“giving the background of the times when Pi made progress ... ” (linha 2) → background

“Petr Beckmann holds up this mirror, giving the background of the times when Pi made progress — and also when it did not... ” (linhas 2 e 3) → mirror 

“Until 1963, he worked as a research scientist for the Czechoslovak Academy of Sciences, when he was invited ... ” (linhas 8 e 9) → research scientist 

“he is fluent in five languages and he has worked out a new generative grammar which enables a computer to construct... ” (linhas 12 e 13) → five languages 

“He also publishes a monthly pro-science, pro-technology, pro-free enterprise newsletter Access to Energy, in which he promotes the viewpoint ... ” (linha 15 e 16)  → newsletter Access to Energy