## #1 – CRYPTOGRAPHY

- Julius Caesar and the so-called
*Caesar cipher*
- World War II: The
*Enigma* machine
- The cipher of Ernesto Ché Guevara and Fidel Castro
- RSA and public-key cryptography
- Quantum cryptography

## #2 – THE TABLET PLIMPTON 322

- What is Plimpton 322?
- When was it made?
- When was it discovered?
- Who is Eleanor Robson?
- What is a Pythagorean triplet?

## #3 – FERMAT’S LAST THEOREM

*x*^{n} + *y*^{n} = *z*^{n}
- 1637: Fermat and the margin of the book
- 1995: Andrew Wiles and the proof
- The Fields medal and Wiles

## #4 – ZERO

- Probably the most important discovery in the mathematical history
- Indian mathematicians

## #5 – NUMERICAL SYSTEMS

- Positional systems (place-value notation) vs non-positional systems
- Babylonian numerical system
- Hindu-Arabic numerical system
- Other civilizations: Egyptians, Chinese, Greeks, Romans, Mayas…
- Computers and binary digital systems: bits

## #6 – PYTHAGORAS’ THEOREM

*a*^{2} + *b*^{2} = *c*^{2}
- Pythagoras and the Pythagoreans
- Hippasus of Metapontum and the discover of irrational numbers
- The theorem in other cultures: Babylonians, Indians, Chinese