"We could imagine infinity but never actually achieve it. Post-Aristotle, infinity was always idealized, never realized - a philosophical construct at best. As something that could never be reached, infinity could never be treated as a proper mathematical object, most believed. Through the millennia, some of the top philosophical and mathematical minds of their day turned their attention to the concept, pondered it at length, and inevitably gave it up."
"His work is outstanding, but some of his ideas are way too taboo for many mathematicians. Completing an infinity implies somehow mastering an impossibly long iterative process, like counting every whole number all the way to infinity, including all the really, really large numbers we can't imagine and don't even have names for. Count to a googolplex of googols multiplied by many more googols. It can't possibly be done, many mathematicians think, so best to leave infinity hiding in the bush."
For thousands of years after Aristotle, infinity was regarded only as an unreachable, idealized concept that could not be treated as a mathematical object. Generations of philosophers and mathematicians considered infinity a mere philosophical construct and ultimately abandoned attempts to realize it. Georg Cantor developed a radically different view, proposing that an infinity could be completed and analyzed mathematically. Cantor's approach implies mastering an interminably long iterative process, such as counting every whole number up to unimaginably large magnitudes. Many mathematicians found this idea taboo and impossible, arguing that counting to numbers like a googolplex of googols cannot be done, so infinity should remain untouched.
Read at Big Think
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