Curious Questions from Mathematics

Archimedes Thoughtful

Image via Wikipedia

The Question:

Today we refer to them as “ah-ha moments.” The most famous of which was experienced by Archimedes. He cried, “Eureka!” as a result of spilling bath water. True or False?

The Answer:True, sorta.

Archimedes’ Legacy
The esteem with which history holds a figure like Archimedes may be tied to the stories—substantiated or otherwise—that become a part of the folklore surrounding that figure. The most famous story concerning Archimedes is another example of this historical perception. It seems that King Hiero II was concerned that a greedy goldsmith had used a certain amount of silver in a crown that was intended to be pure gold.

The king asked Archimedes to determine the purity of his crown without destroying it. While bathing one day—as the story goes—Archimedes realized that the volume of water displaced by his (or any other) body could be used to calculate the density of the body—a method that could measure the density of the crown and thus its content. Archimedes immediately sprang from his bath and ran naked through the streets of Syracuse yelling, “Eureka!” (“I have found it!”)

Although this Archimedean anecdote does not appear in print until several centuries after his death, “Eureka!” remains the first thing that comes to the minds of many modern readers when they encounter the name of Archimedes. If indeed Archimedes did actually solve the problem of the impure crown for his king, it seems much more likely that he used a method that is now called the Archimedes principle. This method, which actually appears in Archimedes’ writings, involved weighing an object while it is submerged in water to determine its buoyant force.

In his own lifetime, Archimedes was renowned as an inventor and military engineer rather than as a mathematician. History, however, remembers Archimedes as one of the most brilliant and original mathematical thinkers who ever lived. In today’s modern world, “pure” and “applied” mathematics are often scrupulously separated by their practitioners. In his time, however, Archimedes was both a brilliant pure mathematician— whose work involving integral calculus predated Isaac Newton and Gottfried Leibniz by almost 2000 years—as well as a gifted applied mathematician— who used geometric techniques to find, among other things, the center of gravity of solid objects. Certainly, Archimedes is a part of the small pantheon of scientific geniuses like Newton and Albert Einstein whose brilliance changed the way in which we see our world.

From the Gale Biography in Context.

  • Eureka! (

One thought on “Curious Questions from Mathematics

  1. Pingback: Archimedes Was the Stuff of Legend | Myth-OS

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