Short answers, pulled from the story.
Cynthia Dwork and Moni Naor first proposed proof of work in 1993 as a way to deter junk email by requiring computational effort from senders. The term "proof of work" was formally coined in a 1999 paper by Markus Jakobsson and Ari Juels.
Hashcash is a proof-of-work system created by British cryptographer Adam Back in 1997 to combat email spam. It requires senders to compute a partial SHA-1 hash inversion, producing a result with a specified number of leading zeros. Recipients verify the work with a single computation.
Bitcoin uses a SHA-256-based proof-of-work algorithm in which miners compete to find a hash meeting a difficulty target, earning newly created bitcoin as a reward. The difficulty adjusts dynamically so that a new block is found approximately every 10 minutes.
A 51% attack occurs when a single entity controls more than half of a proof-of-work network's hashing power, allowing them to rewrite the blockchain, reverse transactions, and double-spend coins. A 2025 paper by Duke University Finance Professor Campbell Harvey estimated that a week-long 51% attack on Bitcoin could cost roughly six billion dollars at October 2025 prices.
University of Cambridge researchers estimated in 2018 that Bitcoin's energy consumption was comparable to that of Switzerland. The high energy use is structural because Bitcoin mining operates as a computational lottery where only one miner's work per block produces a lasting result.
Standard proof of work requires miners to solve arbitrary cryptographic puzzles whose only function is network security. Proof of useful work, as demonstrated in the Ofelimos protocol presented at Crypto 2022, directs that computation toward real optimization problems such as Boolean satisfiability, producing useful results alongside consensus.