I have received an email this day  about Author Awarded 2020 [Nobel Prize in Physics](https://www.aip.org/science-news/nobel2020?utm_source=AIP%20Publishing&utm_medium=email&utm_campaign=11878021_JMP%20Nobel%20Prize%20Oct%202020&dm_i=1XPS,72L51,1G5FY8,SK5UG,1) such that the winners are :  **Roger Penrose**, **Reinhard Genzel** and **Andrea Ghez** ,[Roger Penrose](https://en.wikipedia.org/wiki/Roger_Penrose)  receives one-half of the prize for the discovery that black hole formation is a robust prediction of the general theory of relativity." Genzel and Ghez share one-half "for the discovery of a supermassive compact object at the centre of our galaxy,[Roger Penrose](https://en.wikipedia.org/wiki/Roger_Penrose) is an English mathematical physicist he has made contributions to the mathematical physics of general relativity and cosmology , I have checked some of his works which related to mathematics I have got [this paper](https://aip.scitation.org/doi/abs/10.1063/1.523151) entitled **The Kähler structure of asymptotic twistor space** seems the Author has widely contribution  generally to  mathematics of general relativity like tensors and manifolds , Now my question here is :

>>**Question**
What are contributions of Sir Roger Penrose the winner of Nobel prize 2020 to mathematics of general relativity like tensor and manifolds  ?

We may motivate this question adding a  nice question which it is pointed out in the comment by  @Alexandre Eremenko  such that he asked: Is Sir Roger Penrose the first true mathematician to receive a Nobel prize in pysics? If the answer is yes then Sir Roger Penrose  would say  us "before being a physicist you should be a mathematician"