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Proof by Induction (2021)
José Pablo Iriarte

Contributed by Vijay Fafat

Paul Gifford is a waiting-for-tenure professor of mathematics at a university. His father, a professor-emiritus of mathematics at the same university has just passed away. This death has come at a very inconvenient time for Paul (not that there is a convenient time for a father’s death...) because the two were collaborating on solving something called, “The Perelman hypothesis”, an unspecified, fictional hypothesis of the real-world mathematician, Grigori Perelman (he who solved one of the Millennium Problems, the Poincare Conjecture, as well as the Thurston Geometrization Conjecture, and in the aftermath, turned down a Fields Medal...). The premise of the story is that for a few minutes after clinical death, a digital snapshot - the “Coda” - of the mind may be taken which can be used in a simulation to interact with a limited version of the dead person.

Paul takes the help of his father’s coda to finish the proof. Along the way, the story describes his struggle with obtaining a tenure, the behavior of tenure-committee members and the research process, his father’s emotional detachment with his family, the thought that perhaps mathematical abilities may be inherited (hence, “induction” in the story title) and other such issues which could have been developed if the author had written a novel instead of a short story. As such, the story’s impact gets limited by its short length and limited elbow-room, though it does deliver a few interesting paragraphs. Convincing mathematical jargon is strewn across the story to give it a heavy mathfiction feel.

At one point, the father says something which I found a little perplexing:

(quoted from Proof by Induction)

“[The Jagdish-Rajput conjecture] is that hyperbolic equations correspond to node forms. They’ve tested several hundred terms using a supercomputer and they’ve all checked out.”

His father shook his head. “How’s that help us?”

“Node forms converge. Supposing we can prove their conjecture, we can use that to prove Perelman.”

“This isn’t math. This is grasping at straws. A supercomputer says it works—so what? That’s not theory. Where’s the proof?”

Paulie capped the marker, even though he suspected it could not dry out. “Don’t you see? If the correspondence holds, then—”

“Are you trying to give me a heart attack in the afterlife? Do Jagadish and Rajput have the basis for a theorem, or just a coincidence they can’t explain? Even Euler had conjectures disproven after three hundred years!”

I found the lines about “grasping at straws” and “heart attack” not very believable. In a number of real-life examples, matching of series expansion terms (say in Perturbation theory) acts as a good initial guide for an attack on a given problem. Of course, it is also true that matching a few or even many terms in an expansion does not a proof make, but then no one makes that claim anyway. The matching simply gives more confidence toward the conjecture in question. An accomplished mathematician dismissing this heuristic sounds very odd to me.

I am very grateful to Vijay Fafat for bringing this excellent work of mathematical fiction to my attention and writing a nice review to post here. My viewpoint differs in just a few places, so please allow me to comment.

Vijay is right that it would be ridiculous to completely rule out discussing one conjecture while attempting to prove another. Doing so is not necessarily "desperate" or "grasping at straws". In particular, it should be noted that Andrew Wiles proved Fermat's Last Theorem by proving the Taniyama-Shimura-Weil Conjecture. So, clearly the consideration of other conjectures can sometimes be useful when attempting to resolve a famous open problem. On the other hand, I did not find the (digitally simulated) father's objection to be unbelievable either. When there is an open conjecture, mathematicians in the field will each have their own opinions both on how likely it is to be true and how hard it will be to prove. If the elder Gifford in the story thought either that the Jagdish-Rajput Conjecture was not likely to be true or thought that it would be harder to prove than the Perelman Hypothesis itself, he might well have responded exactly in this way.

One of my favorite things in mathematical fiction are metaphors in which a mathematical idea is used to convey something deep about the human experience. As Vijay has hinted, the notion of proof by induction shows up in the story in several places, including metaphorically in the multi-generational family dynamics. For me, even though this is a short story and there wasn't much room to elaborate on it, the idea was still potent and effective. In fact, it may even have worked better because the author didn't have room to do much with it, leaving it up to the reader to fill in the gaps.

That the names Perelman and Ricci are mentioned along with the word "hyperbolic" certainly suggests that the author had differential geometry in mind as the subject on which the two Giffords were collaborating. However, there is nothing explicit in the story which says so. Similarly, there is nothing that actually says that the "Perelman" whose hypothesis they are working one, is Grigori Perelman. Perhaps I'm being like the mathematician from the joke ("No, we only know that there is one sheep in this country which is black on one side!") but it seems like it could be someone else with the same name.

This story was published in the May/June 2021 issue of Uncanny Magazine and is available for free online at their website.

More information about this work can be found at
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Works Similar to Proof by Induction
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. Division by Zero by Ted Chiang
  2. The Last Theorem by Buzz Mauro
  3. The Wild Numbers by Philibert Schogt
  4. Dark Integers by Greg Egan
  5. Music of the Spheres by Ken Liu
  6. Risqueman by Mike Wood
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  8. Luminous by Greg Egan
  9. The Exception by Alex Kasman
  10. Feigenbaum Number by Nancy Kress
Ratings for Proof by Induction:
RatingsHave you seen/read this work of mathematical fiction? Then click here to enter your own votes on its mathematical content and literary quality or send me comments to post on this Webpage.
Mathematical Content:
5/5 (1 votes)
Literary Quality:
4/5 (1 votes)

GenreScience Fiction,
MotifAcademia, Proving Theorems,
TopicFictional Mathematics,
MediumShort Stories, Available Free Online,

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Exciting News: The 1,600th entry was recently added to this database of mathematical fiction! Also, for those of you interested in non-fictional math books let me (shamelessly) plug the recent release of the second edition of my soliton theory textbook.

(Maintained by Alex Kasman, College of Charleston)