R' Gamliel did indeed live and was very famous. Read all about him in Pirkei Avot.

It is highly unlikely that Paul / Saul ever studied with R' Gamaliel as he taught in Hebrew and all of Paul's misquotes are from bad Greek translations. Hyam Maccoby wrote:

The young Saul, we are told, left Tarsus and came to the Land of Israel, where he studied in the Pharisee academy of Gamaliel (Acts 22:3). . .

Yet Paul himself, in his letters, never mentions that he was a pupil of Gamaliel, even when he is most concerned to stress his qualifications as a Pharisee. Here again, then, the question has to be put: was Paul ever really a pupil of Gamaliel or was this claim made by Luke as an embellishment to his narrative? As we shall see later, there are certain considerations which make it most unlikely, quite apart from Paul's significant omission to say anything about the matter, that Paul was ever a pupil of Gamaliel's.

we learn of Paul's native city, Tarsus, and of his alleged studies under Gamaliel. Note that he says that, though born in Tarsus, he was 'brought up in this city' (i.e. Jerusalem) which suggests that he spent his childhood in Jerusalem. Does this mean that his parents moved from Tarsus to Jerusalem? Or that the child was sent to Jerusalem on his own, which seems unlikely? If Paul spent only a few childhood years in Tarsus, he would hardly describe himself proudly as 'a citizen of no mean city' (Tarsus). Jews who had spent most of their lives in Jerusalem would be much more prone to describe themselves as citizens of Jerusalem. The likelihood is that Paul moved to Jerusalem when he was already a grown man, and he left his parents behind in Tarsus, which seems all the more probable in that they receive no mention in any account of Paul's experiences in Jerusalem. As for Paul's alleged period of studies under Gamaliel, this would have had to be in adulthood, for Gamaliel was a teacher of advanced studies, not a teacher of children. He would accept as a pupil only someone well grounded and regarded as suitable for the rabbinate. The question, then, is where and how Paul received this thorough grounding, if at all. . . there are strong reasons to think that Paul never was a pupil of Gamaliel.

סופי

And everything that Sarah tells you, listen to her voice. Bereshit (Genesis) 21:12