Synthesized answer
The provided passages do not contain information about the central thesis of "The Princeton Companion to Mathematics."
The passages discuss the mathematics of medical imaging, specifically computerized axial tomography (CAT or CT scans), and the inverse problem of reconstructing a function from its integrals [Passage 1, Passage 2]. They mention that the fundamental problem behind CT scans is mathematical and was studied by Johann Radon [Passage 2]. The text also lists "The Princeton Companion to Mathematics" as a source, edited by T. Gowers [Snippet]. However, the central thesis of this companion text is not stated.
Synthesized from the book passages below. Chat with the book on Feynman for follow-up.
From the book
Title: The Mathematics of Medical Imaging by Timothy G. Feeman Description: In 1979, the Nobel Prize for Medicine and Physiology was awarded jointly to Allan McLeod Cormack and Godfrey Newbold Houns eld, the two pioneering scienti- engineers primarily responsible for the development, in the 1960s and early 1970s, of computerized axial tomography, popularly known as the CAT or CT scan. In his papers [13], Cormack, then a Professor at Tufts University, in Massachusetts, dev- oped certain mathematical algorithms that, he envisioned, could be used to create an image from X-ray data. Working…
nd this procedure is essentially mathematical: If we know the values of the integral of a two- or three-dimensional fu- tion along all possible cross-sections, then how can we reconstruct the function itself? This particular example of what is known as an inverse problem was studied by Johann Radon, an Austrian mathematician, in the early part of the twentieth century. Categories: Mathematics Pages: 151 Snippet: ... Mathematics 32 , SIAM , Philadelphia , 2001 . 31. Noble , B. , and J. W. Daniel , Applied Linear Algebra , 3rd ed . , Prentice - Hall , Englewood Cliffs , 1988 . 32. <b>The…