Interesting consequence if P = NP, mathematicians could lose their Jobs? Computer Science |
- Interesting consequence if P = NP, mathematicians could lose their Jobs?
- Machine learning with handwritten recog question
- What are the best books for computer information systems?
- Very basics of Computer
- What are some Udemy courses you found useful?
| Interesting consequence if P = NP, mathematicians could lose their Jobs? Posted: 23 May 2021 07:28 AM PDT So the title is tongue in cheek but I think one of the most significant consequences of P = NP would be the fact that since the formal system under ZF-axioms is effectively axiomatized (meaning its theorems are recursively enumerable), the fact that P = NP would mean that there would exist an efficient algorithm to enumerate every theorem in mathematics that can be encoded in reasonable size. Since most "interesting" theorems that mathematicians try to solve are not very complex to represent, such as Fermat's Last Theorem which is a simple "for all n > 2, this statement holds" type problem, it would mean that such deep theorems could be potentially computed in minutes (given that the construction of the theorem itself is of reasonable size). Given such a tool, we could create a huge database of automatically generated theorems that could grow continuously until all theorems have been added. Of course, we'll never know if every theorem has been outputted (otherwise we would be solving the halting problem) but we would have a collection so large that any conjecture that we could reasonably think of would likely be included in it, if it were a provable theorem under ZF-axioms. Imagine a world where all the biggest problems in mathematics right now, the Hodge conjecture, Riemann hypothesis etc. could be automatically proven (or disproven, just check if the negation is enumerated) with no effort, given that they are provable. My question is, would you be happy/comfortable with such a development? Would it ruin the romance of theorem proving and mathematics in general? btw, if I am making any conceptual misunderstandings in this post, please feel free to correct me. [link] [comments]  |
| Machine learning with handwritten recog question Posted: 23 May 2021 10:12 AM PDT Hihi! I'm a bit new to ML , and was a bit confused to some parts of it. For my project, I'm trying to a handwritten recognition of Nepali Characters using this data set: https://www.kaggle.com/rishianand/devanagari-character-set So the output would be like character_1_ka or something now this would be a string? as opposed to the handwritten digit recognition i think. I understand that x_train is the matrix of pixels, but apparently y_train is a vector, but a vector of what? [link] [comments]  |
| What are the best books for computer information systems? Posted: 23 May 2021 10:06 AM PDT |
| Posted: 23 May 2021 05:42 PM PDT Hello, can someone please share resources to learn every bit of computer basics to advance topics? [link] [comments]  |
| What are some Udemy courses you found useful? Posted: 23 May 2021 04:40 AM PDT |
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