Soon after her birth, her father accepted a job as the director of the Westinghouse facility, resulting in the family move to Buffalo, NY.

As a child in school, Ludwig found a passion for mathematical puzzles and hoped to become a scientist in the future.

As Cinda-Sue Davis, the current director of the Women in Science and Engineering at the University of Michigan, remarked, “We knew that if Martha was on our preliminary exam committee, she would ask us a question about crystallography.” She taught Biological Chemistry 807, a class modeled after Howard Schachman's physical biochemistry course.

While at Cornell, Ludwig conducted her Ph.D. research in biochemistry under Nobel Laureate Vincent du Vigneaud and studied the biosynthesis of ergothionine in D.B.

In 1962 Ludwig's interests switched from classical techniques of biochemistry to the then-emerging field of X-ray crystallography and she joined the laboratory of William Lipscomb to work on the structure of carboxypeptidase.

Ludwig also worked on superoxide dismutase during the 1980s with James Fee, a colleague from the Biophysics Research Division at the University of Michigan.

In 1990, Ludwig continued to collaborate with University of Michigan colleagues including Vincent Massey, to uncover why there was a very low potential associated with the reduction of semiquinone.