In 1930, the mathematician David Hilbert declared that every mathematical problem could be solved using the right set of axioms. The following day, a twenty-four-year-old Kurt Gödel proved him wrong by showing that any consistent logical system must contain truths it cannot prove. This meant that certain truths will always lie beyond our ability to formally verify, no matter how many rules we establish.
This result ended generations of attempts to reduce mathematics to pure, air-tight logic, from Kant to Frege. It remains a sobering reminder that formal systems have permanent boundaries. We should be careful not to mistake the completeness of a framework for a complete understanding of reality.
more: https://aeon.co/essays/the-century-long-search-for-the-limits-to-knowledge
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