Shai Haran (born 1958) is an Israeli mathematician and professor at the Technion – Israel Institute of Technology.
Born in Jerusalem on October 8, 1958, Haran graduated from the Hebrew University in 1979, and, in 1983, received his PhD in mathematics from the Massachusetts Institute of Technology (MIT) on "p-Adic L-functions for Elliptic Curves over CM Fields"[2] under his advisor Barry Mazur from Harvard University, and his mentors Michael Artin and Daniel Quillen from MIT.
[5] He gave a formula for the explicit sums of arithmetic functions expressing in a uniform way the contribution of a prime, finite or real, as the derivative at
Haran also studied the tree structure of the p-adic integers within the real and complex numbers and showed that it is given by the theory of classic orthogonal polynomials.
[12] He constructed Markov chains over the p-adic, real, and complex numbers, giving finite approximations to the harmonic beta measure.
[13] His recent work is focused on the development of mathematical foundations for non-additive geometry, a geometric theory that is not based on commutative rings.