Answer: Leonhard Euler.
Swiss-born Euler is held to be one of the greatest mathematicians in history. He made pioneering contributions to several branches of mathematics and introduced much of the modern mathematical terminology and notation.

Answer: No, it's not!
Adding up the divisors of 36: 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 = 55

Answer: 312211
John Conway's "look and say" sequence has no digits other than 1, 2, and 3 in it, unless the seed number contains such a digit or a run of more than three of the same digit. A degenerate sequence appears with the seed of 22.

Answer: No

Answer: 5
Portman collaborated (using her birth name, Natalie Hershlag) with Abigail A. Baird, who has a collaboration path (Gazzaniga, Michael S. -> Victor, Jonathan D.) leading to Joseph Gillis, who has an Erdős number of 1.

Answer: No

Answer: 160

Answer: 49

Answer: Paul Erdős, of course!
As the Erdős number describes the "collaborative distance" in authorship of mathematical papers between mathematician Paul Erdős and another person it is only natural that Paul Erdős holds this position.

Answer: 91