The Most Outstanding (Future) Challenges Towards Global AMI and Its Plausible Extensions
The most fundamental challenges for the complete fulfillment of the artificial mathematical intelligence’s vision are presented. They involved cognitive formal refinements of fundamental ((meta-)mathematical) notions like set, proof, and exemplification,
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ificial Mathematical Intelligence Cognitive, (Meta)mathematical, Physical, and Philosophical Foundations
Artificial Mathematical Intelligence
Danny A. J. Gómez Ramírez
Artificial Mathematical Intelligence Cognitive, (Meta)mathematical, Physical and Philosophical Foundations
Danny A. J. Gómez Ramírez Research’s Labs Center Parque i Instituto Tecnológico Metropolitano (ITM) Medellín, Antioquia, Colombia
ISBN 978-3-030-50272-0 ISBN 978-3-030-50273-7 (eBook) https://doi.org/10.1007/978-3-030-50273-7 Mathematics Subject Classification: 03-02; 08-02; 13-02; 14-02; 18-02; 68-02 © Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
To Maria Batjacob, Luz Stella Ramírez Correa, José Omar Gómez Torres, and Jesús Benjosé
Preface
Imagine an outstanding researcher who has a great ability to mathematically model particular phenomena in their specific field of research. However, at the end of this modeling process, the researcher often has to solve purely formal (mathematical) problems which require a huge amount of time and effort. Sometimes, this part of the research takes even more time and creative energy than the work required to produce the mathematical data. Then, one day, the researcher discovers there is a technological device that can assist them in the second (and often exhausting) part of the research. In other words, this interactive artificial agent is effectively able to assist the researcher during the conceptual process of generating either humanstyle proofs or counterexamples of the corresponding (mathematical) conjectures in an understandable way. The researcher is astonished because in at least 80% of previous cases, such a device offers the r
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