Possible, as well as a famous example of what sorts of contraditions youĬan get if you forget to exclude it. The story starts with a nice description of why division by zero is not Renee's husband tries such an argument, pointing out that mathematics has been very useful in predicting and understanding reality, but Renee is not comforted by this when she knows now that the numbers 2, pi and 0 are all equal. Understanding of reality, which is not completely certain itself. Model demonstrates the consistency of mathematics, but this is clearlyĪ metamathematical statement that relies on the validity of our Logicians may argue that reality itself as a Major consequence of Gödel's work is the fact that we cannot prove theĬonsistency of our axiomatic systems (such as arithmetic itself).at Here, however, it is not only described accurately but usedĬorrectly in a very fascinating piece of speculative fiction. Gödel's research is often misquoted or misused in popular press and fiction. There is literary irony in the comparison of Renee's feelings about mathematics and her husband's discovery that marriage is not exactly what he thought it was either. (In particular, she is able to correctly prove that any two numbers are, in fact, equal to each other.) Her biologist husband feels that he should understand her situation as he picks her up from the hospital after her suicide attempt, since he also attempted to kill himself once many years earlier, but he is not able to grasp her dispair over this mathematical result. However, this is precisely why she is so devastated when her own research leads to a contradiction that demonstrates that mathematics itself is inconsistent. At the age of seven, she found beauty and comfort in the mathematical patterns associated with perfect squares, and felt this same sense of "rightness" throughout her career as she discovered new theorems that got her acclaim (and job offers). (Thanks to Frank Chess who pointed it out to Mathematics is inconsistent? This is a great piece of Note: This work of mathematical fiction is recommended by Alex for math majors, math grad students (and maybe even math professors) and literati.Īnswers the question: what would happen if we found out that (click on names to see more mathematical fiction
A list compiled by Alex Kasman ( College of Charleston)
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