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Парень попал в тюрьму на 25 лет за убийство и стал там математиком. Не имея даже аттестата об окончании средней школы, он сделал научное открытие.

For $$\alpha _0 = \left[ a_0, a_1, \ldots \right] $$α0=a0,a1,… an infinite continued fraction and $$\sigma $$σ a linear fractional transformation, we study the continued fraction expansion of $$\sigma (\alpha _0)$$σ(α0) and its convergents. We provide the continued fraction expansion of $$\sigma (\alpha _0)$$σ(α0) for four general families of continued fractions and when $$\left| \det \sigma \right| = 2$$detσ=2. We also find nonlinear recurrence relations among the convergents of $$\sigma (\alpha _0)$$σ(α0) which allow us to highlight relations between convergents of $$\alpha _0$$α0 and $$\sigma (\alpha _0)$$σ(α0). Finally, we apply our results to some special and well-studied continued fractions, like Hurwitzian and Tasoevian ones, giving a first study about leaping convergents having steps provided by nonlinear functions.