Why Exactly Seven: Hurwitz's Theorem and the Architecture of Reality
Nine posts. Each one — "seven dimensions". Seven rows of a matrix. Seven Fano points. Seven Lindblad operators. Seven, seven, seven.
If this irritates you — you're not alone. Seven notes, seven days of the week, seven deadly sins, seven chakras. The number 7 is so overloaded with mystical associations that any theory containing it immediately arouses suspicion of numerology.
The suspicion is fair. But in this case — unfounded. The number 7 in UHM is not a postulate of inspiration, nor a kabbalistic find. It is a theorem. Moreover, not one — two. From two completely different areas of mathematics. If you need a culprit — his name is Adolf Hurwitz and his theorem of 1898.
Below — both proofs, the bridge between them, and why the Universe had no choice.