The concept of infinity has intrigued mathematicians for thousands of years. Paradoxes surrounding infinity have even caused some mathematicians to swear off the idea of infinity entirely! While the idea of infinity can seem bizarre, some of the greatest philosophers and mathematicians through history have used infinity to create beautiful mathematical stories and solve challenging problems in physics, engineering, and other disciplines. The concept of infinity has also led to a few of the greatest mathematical problems of all time—some of which remain unsolved to this day.
In this course, we will learn from some of the most famous thinkers to have considered infinity. Looking from ancient Greek philosophers and geometers like Zeno and Archimedes all the way to 19th and 20th century mathematicians like Riemann, Cantor, and Hilbert, we will discuss, debate, hypothesize, and experiment (both in our heads and in the real world) in order to get a better sense of infinity’s strange and beautiful characteristics. We will consider questions like
- Why is infinity a useful idea?
- Are there different kinds of infinity?
- What is the opposite of infinity?
- Where does infinity pop up in math and science?
- How does mathematics relate to other subjects like physics or philosophy?
Course Learning Objectives/Goals
- Critical Thinking: Encouraging students to articulate themselves clearly in order to engage with abstract ideas in a creative and productive manner
- Mathematical Reasoning: Encouraging students to work out problems from clear definitions and first principles like postulates and axioms
- Mathematical Maturity and Preparedness: Encouraging students to see mathematics not merely as a tool but as an art
- To appreciate mathematics not merely for containing extrinsic value because of its usefulness but for containing intrinsic value because of its beauty
- To feel comfortable enough with ideas involving infinity that the students are better able to flourish in advanced high school and college courses which involve Calculus
Ages: 14-17
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UGA Center for Continuing Education & Hotel
1197 South Lumpkin Street, Athens, GA 30602
United States
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Prerequisites:
Students wishing to attend this course must have completed a minimum of Algebra II to be prepared for the concepts and ideas being taught.
Preston Earle graduated from Mercer University in 2019 with degrees in philosophy (BA) and mathematics (BS). While teaching at Stratford Academy in 2021, he was named Region VI STAR teacher. He now teaches AP Calculus AB/BC at Mount de Sales Academy in Macon, Georgia. In his spare time, Preston likes to write questions for math tournaments, play chess, and read Flannery O'Connor.