Please capitalize where necessary: in 1921 he proved his famous theorem on random walks on an integer lattice.
A: In 1921 he proved his famous theorem on random walks on an integer lattice.

Please capitalize where necessary: in 1932 karen blixen had finished her collection of tales, written in english.
A: In 1932 Karen Blixen had finished her collection of tales, written in English.

Please capitalize where necessary: it leads them forward to cosmic consciousness, which is the entrance to real cosmic life in the highest worlds beyond reincarnation and physical darkness, misfortune and suffering.
A: It leads them forward to cosmic consciousness, which is the entrance to real cosmic life in the highest worlds beyond reincarnation and physical darkness, misfortune and suffering.

Please capitalize where necessary: this collection is a very mixed bag.
A:
This collection is a very mixed bag.