B, not a number." Tilly sighed, still half-convinced she was hallucinating it all somehow.  If her mind was playing tricks on her, that was something real, something that could be sorted out, she hoped.  Magic hadn't been real for centuries.
"Oh." Margaret said, very faintly.  She had, in fact, been thinking of the letter B.  "I think I'm going to call the principal."  

The principal didn't know what to do either, and after testing her 'ability' himself, he made a call to the Magical History department of the local university.

Matilda Richards, the first known mage in the last three centuries, now sat outside the office of the head of the department, surrounded by aged artefacts of a world long dead... or so everyone had thought.