Scientists and mathematicians have extremely wide ranges to pursue in expanding the boundaries of their knowledge, so the term “good” is vague at best. The pursuit of knowledge has many forms, which is why academia is entirely about personal ambition and has almost nothing to do with competition. But what terms do scientists and mathematicians use for the major areas? Well, this is folklore, because they have their own language that might be difficult to understand or easy to misconceive for the layperson. I will lay out the terms and their definitions.
-Problem-solving: a major breakthrough on an important problem
-Technique: a masterful use of existing methods or developing a new tool
-Theory: a conceptual framework or choice of notation which systematically unifies and generalizes a body of results
-Insight: a major conceptual simplification or the realization of a unifying principle or theme
-Discovery: the revelation of an unexpected and intriguing new phenomenon, connection, or counterexample
-Application: the use of tools in one field to solve problems in another
-Exposition: a detailed and informative survey on a timely topic or a clear and well-motivated argument
-Pedagogy: contributions to education, a lecture or writing style that enables others to learn and do the subject more effectively
-Vision: a set of conjectures, which are long-range and fruitful
-Taste: a research goal which is inherently interesting and impacts important themes, topics, or questions
-Public relations: an effective show-casing of results to a group of non-experts, either laypeople or experts in other fields
-Meta-(subject): advances in the foundations, philosophy, history, scholarship, or practice of the subject
-Rigorous: all details are correct and given in full
-Beautiful: results are easy to state but hard to prove
-Elegant: achieving a difficult result with a minimum of effort
-Creative: radically new and original techniques, viewpoints, or ideas for results
-Useful: a method which will be used repeatedly in future work on the subject
-Strong: a sharp result that matches the known counterexamples, or a result which deduces an unexpectedly strong conclusion from a seemingly weak hypothesis
-Deep: a result which is manifestly non-trivial, capturing a subtle phenomenon beyond the reach of more elementary tools
-Intuitive: an argument which is natural and easily visualized
-Definitive: a classification of all objects of a certain type, the final word on a topic
Obviously the various sciences have their own opinion on the weight and value they attach to each term.