Apart from the fact that we both shared a Jewish identity I had one thing in common with the late Rabbi Yosef Elyashiv, whose funeral in Israel last week was reportedly attended by 250,000 people. Neither he nor I had ever studied at a yeshivah. In my case, this was more by design than by accident: my career took me into academia at the age of 18 and I have never been inclined to leave. That's not to say I haven't engaged in talmudical studies. I have, but as an autodidact, at my own pace. This has enabled me to come to these texts unencumbered by the slightest pressure to conform - either to a particular interpretation or to any wider view of the Jewish world.

And so it was in the case of Rabbi Elyashiv. Not only did he never study at a yeshivah, he never taught in one. But his knowledge of the sacred texts, and of the commentaries on them, and of the commentaries on the commentaries, was vast. With the death of Rabbi Elazar Schach in 2001, he assumed, by common consent, the leadership of the Lithuanian strictly Orthodox. Within this kehillah his word was law. His endorsement of a particular cause was enough to secure its automatic support among Ashkenazi Charedim everywhere. For instance, when Rabbi Rakow of Gateshead determined to force Lord Sacks to rewrite Dignity of Difference (within which book Lord Sacks had suggested that Judaism did not enjoy a monopoly of religious truth), it was to Rabbi Elyashiv alone that Rakow turned for support. Rabbi Elyashiv ruled that no Jew should have the book in his home. Little wonder Lord Sacks hastened to rewrite the offending passages.

But he had weaknesses. We have it on the authority of one of his daughters that he was a stern and distant father. "When we were children, he didn't know us at all. He didn't speak to us, whether we were good or bad," one was quoted as saying by The Times of Israel last week. His life revolved instead around an obsession with Torah study, and there is plenty of evidence that, as he grew older, his concern was less with the practicality of any particular ruling than with its theoretical symmetry.

One of his earliest rulings concerned a Yemenite girl whose husband had deserted her. Rabbi Elyashiv found a way of annulling the marriage, thus freeing the girl from the status of an agunah.

Contrast this with, for example, his later insistence that a lapsed convert could have the conversion revoked - a ruling that many eminent rabbonim dispute as having no halachic basis, and that has caused untold misery. Elyashiv was adamant that no pressure whatever could be put on a husband who refused his wife a get. He instinctively opposed any move towards equality between men and women, especially in divorce proceedings, and he naturally condemned any recourse to secular studies by Charedi wives, even if they were merely designed to enable the wives to help support their yeshivah-bound husbands. He banned the internet and mobile phone. Only last year, he is reported to have ruled that women who are thought to be behaving or dressing immodestly should be "publicly humiliated".

He ruled that no Jew should have the book in his home

Thinking about Rabbi Elyashiv brought to mind the career of another great exponent of Lithuanian Orthodoxy, Rabbi Nosson Finkel, head of the Mir Yeshiva in Jerusalem, who died last year. Finkel, an all-American boy and consummate baseball player, expanded this famous talmudical academy from around 1,000 students (1990) to almost 6,000, not including 1,500 married students. His policy has been described as "open door". He admitted anyone and everyone, including many hundreds - perhaps thousands - unsuited to yeshivah life but whose parents were anxious for them to dodge military service.

I have to ask - coming from a Polish-Lithuanian Orthodox background myself - what legacy Rabbis Finkel and Elyashiv have left. Neither of them strengthened the Lithuanian tradition. Neither was able to stem the advance of an obscurantist and in some respects heretical Chasidism, against which my hero - the 18th century Gaon of Vilna - struggled all his life. I never once heard either Elyashiv or Finkel denounce this obscurantism or take issue with it. That is a measure of failure, not success, and of weakness, not strength.