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In science, every scientist, such as a mathematician, a physicist or a biologist, has a list of unsolved problems he tries to solve in his lifetime.

Judaism is full of untouched / unsolved / partially solved issues.

Besides responsa, do prominent Rabbis have a "tasklist" - a list of problems in Halachah to solve in their lifetime?

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    Rabbis tend to behave more like judges than like scientists when it comes to novel rulings. While scientists may try to solve problems purely for the sake of knowledge, judges try to avoid making novel rulings until it becomes clear that a decision needs to be made on a previously unexplored area of the law. Rabbis tend to behave like that. They'd rather resolve a practical question based on precedent whenever possible, and will generally refuse to answer "theoretical" questions until there is a practical application.
    – Daniel
    Jul 29, 2018 at 19:44

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You write that "every scientist ... has a list of unsolved problems he tries to solve". I don't think this is true for every scientist but it is true that some disciplines (e.g., mathematics - see here) maintain lists of problems to be solved.

Similarly, most leading poskim are busy enough learning by themselves, writing and answering the reams of questions reaching them (dozens of questions a day is pretty common, R Shlomo Aviner is said to get 400-600!)

However just as in science, some leading poskim are indeed working on unresolved problems and writing ahead of their times. Two such works I know of (but I'm sure there are more and invite others to edit) are

  • R Yechiel Michel Epstein's Aruch HaShulchan he'Atid (Laying the Table of the Future), a parallel work to Aruch HaShulchan summarising and analysing the laws that will apply in Messianic times (from here)
  • R Moshe Avigdor Amiel's Ethics and Legality in Jewish Law where the former Chief Rabbi of Tel Aviv writes about how the Torah would apply to a modern state of Israel run fully according to the Torah
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  • I don't understand how those works are a list of problems to solve.
    – robev
    Jul 31, 2018 at 3:48
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    I marked as answered (I think for others it will work). I'm aware of existing works, such as HaYad, Shu"A, Shu"A HaRav MB etc. And as you mentioned others work on future "handbooks of Halachah". I spent quite some time myself thinking about this issue and it seems that it stems from a difference in principle between science and Torah. While science is an active research, Torah is a "passive" responsa or commentary to existing works. Your answer made it clear for me, thank you.
    – Al Berko
    Jul 31, 2018 at 9:09

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