Grok 3 and the Authorial and Unpublished Mathematical Formulas as a learning tool for Generative AIs: Reactions and developments in the face of advanced calculations.

Description

Abstract (English)

This paper presents the reactions of the generative AI Grok 3 to an unprecedented and original mathematical tool, never published in printed or digital book. The learning of AIs through interactions with users is partially or fully viable, and these are points discussed in this article. Other points emerged during the research with great relevance, mainly in the context of the complexity of algorithms and the computational cost to execute the actions demanded by users. The work was developed in three distinct moments and in the same way with new prompts and chats to avoid doubts about what was retained by the generative AI in this attempt to train from interactions with the user. This article is an unfolding of the challenges of AIs organized by this same author and socialized in the form of an article. The best performance among the AIs was from Grok 3, surpassing its competitors ChatGPTs, all free and paid models, Gemini Advanced 2.0 Flash, Claude 3.7 and DeepSeek R1. Grok 3 finished with 75% accuracy and for this reason it is the only participant of the generative AIs in this article. The main objective is to verify if there is consistency in the execution and learning of the original and unprecedented formulas called Infinite Series with Multiple Ratios (SRMs). Finally, a comparison is made between the resolutions with the mathematical tools of Grok 3 domain and how difficult or simple the handling with the SRMs was. This paper also explores possible applications of SRMs in areas such as finance, engineering, biology, physics, and computer science, highlighting their versatility and efficiency.

Technical info (English)

Third paper v1 – published at 25th march 2025 – https://doi.org/10.5281/zenodo.15083825

Advanced computational mathematics and future point modeling of a predictive system: A collaborative scientific research between a human and a Generative AI.

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This paper presents the performance and reactions of the Generative AI Grok 3 when faced with authorial and disruptive mathematical formulas. The reader will have contact with a tool prepared to impact several areas. The highlight is the training for Generative AIs to recognize and act with large amounts of cyclical and periodic data. The applicability is immeasurable and this article presents some in the areas of finance and biology, among others. This is the second article published here in preprint format. The first was about the challenges of AIs with issues of computational biology, but specifically cell proliferation. The main Generative AIs participated (ChatGPTs, all models), Gemini Advanced 2.0 Flash, Claude Sonnet 3.7, DeepSeek R1 and the big winner was Grok 3 from the company xAI. This is the reason why it was chosen as the AI representative in this second article. I hope you like it, share it with your contact networks and let's do our part in the search for the much dreamed of Artificial General Intelligence (AGI).