Muhammadu Buhari
When armed patrols go by, parents outside the school momentarily gain hope that they may have found their sons.
One theory widely aired on social media - and by some political opponents - was that Buhari had been replaced by a lookalike from Sudan called Jubril.
The country's president called the incident a "national disaster."
Many people are already comparing him to GOP nominee Donald Trump.
WHAT'S HAPPENING
The girls have been held hostage for more than two years.
President Muhammadu Buhari, elected last year largely on his vow to fight corruption, has vowed to recover "mind-boggling" sums of money stolen from the oil sector.
"I write this letter with a heavy heart, knowing you have endured another year separated from your daughters."
The fighting has killed 20,000 and displaced 2 million.
Boko Haram has carried out multiple attacks in northern Nigeria.