His proof was controversial , and there is currently ( as of 2016 ) no consensus on whether his proof is complete .
In 1978 Wilhelm Klingenberg published a proof that smooth compact manifolds without boundary have infinitely many closed geodesics .
Wilhelm Klingenberg 's proof was controversial , and there is currently ( as of 2016 ) no consensus on whether his proof is complete .
In 1978 Wilhelm Klingenberg published a proof that smooth compact manifolds without boundary have infinitely many closed geodesics .