English mathematician John Wallis died in 1703.

John Wallis was born in England in 1616. As mathematics was not considered an important topic for study at that time, Wallis was not exposed to the subject until he was almost 15. Once he discovered it, however, he became so enthralled with the study that he pursued it in his spare time and became one of the most influential scholars in the field. In addition to his love of mathematics, Wallis was a devoted scholar and eventually formed a group of like-minded men who would become the founders of the Royal Society of London, meeting regularly to discuss topics such as medicine, geometry and mechanics. Wallis's skills with calculations and numbers assisted him in an early career choice of cryptography, and during the English Civil War he decoded Royalist messages for the Parliamentarians. His work won him favor with Lord Cromwell, who was responsible for appointing Wallis to two seats at Oxford that were hotly contested. While Wallis's appointments were bitterly criticized because of their political origins, he served well for over 50 years and contributed substantially to the origins of calculus. Wallis was the most influential English mathematician before Newton. He introduced the symbol for infinity and the concept of exponents using negative or fractional numbers (such as 1/x² = x^-2). He was also the first to suggest the law of conservation of momentum for colliding bodies, one of the first of the laws of conservation.

Illuminations
In Allow Me 2 Reiterate (9-12), students are exposed to negative or fractional exponents. In the lesson, students use a graphic calculator, spreadsheet or online tool to assist them in determining the square root of two to a given number of places. From this, students are able to study the repeating-decimal phenomenon of rational numbers, to explore the system property of irrationality of numbers and to experiment with the usefulness of an iterative algorithm.

The unit Code Crackers (9-12) introduces students to cryptology, beginning with the Caesar and Vigenere ciphers.

Science NetLinks
Law Breaking Balloons (6-12) focuses on some of the misconceptions surrounding Newtonian laws of motion. Students observe the seemingly law-defying motion of helium balloons, and then perform experiments that demonstrate that the balloons are indeed subject to Newtonian constraints.

In Patterns of Communication (3-5), students investigate methods of communication using various codes, try to "break the codes" and build a Morse Code buzzer.