Mathematics, Computing, and Information ProcessingArtificial Intelligence Applications
Abstract
Large language models (LLMs) increasingly excel at mathematics tasks, but their unreliability limits their utility in mathematics research. A mitigation is to use LLMs to generate formal proofs in languages such as Lean, in which the compiler verifies every proof step. We present the first demonstration of this method’s value in solving open problems at scale. We built an artificial intelligence agent for formal proof search that autonomously resolved nine of 353 open Erdős problems, proved 44/492 On-Line Encyclopedia of Integer Sequences conjectures, and is being deployed in combinatorics, optimization, graph theory, algebraic geometry, and quantum optics research. Even a basic agent alternating LLM-based generation with Lean-based verification replicated the Erdős successes. These findings demonstrate the power of formal proof search as an enabler of autonomous mathematical discovery.
GAOKAO-Bench is introduced, an intuitive benchmark that employs questions from the Chinese GAOKAO examination as test samples, including both subjective and objective questions that contribute a robust evaluation benchmark for future large language models and offers valuable insights into the advantages and limitations...
Xiaotian Zhang, Chun-yan Li, Yi Zong et al.· arXiv.org· 216 citations· ⚡17
The results are packaged in the Greenfield Startup Model (GSM), which explains the priority of startups to release the product as quickly as possible, and the need to shorten time-to-market, by speeding up the development through low-precision engineering activities.
Carmine Giardino, Nicolò Paternoster, M. Unterkalmsteiner et al.· IEEE Transactions on Softwar...· 178 citations· ⚡14
Software startup companies develop innovative, software-intensive products within limited timeframes and with few resources, searching for sustainable and scalable business models.
M. Unterkalmsteiner, P. Abrahamsson, Xiaofeng Wang et al.· e-Informatica Software Engin...· 157 citations· ⚡17
This work investigates the possibilities of using LLMs in a resume screening setting via a document retrieval framework that simulates job candidate selection and finds that the MTEs are biased, significantly favoring White-associated names in 85% of cases and female-associated names in only 11.1% of cases.
This study conducts a case survey study based on the secondary data of the major pivots happened in 49 software startups, and demonstrates that customer need pivot is the most common among all pivot types.
Sohaib Shahid Bajwa, Xiaofeng Wang, Anh Nguyen-Duc et al.· Empirical Software Engineeri...· 127 citations· ⚡15
This work shows that orders of magnitude enhancement in performance could be obtained by a combination of hardware improvements and tight quantum-HPC integration and introduces high-performance architectures for quantum-probabilistic computing with custom-designed accelerators to tackle today's industry-scale classical...
Masoud Mohseni, Artur Scherer, K. Johnson et al.· arXiv.org· 121 citations· ⚡9
