Mathematical understanding and the physical sciences

摘要

The author claims to have developed interactional expertise in gravitational wave physics without engaging with the mathematical or quantitative aspects of the subject. Is this possible? In other words, is it possible to understand the physical world at a high enough level to argue and make judgments about it without the corresponding mathematics? This question is empirically approached in three ways: (ⅰ) anecdotes about non-mathematical physicists are presented; (ⅱ) the author undertakes a reflective reading of a passage of physics, first without going through the maths and then after engaging with it and discusses the difference between the experiences; (ⅲ) the aforementioned exercise gives rise to a table of Levels of Understanding of mathematics, and physicists are asked about the level mathematical understanding they applied when they last read a paper. Each phase of empirical research suggests that mathematics is not as central to gaining an understanding of physics as it is often said to be. This does not mean that mathematics is not central to physics, merely that it is not essential for every physicist to be an accomplished mathematician, and that a division of labour model is adequate. This, in turn, suggests that a stream of undergraduate physics education with fewer mathematical hurdles should be developed, making it easier to train wider groups of people in physical science comprehension.