Are numbers discovered or invented?
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The philosophical question of whether numbers are discovered or invented is a recurring topic on Lex Fridman's podcast. Here are some insights from various episodes:
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Roger Penrose suggests that mathematics is discovered, likening it to archaeology. He explains that elements like the number (i) (the square root of -1) feel like they were always there, waiting to be found, rather than being pure human inventions 1.
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Zev Weinstein believes math is fundamentally discovered, stating that the only invented portion is its expression. He views mathematical truths as inherent aspects of the universe that we uncover through exploration 2.
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Lee Cronin offers a nuanced view, stating that while the universe might inherently possess mathematical properties, the human abstraction of mathematics is invented. He argues that the language and frameworks we use are constructed, though the underlying principles might be universal 3.
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Sam Harris discusses numbers as an abstract reality, emphasizing that mathematical structures are discovered due to their inherent properties that we cannot impose upon them. He differentiates them from fictional constructs, highlighting their objective truth within the abstract domain 4.
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Po-Shen Loh aligns with the discovery perspective, highlighting that certain mathematical truths, like the importance of (\pi), could be universally recognized by any intelligent species due to their fundamental nature 5.
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Grant Sanderson describes a cyclical relationship where discoveries about the universe inform the creation of useful mathematical tools, suggesting a blend of discovery and invention. He illustrates this with historical perspectives, such as the development of the Pythagorean theorem 6.
These discussions illustrate that while there is a strong argument for mathematics being a discovery of fundamental truths, the tools, languages, and frameworks we use to describe those truths might be human inventions.
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