Watching the sky, you can see the Sun, moon, planets and stars moving above Earth. It is very intuitive to imagine that you are standing still and the objects you are observing are moving above you and this was the view taken by geocentric models of the cosmos.

A Greek model, which was dominant in many parts of the world for hundreds of years, had a spherical Earth at the centre of the universe, with the other heavenly bodies orbiting in perfect circles.

This talk by Peter Rowlett outlines problems and challenges to this model, and the developments which followed, through the theory of Copernicus, mathematical treatments by Kepler and Newton and questions of what drives planetary motion.

Shape of the cosmos

Cryptography is the process by which messages are communicated through secret means. Cipher cryptography converts messages by applying some cipher algorithm with a secret key to a plaintext message, converting it into a ciphertext message that cannot be read by interceptors. Cryptanalysis is the science that attempts to decipher these messages without access to the secret key. This talk focuses on substitution ciphers and demonstrates the processes of encrypting and breaking some examples of these. The focus is on the battle between cryptographers - who create cipher systems - and cryptanalysts - who attempt to break them. As cryptanalysis develops more ingenious ciphers must be created and this constant struggle evolves from Roman generals, through the Golden Age of Islam to political intrigue in Renaissance Europe. This talk provides a gentle introduction and assumes no prior knowledge of cryptography. An article on this topic, "Ciphers through the ages" by Peter Rowlett, appears in issue 10 of iSquared Magazine (Winter 2009/10), on pages 24-27. Find out more about the magazine and how to subscribe, buy the current issue or back copies of previous issues at the iSquared Magazine shop.

Substitution ciphers: Ancient - Renaissance

History of maths and x is an initiative that aims to offer mathematical histories for various topics, x. Each topic is covered in a talk at the University of Nottingham that is available to view online, in an article for iSquared Magazine and is accompanied by a companion podcast released by the Institute of Mathematics and its Applications through the Travels in a Mathematical World podcast.

History of Maths and x

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History of Maths and x episodes:

Shape of the cosmos

Substitution ciphers: Ancient - Renaissance