Timeline for When is one 'ready' to make original contributions to mathematics?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Aug 26, 2019 at 0:41 | comment | added | user1318416 | I liken the process to an explosion once the theory fails to be self-encapsulating. It explodes because subsequent work is more likely to increase the complexity of the given subject matter rather than decrease it. In some fields, even coming to understand the definitions and prerequisite vocabulary is quite the process. | |
| Aug 26, 2019 at 0:26 | comment | added | user1318416 | It would be the theory relating to functional programming and the Curry-Howard Isomorphism as a medium for mathematical statements and their associated proofs. Comparatively simple representations exist independently for representing logical statements (syntax of terms, logical connectives, and quantifiers) and functional programming (think Lisp or lambda calculus), but not their union. | |
| Aug 25, 2019 at 22:26 | comment | added | Gerry Myerson | Very interesting, but exactly which mathematical theory was it that exploded in that case, and what leads you to liken it to an explosion? | |
| Aug 25, 2019 at 19:20 | history | edited | user1318416 | CC BY-SA 4.0 |
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| Aug 25, 2019 at 17:54 | comment | added | user1318416 | @Gerry One good example is the AGDA programming language (agda.readthedocs.io/en/v2.6.0.1/index.html), a dependently-typed programming language designed to encode mathematical proofs. Over time, the number of built-in language features has expanded, but mostly to resolve special cases or counterexamples. Such cases have struggled to assimilate into the main Curry-Howard/functional programming theory. | |
| Aug 25, 2019 at 0:27 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| Aug 25, 2019 at 0:08 | comment | added | Gerry Myerson | "Mathematical theories in such cases will usually undergo a process of explosion" Can you give an example of a mathematical theory exploding? | |
| Aug 24, 2019 at 19:20 | review | First posts | |||
| Aug 24, 2019 at 21:07 | |||||
| Aug 24, 2019 at 19:19 | history | answered | user1318416 | CC BY-SA 4.0 |