**Ticket to Time Machine**

###### by Corina Murg

You are standing in front of a time machine. You are allowed to take one voyage into the past to visit a mathematician. All eyes are on you. This *is* the most difficult decision you will have to make in your mathematical life. What point on the human history timeline would you like to explore? Whom would you be excited about meeting?

Can I please make a suggestion? Place and time: Greek city of Syracuse* (*Syracuse is now a city in Italy)*, *around 220 BC. For a chance to spend the day with the “sand reckoner” of antiquity. THE mathematician and inventor extraordinaire of antiquity and beyond.

*Engraving of Archimedes planning the defense of Syracuse by Andre Thever (1516 – 1590): Les vrais pourtraits et vies des hommes illustres).*

The mathematician who invented catapults that could throw stones onto ships and huge cranes that could reach and lift ships into the air.

The mathematician who proved that the ratio of the circle’s circumference to its diameter is between 3 (3.1408) and 3 (3.1429), a value in line with the (approximate) value of pi of 3.1416 we use today.

The mathematician who invented a higher order number system in order to calculate the number of grains of sand necessary to fill the entire universe: 10^{63}.

The mathematician who (allegedly) used a set of mirrors to focus the sun rays and set the approaching enemy ships on fire.

The mathematician who designed the water screw to draw water from rivers and to pump seawater from ships.

The mathematician who started with a hexagon and built up to a 96-sided polygon to determine that the value of ratio of the circle’s circumference to its radius (π) pi is between 3 (3.1408) and 3 (3.1429), which is in line with the (approximate) value of π of 3.1416 we use today.

The mathematician who proved that the ratio of the volume of a sphere to the volume of the circumscribing cylinder is equal to ⅔.

The mathematician who found an extraordinary way of calculating the area under a curve by summing infinite geometric series. Remember, this was over 2000 years ago!

And yes, the mathematician who ran naked onto the streets of Syracuse shouting *Eureka! Eureka!* (I have found it!) after having discovered how to use water to calculate the volume of irregular objects: Archimedes.

##### Fields Medal (Awarded by the International Mathematical Union)

##### Obverse: Archimedes portrait and quote: *Transire suum pectus mundoque potiri (*Rise above oneself and grasp the world)

##### Reverse: (background): illustration of proof of the ratio of a sphere’s volume to the volume of a cylinder.

Archimedes, the mathematician who died while working on a problem at the sword of a Roman soldier. Archimedes, the mathematician who rose above himself and grasped the world!

Thank you for the mathematics, Mr. Archimedes!

The real story behind Archimedes’ Eureka! by Armand D’Angour on YouTube

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