This book should have changed mathematics forever

Swiss clockmaker Jost Bürgi’s 1600s “Arithmetic and Geometric Progression Tables” contained ingenious “red numbers” mathematical hack, computing 23,027 individual numbers with nine digits of precision.

Bürgi’s table creates “ingenious mathematical shortcut”: turn multiplication problems into simpler addition problems using red/black number mapping.

Bürgi’s table transforms operation hierarchy: “division into subtraction, exponentiation into multiplication, and root finding into division.”

Bürgi arranged “every 500th value from his table neatly into a circle” on title page—“likely not just about Aesthetics” but anticipating “most powerful Computing device on planet for next 350 years.”

Circular slide rule “gives us way to solve problems without doing any math at all”—physical disc rotation performs computation mechanically using Bürgi’s red/black number principle.

“What did Jost Bürgi do with his incredible new discovery? Basically nothing. He kept his Discovery mostly secret for his own work”—sharing only with friend Johannes Kepler.

Kepler worked on Rudolphine Tables “which gave equations and tables for precise location of stars and planets from anywhere on Earth—enormous computational effort greatly aided by Bürgi’s work.”

Kepler included pointed line in final Rudolphine Tables manuscript expressing frustration with Bürgi’s non-publication: “he a hesitating man and guardian of his Secrets abandoned the child at Birth and didn’t raise it for the common benefit.”

“In 10 or so years that Bürgi delayed publication, Scottish mathematician John Napier independently made same Discovery although with more complex and less intuitive derivation” and published full book of tables in 1614.

“For next 350 years until popularization of electronic calculator in 1970s, tables of logarithms and slide rule were primary tools used for all mathematical computation.”

“Today logarithms are more important than ever in mathematics, science and engineering”—particularly in AI/machine learning: “logarithms play critical role in loss functions of neural networks that power this generation of AI.”