# Alex Peek blog

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Saturday, October 13, 2018

## Archimedes and mathematical physics

Photo source: Wikimedia Commons, Andre Thevet

Archimedes (287-212 BC) was a Greek mathematician and physicist best known for using proofs in geometry and his contributions to mathematical physics. Mathematician Alfred North Whitehead said,

"Some of the later Greeks, such as Archimedes, had just views on the elementary phenomena of hydrostatics and optics. Indeed, Archimedes, who combined a genius for mathematics with physical insight, must rank with Newton, who lived nearly two thousand years later, as one of the founders of mathematical physics." (An Introduction to Mathematics, 1911)

Astrophysicist Mario Livio said,

"Using his masterful understanding of mechanics, equilibrium, and the principles of the lever, he weighed in his mind solids or figures whose volumes or areas he was attempting to find against ones he already knew. After determining in this way the answer... he found it much easier to prove geometrically... [He] essentially introduced the concept of a thought experiment into rigorous research." (Is God a Mathematician, 2009)

The rest of this post is some quotes from Archimedes.

### Epistemology

"Those who claim to discover everything but produce not proofs of the same may be confuted as having actually pretended to discover the impossible." (On Spirals, 225 BC)

"How many theorems in geometry which have seemed at first impracticable are in time successfully worked out?" (On Spirals, 225 BC)

"Mathematics reveals its secrets only to those who approach it with pure love, for its own beauty." (AZQuotes.com)

"Man has always learned from the past. After all, you can't learn history in reverse." (AZQuotes.com)

### Physics

"Equal weights at equal distances are in equilibrium and equal weights at unequal distances are not in equilibrium but incline towards the weight which is at the greater distance." (On the Equilibrium of Planes)

"Two magnitudes whether commensurable or incommensurable, balance at distances reciprocally proportional to the magnitudes." (On the Equilibrium of Planes)

"It follows at once from the last proposition that the centre of gravity of any triangle is at the intersection of the lines drawn from any two angles to the middle points of the opposite sides respectively." (On the Equilibrium of Planes)