TDSM 10.27
From The Data Science Design Manual Wikia
For an estimator to be effective, the distance between every point and its neighbors has to be on average smaller than a value d. In 1D, this requires the number of training points n≈1/d points on average.
If the number of features (number of dimension) is p, the minimum distance between 2 points is now dp⇒ the model would need np training points. As p increase linearly, the number of training point increases exponentially.