recent papers exploring the mathematical foundations of artificial intelligence

 Here are some recent papers exploring the mathematical foundations of artificial intelligence:

1. "Formal Mathematical Reasoning: A New Frontier in AI" (December 2024)

   • Authors: Kaiyu Yang, Gabriel Poesia, Jingxuan He, Wenda Li, Kristin Lauter, Swarat Chaudhuri, Dawn Song
   • Summary: This position paper advocates for the integration of formal mathematical reasoning in AI, emphasizing its importance for advancing AI-driven discoveries in science and engineering. The authors discuss the role of formal systems, such as proof assistants, in verifying the correctness of reasoning and providing automatic feedback. citeturn0search1
   • https://arxiv.org/abs/2412.16075?utm_source=chatgpt.com 

2. "Artificial Intelligence: Advanced Mathematical Constructs and Applications" (November 2024)

   • Authors: A. Sultan, S. Sridevi, A. Rohini
   • Summary: This paper explores the mathematical foundations underpinning AI, machine learning (ML), and deep learning (DL). It highlights the significance of calculus, linear algebra, probability, and statistics in developing and optimizing AI algorithms. The authors demonstrate how these mathematical concepts are essential for data representation and model optimization in AI systems. citeturn0search3
   • https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5066774&utm_source=chatgpt.com 

3. "Integrating Discrete Mathematics in Artificial Intelligence: A Computational Perspective with a Vision for Future Technologies" (June 2024)

   • Authors: Shalini Mishra, Garima Singh, Manju Prabhakar
   • Summary: This research article discusses the integration of discrete mathematics into AI, focusing on its computational aspects and potential impact on future technologies. The authors examine how discrete mathematical structures can enhance the development and analysis of AI algorithms. citeturn0search4
   • chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/https://www.isroset.org/pub_paper/IJSRMSS/10-ISROSET-IJSRMSS-09633.pdf?utm_source=chatgpt.com
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4. "A Mathematical Framework of Intelligence and Consciousness Based on Riemannian Geometry" (July 2024)

   • Author: Meng Lu
   • Summary: This manuscript proposes a mathematical framework using Riemannian geometry to describe the structure and dynamics of intelligence and consciousness. It conceptualizes intelligence elements as tokens embedded in a high-dimensional space, with thought processes depicted as sequential activations along geodesics within these manifolds. citeturn0academia13

5. "Artificial Intelligence and Inherent Mathematical Difficulty" (August 2024)

   • Author: Anonymous
   • Summary: This paper explores the relationship between artificial intelligence and the inherent challenges in resolving open mathematical questions. It presents arguments based on computability and complexity theory, illustrating the difficulties in proof discovery and the application of AI-inspired methods to mathematical problem-solving. citeturn0search10
   • https://arxiv.org/abs/2408.03345?utm_source=chatgpt.com

These papers provide valuable insights into the mathematical underpinnings of AI, highlighting the ongoing efforts to establish rigorous theoretical foundations for the field.