Dwork is the daughter of mathematician Bernard Dwork.
The first of the Weil conjectures was proved by Bernard Dwork, and a completely different proof of the first two conjectures via l-adic cohomology was given by Alexander Grothendieck.
Burr received his Ph . D . in 1969 from Princeton University under the supervision of Bernard Dwork; his thesis research involved the Waring Goldbach problem in number theory, which concerns the representations of integers as sums of powers of prime numbers.
Katz graduated from Johns Hopkins University ( BA 1964 ) and from Princeton University, where in 1965 he received his master's degree and in 1966 he received his doctorate under supervision of Bernard Dwork with thesis " On the Differential Equations Satisfied by Period Matrices ".
As the result of local contributions by Bernard Dwork, John Tate, Michiel Hazewinkel and a local and global reinterpretation by J黵gen Neukirch and also in relation to the work on explicit reciprocity formulas by many mathematicians, a very explicit and cohomology free presentation of class field theory was established in the nineties, see e . g . the book of Neukirch.