Different types of usefulness of a field of mathematics:
- One can use the field to construct an empirically adequate model in some scientific discipline (calculus in classical mechanics)
- One can reduce a class of problems from one field to another (commutative algebra in number theory, linear algebra in differential topology)
- The field is 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑖𝑣𝑒 to a whole new class of questions or mode of thinking (topos theory in Grothendieck's algebraic geometry, the formalization of real analysis in the 19th century)
- The field unifies previously disparate ideas allowing us to use insights from one domain in another (set theory/category theory)
- One can gain a brand new perspective more amenable with your mode of thinking or different from a previously dominant view (Galois theory to study polynomial equations, combinatorial species, the use of cohomology for matroids/graphs etc.)
Boarders /
npub19u…tn6t5
2023-07-09 04:52:40
Author Public Key
npub19u906k47vnunmzn4scrr77qmd8nr8pamnf2d232ulnjn77u8a5rqjtn6t5Seen on
wss://relay.nostr.bandPublished at
2023-07-09 04:52:40Event JSON
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"content": "Different types of usefulness of a field of mathematics:\n\n- One can use the field to construct an empirically adequate model in some scientific discipline (calculus in classical mechanics)\n\n- One can reduce a class of problems from one field to another (commutative algebra in number theory, linear algebra in differential topology)\n\n- The field is 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑖𝑣𝑒 to a whole new class of questions or mode of thinking (topos theory in Grothendieck's algebraic geometry, the formalization of real analysis in the 19th century)\n\n- The field unifies previously disparate ideas allowing us to use insights from one domain in another (set theory/category theory)\n\n- One can gain a brand new perspective more amenable with your mode of thinking or different from a previously dominant view (Galois theory to study polynomial equations, combinatorial species, the use of cohomology for matroids/graphs etc.)",
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