Ancient Greece's primordial 4 elements christened in mathematical physics' infancy, Aristotle's celestial spheres, Ptolemy's epicycles, and the creationist Puritans' flat earth: the gaze of scientists -- unbridled by prayerful worship of the past -- abandonning these incorrect assumptions toward exploring testable implications of revolutionarily novel ones has generated every tectonic shift of paradigm through science's history of advancing humanity's impatient stumbles toward perceiving physical truth. Of paramount importance in effecting the consequent quantum leaps in fundamental theory is the treat of falsifiability via experimantal observation. Rather than simply waxing poetic on sublimely cross-pollinating interconnections between co-spousal mathematics and physics, the essayist conjures instead falsifiable conjectures. Triumphant observation of CMB anisotropies played the pivotal role in precision cosmology's eliminating competitors from contention in proven, textbook-caliber cosmogenic theory. Mathematical ideas here considered -- rooted in the powerful roles played by statistics in refining experimentation's sensitivity and by equivalency principles in establishing relativity as gravitation's foundational bedrock -- suggest refinement in data collection and analysis via modifications in purpose and design of instruments and experiments. Exploring mathematical subtlety in electromagnetic theory -- inspired by debate among maverick theorists on professionalism's fringes regarding physics' need for QFT's second quantization and its formalizing photonic discreteness -- motivates reconsideration of bolometric sensitivity. Expanding scale from quantum to cosmic and shifting frame from observer to celestial, the exploration of complementary mathematical subtlety in gravitational theory -- regarding relativity's mass-energy equivalency and its novel application in attributing to galactic radiant energy a portion of the role played by dark matter in explaining anomalous rotation curves -- animates a corresponding reconsideration of redshift, viz., the proposed underestimated role played by gigaparsec-scale gravitational field gradient variation across the observable depth of the universe (shown to lengthen extragalactic photon wavelength) in generating astronomical redshifts previously assumed purely recessional in origin.
kevin l bootes