|Photo: Joe Malkevitch|
Mundane facts about brain data do little to give us insight into this amazing organ. What is there about the human brain that seems to make possible so many wondrous things that humans can accomplish: oral and written language, producing of art and music, and doing mathematics. Or is it really possible that dolphins have already resolved the status of the Riemann Hypothesis but we are unaware of it because we have found no way yet to communicate with them?
As so often seems to happen, at first glance there might not seem to be much to say about this topic. However, there are more facets to this subject than I can treat here or know enough about to say anything intelligent about them. I will merely try to provide you with a "wire" to connect mathematics and brain.
Imaging the Brain
One of the reasons the brain was a mystery for so long is that it is encased in the skull. Under ordinary circumstances one does not have easy access to seeing the brain. Being able to see into the human body took a big leap forward when Wilhelm Roentgen discovered x-rays. Shortly after his discovery of x-rays physicians were already using x-rays to see our bones. However, being encased by the skull, the brain, and other soft tissues were still unknown territory for physicians and physiologists. With contributions from science, engineering and mathematics, physicians have a growing array of imaging tools for seeing inside the skull. At first these brain imaging techniques involved 2-dimensional cross sections of the brain. Many of these techniques are identified with the field of tomography. The Greek word for a "cut" or "section" is "tomas." (Tomography has applications in fields other than medicine., for example, geology.) As the field of tomography has matured, it has been possible to generate three-dimensional medical imaging systems for the brain. These systems allow static views of the brain; increasingly it is also possible to make movies that show the dynamic behavior of the brain. The systems that are now available both to medical practitioners and researchers are:
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Source: American Mathematical Society