At the beginning of the last century, mathematics was in a state of crisis. Resolving the problems led to new discoveries that forever changed our understanding of math.
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Mathematics's Foundational Crisis
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foundational crisisfoundational crisis of mathematicsRussell's paradoxset theoryhilbertdavid hilberthilbert's programundecidabilityincompletenessfirst incompletenesssecond incompletenesskurt godelgodelwhiteheadrussellBertrand Russellmathematicsfoundationsaxiomsprinciple of explosionconsistencycompletenessinconsistentparadox