http://www.ams.org/news?news_id=6175
In the article I just read about him in popular mechanics (I couldn’t find it online), it says “But Havens couldn’t Google it...”
I find that fascinating, if he had been able to google it and see that it was “unsolvable” who knows what would have happened but instead he worked at it and ultimately solved an unsolvable equation.
Musar shmooz anyone?
For α0=[a0,a1,…] an infinite continued fraction and σ a linear fractional transformation, we study the continued fraction expansion of σ(α0) and its convergents. We provide the continued fraction expansion of σ(α0) for four general families of continued fractions and when |detσ|=2. We also find nonlinear recurrence relations among the convergents of σ(α0) which allow us to highlight relations between convergents of α0 and 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.
Absolute Chinese to me
Very inspiring story though.
(As an aside, solitary confinement is an inhumane cruel and unusual punishment that should be outlawed in penitentiaries in any civilized country, unless the inmate poses a clear and present danger to others. It is entirely overused in a despicable manner.)