This paper explores the potential of Large Language Models (LLMs) as tools for mathematicians. It examines how LLMs can assist with tasks like generating conjectures, finding proofs, simplifying expressions, and translating between mathematical formalisms. While acknowledging current limitations such as occasional inaccuracies and a lack of deep mathematical understanding, the authors demonstrate LLMs' usefulness in exploring mathematical ideas, automating tedious tasks, and providing educational support. They argue that future development focusing on formal reasoning and symbolic computation could significantly enhance LLMs' capabilities, ultimately leading to a more symbiotic relationship between mathematicians and AI. The paper also discusses the ethical implications of using LLMs in mathematics, including concerns about plagiarism and the potential displacement of human mathematicians.
Maxima, a powerful computer algebra system (CAS), is now accessible directly in web browsers thanks to a project leveraging Embedded Common Lisp (ECL) compiled to WebAssembly (WasM). This allows users to perform complex symbolic computations, including algebra, calculus, and numerical analysis, without any local installation. The browser-based interface provides a REPL (read-eval-print loop) for interactive calculations and utilizes MathJax for displaying formatted mathematical expressions. This project makes Maxima's capabilities more readily available, eliminating the need for dedicated software or server-side setups.
Commenters on Hacker News express excitement about Maxima running in the browser via WASM and ECL. Several highlight the potential for educational uses and interactive symbolic computation in web environments. Some discuss the performance overhead of WASM and suggest improvements, like pre-compilation for faster startup. The ability to share computational documents easily and integrate with other web technologies is praised. A few users mention other similar projects, including one using ClojureScript and another involving a Python CAS in the browser. The general sentiment is positive, with commenters intrigued by the possibilities this opens up for accessibility and collaborative mathematical work. One commenter expresses interest in building symbolic computation directly into a browser rather than running it as a VM.
Summary of Comments ( 4 )
https://news.ycombinator.com/item?id=42899184
Hacker News users discussed the potential for LLMs to assist mathematicians, but also expressed skepticism. Some commenters highlighted LLMs' current weaknesses in formal logic and rigorous proof construction, suggesting they're more useful for brainstorming or generating initial ideas than for producing finalized proofs. Others pointed out the importance of human intuition and creativity in mathematics, which LLMs currently lack. The discussion also touched upon the potential for LLMs to democratize access to mathematical knowledge and the possibility of future advancements enabling more sophisticated mathematical reasoning by AI. There was some debate about the specific examples provided in the paper, with some users questioning their significance. Overall, the sentiment was cautiously optimistic, acknowledging the potential but emphasizing the limitations of current LLMs in the field of mathematics.
The Hacker News post titled "Large Language Models for Mathematicians," linking to the arXiv preprint "Large Language Models for Mathematicians," has generated a moderate discussion with several insightful comments.
Several commenters discuss the potential benefits and drawbacks of using LLMs for mathematical research. One commenter points out that LLMs could be useful for "grunt work" like writing boilerplate code or checking basic calculations, freeing up mathematicians to focus on more creative tasks. However, they also caution against relying too heavily on LLMs for proofs, as they may not be fully reliable. Another commenter echoes this sentiment, suggesting that LLMs might be more helpful for generating "ideas or conjectures" rather than rigorously proving them. They highlight the importance of human oversight and critical thinking when using these tools.
One thread focuses on the specific examples provided in the paper. A commenter questions the validity of claiming an LLM "solved" a problem if it simply recognized a known solution from its training data. They argue that true mathematical understanding involves more than pattern matching. Another commenter challenges this, suggesting that even recognizing and applying known solutions to new problems is a valuable skill.
The discussion also touches on the broader implications of LLMs for the field of mathematics. One commenter speculates about the future role of mathematicians, wondering if LLMs could eventually automate significant portions of mathematical research. They express both excitement and concern about this possibility. Another commenter raises the question of whether LLMs could discover genuinely new mathematical concepts or theorems, or if they are fundamentally limited to recombining existing knowledge. This leads to a brief discussion of the nature of mathematical creativity and the potential for LLMs to contribute to it.
Finally, some commenters offer more practical perspectives. One suggests that LLMs could be particularly useful for educational purposes, helping students learn and practice mathematical concepts. Another commenter mentions the potential for LLMs to assist with literature reviews, enabling mathematicians to more easily access and synthesize relevant research.
Overall, the comments reflect a nuanced perspective on the potential of LLMs in mathematics. While acknowledging the limitations and potential risks, many commenters express optimism about the ways in which these tools could enhance mathematical research and education in the future. The discussion highlights the ongoing debate about the role of AI in scientific discovery and the evolving relationship between humans and machines in the pursuit of knowledge.