" But a person who defiantly reviles Hashem that person shall be cut, cut off (hikores tikores) (Num. 15, 31)/ R. Akiva says: " hikores -in this world, tokores - in the World to Come. R. Ishmael says: "It also states, "that individual shall be cut off". Do I understand that to mean that he will be cut off in yet a third world? What does it teach us? (Nothing), the Torah speaks in the language of men. (Sifre Bamidbar 112) .
In 1888, R. David Tsvi Hoffman, a noted Posek and Rector of the famed Hildesheimer Rabbinic Seminary in Berlin , published a German language study in which he demonstrated that Halachic midrash stems from two disparate schools, each with its own terminology, interpretative approach and authorities quoted . He showed that the Mekhilta  and Sifre Numbers form one group of works and the Sifra and Sifre to Deuteronomy, another. The former come to us from the school of R. Ishmael and the latter from the school of R. Akiva . J. N. Epstein elaborated on this finding and devoted the third section of his seminal work, Mavo L'Sifrut Hattanaim, Tel Aviv, Dvir, 1957) to it .
R. Ishmael is mentioned 29 times and his students R. Yonasan and R. Yoshia 18 and 15 times respectively in the first tractate of the Mekhilta (Pischa). In the next four tractates, that are agadic and not halachic in nature, he is mentioned once in the first three and not even once in the fourth. He then again is referred to extensively in the succeeding tractates. The same situation holds true in Sifre Numbers, where 78-106, 131, 1234-141 contain almost no mention of R. Ishmael but the rest extensively cite him .
An important characteristic of many, if not most disputes between R. Akiva and R. Ishmael is that they do not result in halachic differences. Much of the time, the disagreement is solely about the correct source verse for an established Halacha. At other times the issue is theological or aggadic. This is very different from the disagreements between the Houses of Hillel and Shammai in which there is almsot always a halachic disagreement.
This point argues that R. Ishmael and R. Akiva set out to provide Scriptural references and to support received traditions. In other words, they took the proto-Mishna and systematically sought to link its laws to verses. What may have impelled them to do so?
I suggest that the exigencies of the time required this approach. In the days of these two great Sages and even before, various heretical movements threatened survival of traditional Judaism. Appeal to Oral Law meant little to these sectarians and only a Scriptural proof carried some weight.
It may be suggested that the method of providing Biblical support for existing laws, Biblical or Rabbinic in origin, may have come into use in order to counter movements that denied Oral Law and would not accept any law that could not be anchored in Scripture. There is, I think, an explicit source to this contention. "… the Saducees wrote a Book of Decrees…and when they wrote it out…if someone asked them, (they would say) go and look in the book…they would not know how to bring proof from the Torah. The Sages said to them, "Surely it says, 'According to the Torah they will teach you" (Megilat Taanit Ch 4)" . This citation from Megillat Taanis, the first work of Oral Law to be committed to writing , suggests that an appeal to a book such as Mishna could not possibly succeed for the heretics would simply respond, "You have your book and we have ours". Thus, R. Ishmael and R. Akiva were occupied largely with establishing each received law on the basis of Scripture.
1 Although this passage is strictly speaking from the end of Shelach rather than from Korach (which is out parsha), I chose it because it is such a good example.
2 This work was translated into Hebrew as L'Cheker Midrashei Hatannaim and published in a compilation Mesilot LeTorat hatannaim, Tel Aviv, 1928. All citations are from A. Yadin, Scripture as Logos: Rabbbi Ishmael and the origins of Midrash, University of Pennsylvania Press, 2004.
3 The Mekhilta is called Sifre to Shemos by some Rishonim, including Rashbam to Bava Basra 124b. For a list of others, see David Metzger's introduction to Kovetz M'farshei Mechilta.
4 This appears to represent an established fact. It has been misused by A. J. Heschel in his Torah min Hashemaim to posit theological bases for all disputes between R. Ishmael and R. Akiva. Readers of this series know that I strongly disagree with such methodology on ideological as well substantive grounds. J. Harris in How do we know this: Midrash and fragmentation of Judaism Albany SUNY-Press, 1995, denies R. Hoiffman's conclusion but offers no analysis to counter his.
5 Epstein shows that Toras Kohnaim, Kedoshim, also stems from R. Ishmael's school.
6See also Menachos 65a where R. Yochanan Ben Zakkai used Scriptural proofs to confound the heretics.
7 See Radal' Introduction to Pirkei D'Rabbi Eliezer.