mathematics

Proof by Induction

Proof by Induction is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Proof by Induction rather than just read about it. In short: "Proof by Induction" is a 2021 science fiction short story by José Pablo Iriarte. It was first published in Uncanny Magazine.

Key takeaways

Proof by Induction belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Proof by Induction to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Proof by Induction from memory before moving on to harder problems.

Reference excerpt

"Proof by Induction" is a 2021 science fiction short story by José Pablo Iriarte. It was first published in Uncanny Magazine.

Synopsis Paulie is a mathematician who uses a recording of his dead father's mind in an attempt to solve a particularly difficult problem.

Reception "Proof by Induction" was a finalist for the 2022 Hugo Award for Best Short Story, and for the Nebula Award for Best Short Story of 2021.

References

External links Text of the story, at Uncanny Magazine Essay by Iriarte on the process of writing the story Audio Version, narrated by Wil Wheaton at episode 2 of It’s Storytime, with Wil Wheaton

Worked examples

Example 1 — a first encounter with Proof by Induction

Start with the simplest possible case. Write down what Proof by Induction claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Proof by Induction before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Proof by Induction ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Proof by Induction

In research: Proof by Induction appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Proof by Induction in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Proof by Induction is common in secondary-school and first-year university syllabi. It links to neighbouring topics 2021 short stories, Cultural depictions of mathematicians, Science fiction short stories, so understanding it makes those chapters shorter.
In everyday life: Look for Proof by Induction outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Proof by Induction in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Proof by Induction means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Proof by Induction out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Proof by Induction in simple terms?

"Proof by Induction" is a 2021 science fiction short story by José Pablo Iriarte. It was first published in Uncanny Magazine.

Why does Proof by Induction matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Proof by Induction?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Proof by Induction.