Apriori Knowledge in an Era of Computational Opacity: The Role of AI in Mathematical Discovery
- URL: http://arxiv.org/abs/2403.15437v1
- Date: Fri, 15 Mar 2024 21:38:26 GMT
- Title: Apriori Knowledge in an Era of Computational Opacity: The Role of AI in Mathematical Discovery
- Authors: Eamon Duede, Kevin Davey,
- Abstract summary: We argue that if a proof-checker is attached to such machines, then we can obtain apriori mathematical knowledge from them.
Many accept that we can acquire genuine mathematical knowledge of the Four Color Theorem from Appel and Haken's program.
- Score: 0.7673339435080445
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Computation is central to contemporary mathematics. Many accept that we can acquire genuine mathematical knowledge of the Four Color Theorem from Appel and Haken's program insofar as it is simply a repetitive application of human forms of mathematical reasoning. Modern LLMs / DNNs are, by contrast, opaque to us in significant ways, and this creates obstacles in obtaining mathematical knowledge from them. We argue, however, that if a proof-checker automating human forms of proof-checking is attached to such machines, then we can obtain apriori mathematical knowledge from them, even though the original machines are entirely opaque to us and the proofs they output are not human-surveyable.
Related papers
- Formal Mathematical Reasoning: A New Frontier in AI [60.26950681543385]
We advocate for formal mathematical reasoning and argue that it is indispensable for advancing AI4Math to the next level.
We summarize existing progress, discuss open challenges, and envision critical milestones to measure future success.
arXiv Detail & Related papers (2024-12-20T17:19:24Z) - Machine learning and information theory concepts towards an AI
Mathematician [77.63761356203105]
The current state-of-the-art in artificial intelligence is impressive, especially in terms of mastery of language, but not so much in terms of mathematical reasoning.
This essay builds on the idea that current deep learning mostly succeeds at system 1 abilities.
It takes an information-theoretical posture to ask questions about what constitutes an interesting mathematical statement.
arXiv Detail & Related papers (2024-03-07T15:12:06Z) - AI for Mathematics: A Cognitive Science Perspective [86.02346372284292]
Mathematics is one of the most powerful conceptual systems developed and used by the human species.
Rapid progress in AI, particularly propelled by advances in large language models (LLMs), has sparked renewed, widespread interest in building such systems.
arXiv Detail & Related papers (2023-10-19T02:00:31Z) - Algorithm-assisted discovery of an intrinsic order among mathematical
constants [3.7689882895317037]
We develop a computer algorithm that discovers an unprecedented number of continued fraction formulas for fundamental mathematical constants.
The sheer number of formulas unveils a novel mathematical structure that we call the conservative matrix field.
Such matrix fields unify thousands of existing formulas, generate infinitely many new formulas, and lead to unexpected relations between different mathematical constants.
arXiv Detail & Related papers (2023-08-22T23:27:47Z) - A Survey on Brain-Inspired Deep Learning via Predictive Coding [85.93245078403875]
Predictive coding (PC) has shown promising performance in machine intelligence tasks.
PC can model information processing in different brain areas, can be used in cognitive control and robotics.
arXiv Detail & Related papers (2023-08-15T16:37:16Z) - Can I say, now machines can think? [0.0]
We analyzed and explored the capabilities of artificial intelligence-enabled machines.
Turing Test is a critical aspect of evaluating machines' ability.
There are other aspects of intelligence too, and AI machines exhibit most of these aspects.
arXiv Detail & Related papers (2023-07-11T11:44:09Z) - Mathematics, word problems, common sense, and artificial intelligence [0.0]
We discuss the capacities and limitations of current artificial intelligence (AI) technology to solve word problems that combine elementary knowledge with commonsense reasoning.
We review three approaches that have been developed, using AI natural language technology.
We argue that it is not clear whether these kinds of limitations will be important in developing AI technology for pure mathematical research.
arXiv Detail & Related papers (2023-01-23T21:21:39Z) - A Survey of Deep Learning for Mathematical Reasoning [71.88150173381153]
We review the key tasks, datasets, and methods at the intersection of mathematical reasoning and deep learning over the past decade.
Recent advances in large-scale neural language models have opened up new benchmarks and opportunities to use deep learning for mathematical reasoning.
arXiv Detail & Related papers (2022-12-20T18:46:16Z) - Inductive Biases for Deep Learning of Higher-Level Cognition [108.89281493851358]
A fascinating hypothesis is that human and animal intelligence could be explained by a few principles.
This work considers a larger list, focusing on those which concern mostly higher-level and sequential conscious processing.
The objective of clarifying these particular principles is that they could potentially help us build AI systems benefiting from humans' abilities.
arXiv Detail & Related papers (2020-11-30T18:29:25Z) - Toward the quantification of cognition [0.0]
Most human cognitive abilities, from perception to action to memory, are shared with other species.
We seek to characterize those capabilities that are ubiquitously present among humans and absent from other species.
arXiv Detail & Related papers (2020-08-12T21:45:29Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.