Paradoxes of Infinity

​This research focuses on the nuances of reasoning about, and with, mathematical infinities. At its core, this research is an exploration of techniques and abilities to cope cognitively with abstract mathematics.  It seeks to offer a refined understanding of the tacit ideas and philosophies which can influence individuals' understanding infinity and resolution of ambiguities and paradoxical situations.

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Readings & Activities

Epistemology & Theories of Learning:

• Mamolo, A. (2017). April and the infinitely many ping pong balls.  For the Learning of Mathematics, 37​(3), 2-8.
• ​Mamolo, A. (2014). How to act? A question of encapsulating infinity.  Canadian Journal of Science, Mathematics, and Technology Education, 14(1), 1-22.
• Mamolo, A. (2014). Cardinality and cardinal number of an infinite set: A nuanced relationship. Proceedings of the 38th International conference for the Psychology of Mathematics Education, Vancouver, B.C.
• Mamolo, A. (2010). Glimpses of Infinity: Intuition, Paradoxes, and Cognitive Leaps. Saarbrücken, Germany:  VDM Verlag.
• Zazkis, R.,& Mamolo, A. (2009). Sean vs. Cantor: Using mathematical knowledge in ‘experience of disturbance’.  For the Learning of Mathematics, 29(3), 53 – 56.

Explore Paradoxes, Twists & Riffs:

• ​Wijeratne, C., Mamolo, A., & Zazkis, R. (2014). Hilbert’s Grand Hotel with a Series Twist.  International Journal of Mathematical Education in Science and Technology.
• Mamolo, A.& Bogart, T. (2011). Riffs on the infinite ping-pong ball conundrum. International Journal of Mathematical Education in Science and Technology, 42(5), 615 – 623.
• Mamolo, A., & Zazkis, R. (2008). Paradoxes as a window to infinity. Research in Mathematics Education, 10(2), 167–182.