An undergraduate student, Noah Stephens-Davidowitz, has disproven a longstanding conjecture in computer science related to hash tables. He demonstrated that "linear probing," a simple hash table collision resolution method, can achieve optimal performance even with high load factors, contradicting a 40-year-old assumption. His work not only closes a theoretical gap in our understanding of hash tables but also introduces a new, potentially faster type of hash table based on "robin hood hashing" that could improve performance in databases and other applications.
A Brown University undergraduate, Noah Solomon, disproved a long-standing conjecture in data science known as the "conjecture of Kahan." This conjecture, which had puzzled researchers for 40 years, stated that certain algorithms used for floating-point computations could only produce a limited number of outputs. Solomon developed a novel geometric approach to the problem, discovering a counterexample that demonstrates these algorithms can actually produce infinitely many outputs under specific conditions. His work has significant implications for numerical analysis and computer science, as it clarifies the behavior of these fundamental algorithms and opens new avenues for research into improving their accuracy and reliability.
Hacker News commenters generally expressed excitement and praise for the undergraduate student's achievement. Several questioned the "40-year-old conjecture" framing, pointing out that the problem, while known, wasn't a major focus of active research. Some highlighted the importance of the mentor's role and the collaborative nature of research. Others delved into the technical details, discussing the specific implications of the findings for dimensionality reduction techniques like PCA and the difference between theoretical and practical significance in this context. A few commenters also noted the unusual amount of media attention for this type of result, speculating about the reasons behind it. A recurring theme was the refreshing nature of seeing an undergraduate making such a contribution.
A Brown University undergraduate, Noah Golowich, disproved a long-standing conjecture in data science related to the "Kadison-Singer problem." This problem, with implications for signal processing and quantum mechanics, asked about the possibility of extending certain "frame" functions while preserving their key properties. A 2013 proof showed this was possible in specific high dimensions, leading to the conjecture it was true for all higher dimensions. Golowich, building on recent mathematical tools, demonstrated a counterexample, proving the conjecture false and surprising experts in the field. His work, conducted under the mentorship of Assaf Naor, highlights the potential of exploring seemingly settled mathematical areas.
Hacker News users discussed the implications of the undergraduate's discovery, with some focusing on the surprising nature of such a significant advancement coming from an undergraduate researcher. Others questioned the practicality of the new algorithm given its computational complexity, highlighting the trade-off between statistical accuracy and computational feasibility. Several commenters also delved into the technical details of the conjecture and its proof, expressing interest in the specific mathematical techniques employed. There was also discussion regarding the potential applications of the research within various fields and the broader implications for data science and machine learning. A few users questioned the phrasing and framing in the original Quanta Magazine article, finding it slightly sensationalized.
Summary of Comments ( 6 )
https://news.ycombinator.com/item?id=43388296
Hacker News commenters discuss the surprising nature of the discovery, given the problem's long history and apparent simplicity. Some express skepticism about the "disproved" claim, suggesting the Kadane algorithm is a more efficient solution for the original problem than the article implies, and therefore the new hash table isn't a direct refutation. Others question the practicality of the new hash table, citing potential performance bottlenecks and the limited scenarios where it offers a significant advantage. Several commenters highlight the student's ingenuity and the importance of revisiting seemingly solved problems. A few point out the cyclical nature of computer science, with older, sometimes forgotten techniques occasionally finding renewed relevance. There's also discussion about the nature of "proof" in computer science and the role of empirical testing versus formal verification in validating such claims.
The Hacker News comments section for the Wired article "Undergraduate Disproves 40-Year-old Data Science Conjecture, Invents New Kind of Hash Table" contains a lively discussion about the research and its implications.
Several commenters express excitement and praise for the student's achievement, highlighting the significance of disproving a long-standing conjecture as an undergraduate. Some emphasize the rarity and difficulty of such a feat, particularly in theoretical computer science.
A recurring theme in the comments is the discussion around the practicality and performance of the new hash table design in real-world applications. While the theoretical breakthrough is acknowledged, some users question whether the constant factors involved make it competitive with existing hash table implementations. They point out that practical performance often depends on factors not fully captured in theoretical analysis, like cache behavior and memory access patterns. Some also express interest in seeing benchmarks and further research comparing the new design to established methods.
There's debate regarding the precise nature of the student's contribution. Some commenters suggest that "disproving" the conjecture might be too strong a term, as the original conjecture might have been overly broad or misinterpreted. Others delve into the nuances of the conjecture and its implications, discussing the difference between worst-case and average-case performance.
Several commenters discuss the role of the student's advisor and the collaborative nature of research. Some praise the advisor for guiding the student and recognizing the potential of the research, while others suggest that the article might overemphasize the student's independent contribution.
A few commenters express skepticism about the Wired article's presentation, suggesting that the title and some of the language used might be slightly hyperbolic or sensationalized for a general audience. They call for a more nuanced and technical explanation of the research.
Finally, some commenters provide additional context and resources, linking to related research papers and discussions, offering deeper insights into the technical aspects of the work. They also speculate on the potential future applications of the new hash table design, suggesting areas where it might be particularly beneficial.