tag:blogger.com,1999:blog-1219943390209086498.post6517150930735143634..comments2019-01-09T16:16:37.309+08:00Comments on A Shed Down Under: Understanding MathematicsJohn S. Jacobhttp://www.blogger.com/profile/07136673809517474111noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-1219943390209086498.post-55833473491793017942018-07-21T15:38:10.857+08:002018-07-21T15:38:10.857+08:00the fact that it can be expanded is evidence that ...the fact that it can be expanded is evidence that it's on the right track. The language in the post I feel does not limit this understanding to only well-known popular branches of mathematics; neither does this post only say what mathematics is not. We get past that part pretty early on in the piece. But saying that it is a process or a language or some other vaguely defined analogous thing I find is not very informative or useful. This is what I set out to do: positively state what it is. To do this I found it necessary to distinguish between the invented ability to write or manipulate - effectively carry on the process of doing mathematical work - and the very essence of the discovered nature of the properties of quantitative objects and concepts.<br /><br />John S. Jacobhttps://www.blogger.com/profile/07136673809517474111noreply@blogger.comtag:blogger.com,1999:blog-1219943390209086498.post-35621789033754993052018-07-14T07:07:03.701+08:002018-07-14T07:07:03.701+08:00Very nice, but could be expanded. Rather than a l...Very nice, but could be expanded. Rather than a list of things Mathematics is not, why not take a more holistic approach and say that, in the set of all things that Mathematics is or can be under the taxonomy definition, the following are found: a tool, a language, a game, etc. To a theoretical physicist, it is most definitely a language, among other things. Just ask the non-initiated who listens to a discussion between theorists. I would emphasize as well the existence of non-quantitative (i.e., non-numerical) mathematical systems: axiomatic topology, for example. Mathematics should also be appreciated as more than a thing (or two things). It is also a process, which is why it is so valuable in the educational curriculum of anyone, whether their life is quantitatively oriented or not. RJJhttps://www.blogger.com/profile/16216335935331900355noreply@blogger.com