The article discusses how falling costs of formal verification, partly due to cheaper compute and new tools, make it practical to apply rigorous mathematical proof to software, potentially catching bugs that traditional testing misses at a reasonable price.
Mathematician Timothy Gowers warns readers to brace themselves before reading further, suggesting the content that follows will be particularly impactful or surprising for mathematicians.
The article examines why a previously derived mathematical identity only holds for x > 1 and y > 1, using Mathematica to plot the condition and showing that the identity's validity is restricted to that domain.