The Meanings of Mathematics
Mathematics is used to communicate information about a wide range of different subjects. Here are three broad categories:
- Mathematics describes the real world: many areas of mathematics originated with attempts to describe and solve real world phenomena - from measuring farms (geometry) to falling apples (calculus) to gambling (probability). Mathematics is widely used in modern physics and engineering, and has been hugely successful in helping us to understand more about the universe around us from its largest scales (physical cosmology) to its smallest (quantum mechanics). Indeed, the very success of mathematics in this respect has been a source of puzzlement for some philosophers (see The Unreasonable Effectiveness of Mathematics in the Natural Sciences by Eugene Wigner).
- Mathematics describes abstract structures: on the other hand, there are areas of pure mathematics which deal with abstract structures, which have no known physical counterparts at all. However, it is difficult to give any categorical examples here, as even the most abstract structures can be co-opted as models in some branch of physics (see Calabi-Yau spaces and string theory).
- Mathematics describes mathematics: mathematics can be used reflexively to describe itself—this is an area of mathematics called metamathematics.
Mathematics can communicate a range of meanings that is as wide as (although different from) that of a natural language. As English mathematician R.L.E. Schwarzenberger says:
- My own attitude, which I share with many of my colleagues, is simply that mathematics is a language. Like English, or Latin, or Chinese, there are certain concepts for which mathematics is particularly well suited: it would be as foolish to attempt to write a love poem in the language of mathematics as to prove the Fundamental Theorem of Algebra using the English language. - Schwarzenberger (2000)
Read more about this topic: Language Of Mathematics
Famous quotes containing the words meanings and/or mathematics:
“You can’t write about people out of textbooks, and you can’t use jargon. You have to speak clearly and simply and purely in a language that a six-year-old child can understand; and yet have the meanings and the overtones of language, and the implications, that appeal to the highest intelligence.”
—Katherine Anne Porter (1890–1980)
“Mathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don’t happen to have all the data. In mathematics we have all the data ... and yet we don’t understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence.”
—Simone Weil (1909–1943)