According to tradition, Rabbi Akiva lived for 120 years. If he died shortly after the Bar Kokhva rebellion, he lived to about 135 C.E., so if he was 120 at that time he would have been about 55 at the time of the destruction of the Temple (70 C.E.). This is consistent with the tradition that he did not study Torah until he was over 40; his name first appears in the Tannaitic literature in the Yavneh period.
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