“A book about the great divide in modern mathematics” – James R Meyer
The website itself looks deeply into various aspects of logic that relate to infinity. The book includes various fascinating insights relating to mathematics.
Quote: “How is it that a person trained in the application of logic can continue to ignore the contradiction that lies at the heart of conventional set theory – that one limitlessly large quantity can be smaller than another limitlessly large quantity?”
“Article: Logic and Infinity – The Errors of Calculus” – Steve Patterson
Provides a detailed analysis of infinity, and an insight into how the results of calculus are misunderstood, i.e., believed to represent infinity.
Quote: “Mathematicians or physicists might respond, (“That’s a bunch of Greek philosophizing. Calculus just works. We can make extremely precise predictions incorporating infinities into our calculations, so it obviously isn’t a logical error")... Logic trumps mathematics, physics, and every other discipline. Zeno had that part right.”
“Why Past History Cannot Be Infinite: There Must Be a Beginning” – Kirk Durston
Why an infinite past is impossible – identifying the break in the continuity of time. Includes a link to a debate between Sean Carroll and William Lane Craig.
Quote: “Well, consider Carroll’s suggestion that all we need for an infinite past is for time to elapse from (“minus infinity.”) But his suggestion means that past history would have had to “count through” a countably infinite set of years with ℵ0 members”
“What Scientific Idea Is Ready For Retirement?” – Max Tegmark
Describes how various paradoxes are caused by infinity – the big bang, inflation, and the so-called measure problem. Explains why so many physicists and mathematicians have become seduced by infinity.
Quote: “This means that today's best theories similarly need a major shakeup, by retiring an incorrect assumption. Which one? Here's my prime suspect: ∞... Without the infinitely small, inflation can't make the infinitely big, so you get rid of both infinities in one fell swoop—together with many other problems plaguing modern physics...”
“Infinity's End: Time To Ditch the Never-Ending Story?” – Amander Gefter
An introduction to the perplexing nature of infinity – providing an insight into some of the most extreme infinity paradoxes that relate to reality. Historical quotes, the universe vs computers, and more.
Quote: “But if infinity is such an essential part of mathematics, the language we use to describe the world, how can we hope to get rid of it? Wildberger has been trying to figure that out, spurred on by what he sees as infinity's disruptive influence on his own subject... physicist Max Planck showed how to deal with another nonsensical infinity...”