Want to learn the ideas in Against the Gods better than ever? Read the world’s #1 book summary of Against the Gods by Peter L. Bernstein here.

Read a brief 1-Page Summary or watch video summaries curated by our expert team. Note: this book guide is not affiliated with or endorsed by the publisher or author, and we always encourage you to purchase and read the full book.

Video Summaries of Against the Gods

We’ve scoured the Internet for the very best videos on Against the Gods, from high-quality videos summaries to interviews or commentary by Peter L. Bernstein.

1-Page Summary of Against the Gods

The Ancients

Gambling was part of the Greeks’ creation myth. Their gods played dice to decide who would rule the heavens, seas and underworld. However, ancient Greek scientists didn’t study probability. Neither did those in the Talmud, although they used odds for permissible laws. It wasn’t until Renaissance thinkers turned their attention to developing mathematics that they needed numbers for gambling and other things like it.

The Hindu numbering system originated in 500 A.D. It was brought to the Arab world by 700 A.D., and they spread it around the world after that time period. The concept of zero was a major innovation, because it allowed people to calculate using only 10 symbols: 0, 1, 2, 3, 4_and so on.

Leonardo Pisano, a mathematician who was also known as Fibonacci, explored the power of Arabic numerals and their applications in Liber Abaci or Book of the Abacus. His work was published in 1202 when most people still relied on Roman numerals. The “Fibonacci ratio” is mathematically expressed by what the Greeks called “the golden mean.” He made great strides with his mathematical explorations but they were not applied to risk management until today.

The Renaissance

Luca Paccioli, a Franciscan monk and accomplished mathematician, may not have invented double-entry accounting but he did more to popularize it than anyone before him. He proposed a puzzle about how to divide the stakes in an interrupted gambling game. The study of gambling was the nursery of the science of risk. Girolamo Cardano, who was both physician and avid gambler, made important progress toward building the science of probability by writing on many subjects including mathematics. Even Galileo studied dice as part of his duty to his patron, Grand Duke Ferdinand I de’ Medici.

The two most important founders of probability theory were Blaise Pascal and Pierre de Fermat. Pascal was a child prodigy in mathematics, and he went on to become the founder of modern probability theory with his work on understanding statistics. He worked with Fermat, who was an extraordinary mathematician as well as a lawyer and linguist. Together they tried to solve the puzzle of Fibonacci’s ratio by using probability theory. They advanced this field even further when they developed arguments for belief in God that proved faith is the only rational response to the universe. Pascal said that if you obey religious law and try to pursue holiness, then you’re essentially betting on God’s existence because it’s more likely than not that there is no God; but if you don’t follow religious law, then you’re betting there is no God because human life is finite so your loss isn’t great if there isn’t a reward beyond death. Betting against infinite gain for finite losses makes sense rationally speaking—especially since we can never be certain about whether or not there really is a God out there somewhere.

Origins of Statistical Forecasting

Statistical sampling is crucial to the use of statistics and probability. It’s also a critical component of risk management, which is used in finance and other areas. John Graunt was the first person to use statistical sampling for financial purposes by analyzing London Bills of Mortality. He pioneered the use of averages in his work Natural and Political Observations Made Upon the Bills of Mortality.

Edmund Halley studied the work of Graunt and used it to calculate mortality rates. This data would eventually become the basis for life insurance. However, governments were selling annuities at a uniform price even though they had no idea how risky they were.