"The little squares look the same," Elijah answered.
"Do the colors have to look the same, or just the lines?" she asked. "And if the squares repeat, must the coloring repeat after one square, after ten squares, or at all?"
Elijah stared at his drawing. He had been treating three different ideas as if they meant the same thing, and no one had pointed that out before. He reached for his pencil and began writing definitions along the edges of the paper. Okonkwo watched with interest, not because she believed a miracle had arrived, but because the boy's first response to discovering he was wrong was curiosity rather than embarrassment.
She introduced him to graphs, to vertices and edges, to the famous four-color theorem, and to the difference between drawing a shape and proving something about every possible shape. She also showed him a collection of older papers on a fictional problem local researchers called the Hartwell periodic-extension conjecture. In 1987, mathematician James Hartwell had asked for a uniform constructive method of extending four-color assignments across an entire class of repeating planar region networks while meeting specified boundary compatibility rules. The ordinary four-color theorem already addressed whether planar graphs could be colored at all; Hartwell's narrower problem was about producing a compatible repeating assignment under extra conditions, with a finite certificate explaining why the construction would not fail at distant seams.
It was the kind of specialized question a child would never have stumbled across in a school textbook. Hartwell's statement had also changed slightly across decades of papers, as researchers clarified which compatibility conditions belonged in the definition. Some formulations were plainly false; others had resisted attempts to settle them. Elijah could not pronounce half the technical vocabulary, but the pictures made sense. He saw the same kind of awkward seam that had appeared on his cafeteria-tile drawings, and he recognized the feeling of a question that had not yet been asked carefully enough.
"Am I allowed to work on this?" he asked.
Okonkwo laughed, surprised. "You are allowed to work on any question you can understand, Elijah. But there is a difference between being allowed to explore and knowing you've solved it. We're going to be very careful about that." She handed him a clean notebook and promised to help him find sources. He refused the new notebook because it looked expensive, then accepted it when she explained that a retired librarian had donated a whole box of them.
He wrote his name on the cover in capital letters. Beneath it, he drew four tiny squares in blue, red, yellow, and green. There was no dramatic music, no sudden revelation, and no hint that a symposium in Boston would one day pause to study those pages. There was only a small boy in a warm room above a laundromat, trying to understand why colors that behaved themselves inside a picture became troublesome when the picture went on forever.