Abstract

Tomography strives to image (hopefully non-destructively) the interior of a non-transparent body: human body in medical applications, subsurface in geology, geophysics and seismology, internal defects in industrial non-destructive testing, hidden illicit nuclear sources in homeland security, and the list can go on … As manifold are the tomography’s applications, are also the physical types of tomographic images and mathematics involved. The word “miracle” in the title indicates not only the large variety of important tomographic applications, but also the dear to the mathematician’s heart multitude of techniques coming from all areas of mathematics. This lecture will provide an overview of (some of) tomographic ideas, techniques, and issues encountered there. No prior knowledge of tomography will be assumed.