Advancing Mathematical Research via Human-AI Interactive Theorem Provingcs.AI updates on arXiv.org arXiv:2512.09443v2 Announce Type: replace-cross
Abstract: We investigate how large language models can be used as research tools in scientific computing while preserving mathematical rigor. We propose a human-in-the-loop workflow for interactive theorem proving and discovery with LLMs. Human experts retain control over problem formulation and admissible assumptions, while the model searches for proofs or contradictions, proposes candidate properties and theorems, and helps construct structures and parameters that satisfy explicit constraints, supported by numerical experiments and simple verification checks. Experts treat these outputs as raw material, further refine them, and organize the results into precise statements and rigorous proofs. We instantiate this workflow in a case study on the connection between manifold optimization and Grover’s quantum search algorithm, where the pipeline helps identify invariant subspaces, explore Grover-compatible retractions, and obtain convergence guarantees for the retraction-based gradient method. The framework provides a practical template for integrating large language models into frontier mathematical research, enabling faster exploration of proof space and algorithm design while maintaining transparent reasoning responsibilities. Although illustrated on manifold optimization problems in quantum computing, the principles extend to other core areas of scientific computing.
arXiv:2512.09443v2 Announce Type: replace-cross
Abstract: We investigate how large language models can be used as research tools in scientific computing while preserving mathematical rigor. We propose a human-in-the-loop workflow for interactive theorem proving and discovery with LLMs. Human experts retain control over problem formulation and admissible assumptions, while the model searches for proofs or contradictions, proposes candidate properties and theorems, and helps construct structures and parameters that satisfy explicit constraints, supported by numerical experiments and simple verification checks. Experts treat these outputs as raw material, further refine them, and organize the results into precise statements and rigorous proofs. We instantiate this workflow in a case study on the connection between manifold optimization and Grover’s quantum search algorithm, where the pipeline helps identify invariant subspaces, explore Grover-compatible retractions, and obtain convergence guarantees for the retraction-based gradient method. The framework provides a practical template for integrating large language models into frontier mathematical research, enabling faster exploration of proof space and algorithm design while maintaining transparent reasoning responsibilities. Although illustrated on manifold optimization problems in quantum computing, the principles extend to other core areas of scientific computing. Read More
The U.S. Cybersecurity and Infrastructure Security Agency (CISA) has urged federal agencies to patch the recent React2Shell vulnerability by December 12, 2025, amid reports of widespread exploitation. The critical vulnerability, tracked as CVE-2025-55182 (CVSS score: 10.0), affects the React Server Components (RSC) Flight protocol. The underlying cause of the issue is an unsafe deserialization Read More
Hamas’s best hackers have been maturing, building better malware, and spreading their attacks more widely across the region. Read More
10 GitHub Repositories to Master Machine Learning DeploymentKDnuggets Master the essential skill of deploying machine learning models with courses, projects, examples, resources, and interview questions.
Master the essential skill of deploying machine learning models with courses, projects, examples, resources, and interview questions. Read More
A stealthy campaign with 19 extensions on the VSCode Marketplace has been active since February, targeting developers with malware hidden inside dependency folders. […] Read More
This week’s cyber stories show how fast the online world can turn risky. Hackers are sneaking malware into movie downloads, browser add-ons, and even software updates people trust. Tech giants and governments are racing to plug new holes while arguing over privacy and control. And researchers keep uncovering just how much of our digital life […]
Wiz disclosed a still-unpatched vulnerability in self-hosted Git service Gogs, which is a bypass for a previous RCE bug disclosed last year. Read More
A new variation of the ClickFix attack dubbed ‘ConsentFix’ abuses the Azure CLI OAuth app to hijack Microsoft accounts without the need for a password or to bypass multi-factor authentication (MFA) verifications. […] Read More
How Harmonic Security improved their data-leakage detection system with low-latency fine-tuned models using Amazon SageMaker, Amazon Bedrock, and Amazon Nova ProArtificial Intelligence This post walks through how Harmonic Security used Amazon SageMaker AI, Amazon Bedrock, and Amazon Nova Pro to fine-tune a ModernBERT model, achieving low-latency, accurate, and scalable data leakage detection.
This post walks through how Harmonic Security used Amazon SageMaker AI, Amazon Bedrock, and Amazon Nova Pro to fine-tune a ModernBERT model, achieving low-latency, accurate, and scalable data leakage detection. Read More
How Swisscom builds enterprise agentic AI for customer support and sales using Amazon Bedrock AgentCoreArtificial Intelligence In this post, we’ll show how Swisscom implemented Amazon Bedrock AgentCore to build and scale their enterprise AI agents for customer support and sales operations. As an early adopter of Amazon Bedrock in the AWS Europe Region (Zurich), Swisscom leads in enterprise AI implementation with their Chatbot Builder system and various AI initiatives. Their successful deployments include Conversational AI powered by Rasa and fine-tuned LLMs on Amazon SageMaker, and the Swisscom Swisscom myAI assistant, built to meet Swiss data protection standards.
In this post, we’ll show how Swisscom implemented Amazon Bedrock AgentCore to build and scale their enterprise AI agents for customer support and sales operations. As an early adopter of Amazon Bedrock in the AWS Europe Region (Zurich), Swisscom leads in enterprise AI implementation with their Chatbot Builder system and various AI initiatives. Their successful deployments include Conversational AI powered by Rasa and fine-tuned LLMs on Amazon SageMaker, and the Swisscom Swisscom myAI assistant, built to meet Swiss data protection standards. Read More
