Lesson History of mathematics

Archimedes (c. 287-212 BC)  

Archimedes was possibly the greatest mathematician of all time. He's best known for 

his contributions to our early understanding of physics by figuring out how levers 

work and in the famous legend of his discovery of how water is displaced by a 

submerged object: While taking a bath, Archimedes watched the water sloshing up to 

the top of his tub, and in the excitement of his discovery, he ran through the streets 

naked and shouting "Eureka!"  

As a mathematician, however, Archimedes was able to outdo even his own 

accomplishments in physics. He was able to estimate the value of pi to a remarkably 

precise value and to calculate the area underneath a parabolic curve.  

What's truly amazing is that he made these calculations using techniques surprisingly 

close to ideas from modern calculus that were invented about 1,800 years later.  

Archimedes calculated pi and areas under curves by approximating them with 

straight-edged polygons, adding more and more refined shapes so that he would get 

closer and closer to the desired value. This is strongly reminiscent of the modern idea 

of an infinite limit. As far as his mathematical sophistication was concerned, 

Archimedes was nearly two millennia ahead of his time.