28 May 2016 08:49 PM EST
Helping to map the strange boundary across the finite and the infinite, two young mathematicians have found a bridge across the finite-infinite divide, with a surprising new proof.
The boundary does not pass between some huge finite number and the next, infinitely large one. Instead, it separates two kinds of mathematical statements: “finitistic” ones, which can be proved without invoking the concept of infinity, and “infinitistic” ones, which rest on the assumption—not evident in nature—that infinite objects exist.
Theodore Slaman, a professor of mathematics at the University of California, Berkeley, said mapping and understanding this division is “at the heart of mathematical logic." The endeavor leads directly to questions of mathematical objectivity, the meaning of infinity and the relationship between mathematics and physical reality.
The new proof was completed by 34 year old Keita Yokoyama, and 27 year old Ludovic Patey.
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