The Existential Theory of Research: Why Discovery Is Hard

Computer Science > Artificial Intelligence [Submitted on 15 Apr 2026] The Existential Theory of Research: Why Discovery Is Hard Angshul Majumdar Can scientific discovery be made arbitrarily easy by choosing the right representation, collecting enough data, and deploying sufficiently powerful algorithms? This paper argues that the answer is fundamentally negative. We introduce the Existential Theory of Research (ETR), a formal framework that models discovery as the recovery of structured explanations under constraints of representation, observation, and computation. Within this framework, we show that these three components cannot be simultaneously optimized: no method can guarantee universally simple explanations, arbitrarily compressed observations, and efficient exact inference. This limitation is not model-specific, but arises from a synthesis of uncertainty principles in sparse representation, sample complexity bounds in high-dimensional recovery, and the computational hardness of exact inference. We further show that representation mismatch alone can inflate intrinsic simplicity into apparent complexity, rendering otherwise tractable problems observationally and computationally prohibitive. To quantify these effects, we introduce an uncertainty functional that captures the joint difficulty of discovery. The results suggest that scientific difficulty is not accidental, but a structural consequence of the geometry and complexity of inference. Subjects: Artificial Intelligence (cs.AI); Signal Processing (eess.SP) Cite as: arXiv:2604.19810 [cs.AI]   (or arXiv:2604.19810v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2604.19810 Focus to learn more Submission history From: Angshul Majumdar Dr. [view email] [v1] Wed, 15 Apr 2026 10:49:28 UTC (12 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-04 Change to browse by: cs eess eess.SP References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)