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Then, in November, she posted on YouTube a video about doodling in math class, which married a distaste for the way math is taught in school with an exuberant exploration of math as art .

At first glance, Ms. Hart’s fascination with mathematics might seem odd and unexpected. She graduated with a degree in music, and she never took a math course in college.

The ensuing attention has come with job offers and an income. In one week in December, she earned $300 off the advertising revenue that YouTube shares with video creators. She is also happy that, unlike in her early efforts, which drew an audience typical of mathematics research — older and male, mostly — the biggest demographic for her new videos, at least among registered users, are teenage girls.

Dr. Atkinson, an expert at applying mathematical methods to linguistics, has found a simple but striking pattern in some 500 languages spoken throughout the world: A language area uses fewer phonemes the farther that early humans had to travel from Africa to reach it.

Dr. Atkinson is one of several biologists who have started applying to historical linguistics the sophisticated statistical methods developed for constructing genetic trees based on DNA sequences.