SchoolTube Community
The world of academic publishing is often associated with lengthy, complex papers filled with jargon. But did you know that some of the most impactful mathematical breakthroughs have been published in incredibly short papers? We're talking about papers so concise they might make a haiku look like a novel!
Let's dive into the fascinating world of the shortest mathematical papers and explore how these bite-sized publications have made a big splash.
Disproving Centuries-Old Conjectures
One famous example is the paper by Lander and Parkin that disproved Euler's conjecture, a long-standing mathematical idea related to Fermat's Last Theorem. Imagine tackling a problem that had puzzled mathematicians for centuries, only to disprove it with a paper so concise it could fit on a postcard! That's precisely what Lander and Parkin achieved. Their paper, a model of brevity, provided a single counterexample to Euler's conjecture, effectively debunking it.
Covering Triangles: A Geometric Puzzle
Another intriguing example comes from the realm of geometry. Mathematicians John Conway and Alex Soifer authored a paper that explored how many smaller equilateral triangles are needed to cover a larger one. Their paper, titled "Can n² + 1 Unit Equilateral Triangles Cover an Equilateral Triangle of Side > n, with One Vertex a Vertex of the Triangle?," is almost as short as its title! While they didn't definitively answer the question posed, they demonstrated that n² + 2 triangles would suffice, offering a tantalizing glimpse into the complexities of geometric tiling.
Beyond Mathematics: Brevity in Other Fields
The quest for concise publishing isn't limited to mathematics. In the field of applied behavior analysis, a paper titled "The Unsuccessful Self-Treatment of a Case of Writer's Block" speaks volumes in its silence. Similarly, a chemistry journal humorously included an empty entry titled "Comprehensive Overview of Chemical-Free Consumer Products." These examples highlight how brevity can be employed for impact and even humor across various disciplines.
John Nash: A Legacy of Impactful Conciseness
Perhaps the most compelling example of impactful brevity comes from the work of John Nash, the renowned mathematician whose life inspired the film "A Beautiful Mind." Nash's groundbreaking work on game theory, which earned him a Nobel Prize in Economics, was published in a remarkably concise paper. His doctoral thesis, a mere 26 pages, further exemplifies how profound ideas can be conveyed with remarkable efficiency.
The Power of Impact per Word
While the examples above showcase the shortest papers, it's essential to consider the concept of "impact per word." A truly remarkable short paper achieves a lot within its limited space. John Nash's work, for instance, revolutionized game theory and economics, making it a strong contender for the most impactful mathematical paper per word.
The Allure of the Short Paper Myth
In the world of mathematics, a persistent urban legend speaks of a PhD thesis that proved a long-standing mathematical problem in just one page. While this remains a myth, it highlights the allure of elegant and concise solutions in the mathematical community.
The pursuit of brevity in mathematical writing showcases the power of clear and concise communication. These short papers challenge the notion that complex ideas require lengthy explanations. They remind us that sometimes, the most profound insights can be conveyed with astonishing brevity, leaving a lasting impact on the world of mathematics and beyond.
You may also like