Art of Problem Solving
AoPS Online AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy AoPS Academy
Small live classes for advanced math
and language arts learners in grades 1-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

It's February and we'd love to help you find the right course plan!
How Classes Work
Course Catalog
Recommendations
Subject Courses
Before Prealgebra Ready for Prealgebra After Prealgebra Some Algebra 1 After Algebra 1 After Geometry After Algebra 2 After Precalculus Beyond Calculus
Contest Preparation
MATHCOUNTS/AMC 8 AMC 10 AMC 12 AIME USAMO
Computer Programming
Little or No Experience Some Experience Extensive Experience
Physics Courses
Little or No Experience Some Experience Extensive Experience
Prospective Students & Parents
Math Jams
Need Help?

Need help finding the right class? Have a question about how classes work?

Click here to Ask AoPS!

Paradoxes and Infinity

In this class we'll explore several popular paradoxes and attempt to wrap our brains around the world of infinity. For example, we'll discover a hotel that's never full: somehow, this hotel can always add another guest, or two, or three. We'll also run into paradoxes about goats, haystacks, pop-quizzes and more. If you're interested in mind-bending ideas and theories and have a background in basic algebra, this class is for you!

6 hours
6 hours  

Schedule

Sat & Sun
Apr 12 - Apr 13 		4:00 - 7:00
PM ET  –
Apr 12 - Apr 13
4:00 - 7:00 PM Eastern
3:00 - 6:00 PM Central
2:00 - 5:00 PM Mountain
1:00 - 4:00 PM Pacific
Click here to see more time zones
TBA $150
$150
ENROLL
Mon, Tue, Wed & Thurs
Jul 14 - Jul 17 		7:30 - 9:00
PM ET
Jul 14 - Jul 17
7:30 - 9:00 PM Eastern
6:30 - 8:00 PM Central
5:30 - 7:00 PM Mountain
4:30 - 6:00 PM Pacific
Click here to see more time zones
TBA $150
$150
ENROLL

AoPS Holidays

There are no classes May 24 ‐ 26, July 4 ‐ 6, August 29 ‐ September 1, October 31, November 24 ‐ November 30, and December 20, 2025 ‐ January 2, 2026.

Topics

1 Paradoxes in Philosophy
2 Paradoxes in Mathematics
3 Hilbert's Grand Hotel and Infinite Cardinals
4 Zeno's Paradox of Dichotomy

Great course. As a senior in high school I decided to take this course as I had never been exposed to math that required problem solving in my education, let alone discrete math. With this class I went from almost no discrete math knowledge (and commensurately poor problem solving skills) to a place where I will be taking the 400-level combinatorics sequence at my University in a few months and have had concurrent improvement in my problem solving ability.