Infinite Powers: 8 key ideas
The core ideas of Infinite Powers, each in under a minute, written in our own words. Want the full depth? Get the book.
- IDEA 1 OF 8
Calculus explains a changing world
Strogatz argues that calculus is one of humanity's greatest ideas, a tool for understanding anything that changes.
It explains the motion of planets, the spread of diseases and the workings of modern technology.
- IDEA 2 OF 8
Break problems into infinite pieces
Strogatz describes the infinity principle at the heart of calculus.
Difficult shapes and motions can be understood by cutting them into infinitely many tiny pieces and adding them back together.
- IDEA 3 OF 8
Archimedes started early
Strogatz describes how Archimedes used slices and approximations to find areas and volumes.
His methods foreshadowed calculus by two thousand years. His work showed that a hard problem can be solved by breaking it into tiny parts.
- IDEA 4 OF 8
Motion inspired new maths
Strogatz describes how Galileo studied falling objects and Kepler studied planetary orbits.
Their questions pushed mathematicians towards calculus. Describing how things move needed a new kind of mathematics that could handle smooth, constant change.
- IDEA 5 OF 8
Two inventors and a quarrel
Strogatz describes how Newton and Leibniz each developed calculus.
They and their followers argued bitterly over who came first. Both men are now credited, and the dispute shows how ideas can arise in different places at once.
- IDEA 6 OF 8
Derivatives measure change
Strogatz explains derivatives, which measure how quickly something changes at any moment.
Speed is a derivative of position. A car's speedometer shows this idea, giving the rate of change of distance at a single instant.
- IDEA 7 OF 8
Integrals add up pieces
Strogatz explains integrals, which add up infinitely many small parts to find totals such as area.
They are the reverse of derivatives. Adding up tiny slices can give the size of a curved shape that has no simple formula.
- IDEA 8 OF 8
Calculus runs modern life
Strogatz shows how calculus powers GPS, medical scans and the design of aircraft.
Much modern technology depends on it. The same ideas help engineers predict how things change, from the path of a signal to the flow of air.
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