The Shortest Ever Papers - Numberphile

TL;DR

Short papers disprove longstanding mathematical conjectures, showcasing impactful brevity.

Transcript

[Tony]: I thought we'd have a look at some of the shortest papers that have ever been written. One of the sort of most famous ones was this one here by Lander and Parkin. Which you can literally see, look how short it is! There's virtually nothing there. But the content's really good because it actually disproves a very long-standing conjecture tha... Read More

Key Insights

• 🧍 Short papers like Lander and Parkin's can disprove long-standing mathematical conjectures.
• 🔺 Conway and Sofer's paper showcased the necessity of n squared plus two equilateral triangles to cover a given triangle.
• 👾 John Nash's thesis exemplifies the impact of brevity in academic writing, revolutionizing game theory.
• 🥺 Brevity in writing can lead to impactful results, as seen in short but influential papers.
• 👳 Urban myths about extremely short theses, like the one-page PhD thesis, often circulate but are mostly unfounded.
• 🤯 Audible.com offers a wide range of titles, including biographies like "A Beautiful Mind" and novels like "The Humans," perfect for readers with a math twist.
• ❓ Utilizing audiobooks from Audible can enhance reading experiences with features like Whispersync for voice and a vast collection of titles.

Questions & Answers

Q: How did Lander and Parkin's short paper disprove a long-standing conjecture?

Lander and Parkin's paper disproved Euler's conjecture that there are no integer solutions for k greater than n, showcasing the power of brevity in mathematical proofs.

Q: What was the question addressed in Conway and Sofer's paper on equilateral triangles?

Conway and Sofer's paper investigated the number of equilateral triangles required to cover a given equilateral triangle of a certain size, ultimately proving the necessity of n squared plus two triangles.

Q: Why is John Nash's thesis considered impactful despite its brevity?

John Nash's thesis, despite being only 26 pages long, revolutionized game theory and economics, earning him a Nobel Prize for its profound impact and concise content.

Summary & Key Takeaways

• Short papers like Lander and Parkin's disprove centuries-old conjectures.

• John Conway and Alex Sofer's paper disproved a question on equilateral triangles' coverage.

• Impactful short writings like John Nash's thesis have revolutionized fields.