Reuben Hersh有感于Courant的《数学是什么》（What is Mathematics?）只是“秀”了数学却没有正面回答问题，就写了一本What is Mathematics, Really?（Oxford版，1997）从“人文主义”（humanism）——区别于传统的各种数学主义，如Platonism, logicism, intuitionism, constructivism, conventionalism, structuralism, fictionalism等角度考察数学——数学是一种“社会-文化-历史活动”（A humanist sees mathematics as a social-cultural-historic activity），“数学是一种生命形式”（a form of life）。他列了数学哲学12条：

1. Breadth

2. Connected with epistemology and philosophy of science

3. Valid against practice: research, applications, teaching, history, computing, intuition

4. Elegance

5. Economy

6. Comprehensibility

7. Precision

8. Simplicity

9. Consistency

10. Originality/novelty

11. Certitude/indubitability

12. Acceptability

   陶哲轩（Terence Tao）也列过很多条“好数学”的标准，除去一些“普通条款”（如解决重大难题，发展新技术，系统化，重要应用，大众普及等等），还有几条特别的，如好的愿景（vision），好的品味（taste），好的元数学（或数学基础），

Good mathematical vision (e.g. a long-range and fruitful program or set of conjectures)

Good mathematical taste (e.g. a research goal which is inherently interesting and impacts important topics, themes, or questions)

Good meta-mathematics (e.g. advances in the foundations, philosophy, history, or practice of mathematics)

Beautiful mathematics (e.g. the amazing identities of Ramanujan; results which are easy (and pretty) to state but not to prove)

Elegant mathematics (e.g. Paul Erd˝os’ concept of “proofs from the Book”; achieving a difficult result with a minimum of effort)

Intuitive mathematics (e.g. an argument which is natural and easily visualisable)

我想任何科学都应该学习这些优良品质。如果一门科学还只是一味讲“解决问题”而没想到“好”和“美”，那就只是“猿文的科学”而不是“人文的科学”。