What is good mathematics

By Terence Tao. 2007

78 citations recorded by the source corpus.

(i) Good mathematical problem-solving (e.g. a major breakthrough on an important mathematical problem); (ii) Good mathematical technique (e.g. a masterful use of existing methods, or the development of new tools); (iii) Good mathematical theory (e.g. a conceptual framework or choice of notation which systematically unifies and generalises an existing body of results); (iv) Good mathematical insight (e.g. a major conceptual simplification, or the realisation of a unifying principle, heuristic, analogy, or theme); (v) Good mathematical discovery (e.g. the revelation of an unexpected and intriguing new mathematical phenomenon, connection, or counterexample); (vi) Good mathematical application (e.g. to important problems in physics, engineering, computer science, statistics, etc., or from one field of mathematics to another); (vii) Good mathematical exposition (e.g. a detailed and informative survey on a timely mathematical topic, or a clear and well-motivated argument); (viii) Good mathematical pedagogy (e.g. a lecture or writing style which enables others to learn and do mathematics more effectively); (ix) Good mathematical vision (e.g. a long-range and fruitful program or set of conjectures); (x) Good mathematical taste (e.g. a research goal which is inherently interesting and impacts important topics, themes, or questions); (xi) Good mathematical public relations (e.g. an effective showcasing of a mathematical achievement to non-mathematicians, or from one field of mathematics to another); (xii) Good meta-mathematics (e.g. advances in the foundations, philosophy, history, or practice of mathematics); (xiii) Rigorous mathematics (with all details correctly and carefully given in full, etc.); (xiv) Beautiful mathematics (e.g. the amazing identities of Ramanujan; results which are easy (and pretty) to state but not to prove); (xv) Elegant mathematics (e.g. Paul Erdős’ concept of “proofs from the Book”; achieving a difficult result with a minimum of effort);

Subfields: Discrete Mathematics and Combinatorics, Electrical and Electronic Engineering, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/17c366f4554e519b03235adcfa86c07eb4fde47b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Discrete Mathematics and Combinatorics

  1. Matthew Inglis
  2. Keith Weber
  3. Andrew Aberdein

In Electrical and Electronic Engineering

  1. Matthew Inglis
  2. Keith Weber
  3. Andrew Aberdein

In Geometry and Topology

  1. Matthew Inglis
  2. Juan Pablo Mejía-Ramos
  3. Keith Weber
  4. Andrew Aberdein
  5. Francesca Morselli
  6. Fulvia Furinghetti

Citations in the corpus