too simple to be simple in nLab
Quite often, classical references will define ‘simple’ (or an analogous term) in naïve way, so that a ‘trivial’ object is simple, but later it will become clear that more sophisticated theorems (especially classification theorems) work better if the definition is changed so that the trivial object is not simple. Usually this can be done by changing ‘if’ to ‘iff’ (or sometimes changing ‘or’ to ‘xor’) in the classical definition.
too simple to be simple in nLab nLab too simple to be simple Skip the Navigation Links | Home Page | All Pages | Latest Revisions | Discuss this page | Too simple to be simple Too simple to be simple Idea Examples Relationship to biased definitions Idea There is a general principle in mathematics that A trivial object is too simple to be simple. Quite often, classical references will define ‘simple’ (or an analogous term) in naïve way, so that a ‘trivial’ object is simple, but later it will become clear that more sophisticated theorems (especially classification theorems) work better if the de
saved by
related reading
- The fall of the theorem economydavidbessis.substack.com
- Napkin.pdfvenhance.github.io
- There’s more to mathematics than rigour and proofs | What's newterrytao.wordpress.com
- Simplicity is An Advantage but Sadly Complexity Sells Bettereugeneyan.com
- Simple Made Easy - InfoQinfoq.com
- Logical difficulties in modern mathematics | njwildberger: tangential thoughtsnjwildberger.com
- Philosophy of Mathematics (Stanford Encyclopedia of Philosophy)plato.stanford.edu
- Mereological nihilismen.wikipedia.org
- Abstract simplicial complexen.wikipedia.org
- (Stanford Encyclopedia of Philosophy)plato.stanford.edu
- Computational Complexity Theory (Stanford Encyclopedia of Philosophy)plato.stanford.edu
- Infinity Category Theory Offers a Bird's-Eye View of Mathematics | Scientific Americanscientificamerican.com