This companion presents mathematics as a field concerned with solving inverse problems, specifically how to reconstruct a function from the integrals of its cross-sections. It highlights Johann Radon's early 20th-century work on this type of problem. The book connects this fundamental mathematical challenge to real-world applications like medical imaging, exemplified by the development of computerized axial tomography (CAT/CT scans). It shows how mathematicians like Allan McLeod Cormack developed algorithms to create images from X-ray data, a procedure that relies on solving these inverse problems.
The overview emphasizes that the core of sophisticated technologies like CT scanning is a mathematical inverse problem. Readers gain insight into the theoretical underpinnings of widely used scientific tools and learn about mathematicians who contributed to solving these complex challenges. The book illustrates the direct relationship between abstract mathematical principles and tangible advancements in fields such as medicine.
Key concepts
- Inverse problem — The mathematical challenge of reconstructing a function given the integrals of its cross-sections.
- Johann Radon — An Austrian mathematician who studied inverse problems related to function reconstruction.
- Computerized axial tomography (CAT/CT scan) — A medical imaging technology whose development relies on solving mathematical inverse problems.
- Allan McLeod Cormack — A scientist who developed mathematical algorithms for creating images from X-ray data, central to CT scanning.