Satoshi Nakamoto, the pseudonymous inventor of the Bitcoin proof of work algorithm. While he wouldn't normally top the list of 'most influential mathematicians', he has the key traits of being a mathematician and the most influential person that could reasonably hold that title. Unlike most other contenders alive in the 21st century Satoshi actually published his work in it. And where most mathematicians claim to fame is proving or refuting a conjecture that already had an informal consensus on the eventual result, Satoshi stunned all by providing a solution to the Byzantine Generals Problem, which had previously been considered impossible. This work directly led not only to Bitcoin but all other contemporary cryptocurrencies, which according to Time magazine was a three trillion dollar industry in November of 2021. Many experts believe that Satoshi's solution to Byzantine Generals could eventually provide the theoretical foundation for new forms of government and social organization.
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