- Learning about mathematics, starting with Infinity and Phd. Emily Riehl, Mathematician Explains Infinity in 5 Levels of Difficulty | WIRED
Nice video. Infinity is a fascinating concept.
An analogue of Cantor’s diagonal argument, used in proving the uncountability of the real numbers, was used to prove that there are uncomputable functions in the study of theoretical computer science.
Reference: Georg Cantor Georg Cantor - Wikipedia
The topic title brought to mind a presentation by an Orthodox priest at a conference for liturgical-sacramental types where he maintained that the church Fathers understood set theory so that a great deal of their theology could actually be illustrated using Venn diagrams.
Infinities are something I find fascinating but never got to a math course that actually addressed them.
It’s interesting to see that Cantor’s work on transfinite numbers was attacked by some for its theological implications. Nowadays, mathematicians, unlike biologists, don’t face such attacks (however misguided) for theological implications of their work. Although, when I look at a paper containing pretty abstract math, I mostly shake my head and think “As the heavens are higher than the earth, so are my ways higher than your ways and my thoughts than your thoughts." – Isaiah 55:9
When my older brother was studying math at Berkeley he said that the stacks of PhD theses of wildly abstract math were constantly haunted by physicists and others looking for math that fit some phenomenon they’d encountered. I always thought it was interesting that some PhD candidate could think up some form of math that bore no resemblance to the word as understood at the time yet some researcher could come along years later and find among all those theses one that described something new in science!
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