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40 Notices of the AMs VoluMe 65, NuMber 1 1. Background MRI scans are crucial tools in modern medicine: 40 million scans are performed yearly in the US. Individual 2-D MR images portray soft tissues that X-ray CT can’t resolve, without the radiation damage that X-rays produce. MRIs are essential in some fields, for example to neurologists seeking to pinpoint brain tumors or study demyelinating diseases and dementia. MRI technology is remarkably flexible, constantly spawning new applications. Dynamic MRIs allow cardiologists to view movies showing muscular contractions of the beating heart. 3-D head MRIs allow neurosurgeons to meticulously plan life-and-death brain surgeries, in effect to conduct virtual fly-throughs ahead of time. Traditionally MRIs required lengthy patient immobilization—in some cases hours. Long scan times limit the number of patients who can benefit from MRI, and increase the cost of individual MRIs. Long scan times also make it difficult to serve fidgety children. Ambitious variations of MR imaging—such as dynamic cardiac imaging and 3-D MRI—require far longer scan times than simple 2-D imaging; such long scan times have typically been awkward or even prohibitive. Yet patients with arrhythmias and afib could get better treatment based on dynamic cardiac imaging; patients with aggressive prostate cancer could get much more accurate biopsies under 3-D MRI guidance; and many neurosurgeries could be much safer and more effective if surgeons could plan surgeries with 3-D MRIbased fly-throughs beforehand. Help is on the way: inspired by federally funded mathematical sciences research, patients everywhere will soon From Blackboard to Bedside: High-dimensional Geometry is Transforming the MRI Industry Aide Mémoire for a Congressional Briefing