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The Nature of Mathematics – an interview with Professor Karlis Podnieks
| Content Provider | Semantic Scholar |
|---|---|
| Author | Podnieks, Karlis Tabak, John |
| Copyright Year | 2011 |
| Abstract | Many people think that mathematical models are built using well-known “mathematical things” such as numbers and geometry. But since the 19th century, mathematicians have investigated various non-numerical and non-geometrical structures: groups, fields, sets, graphs, algorithms, categories etc. What could be the most general distinguishing feature that would separate mathematical models from non-mathematical ones? I would describe this feature by using such terms as autonomous, isolated, stable, self-contained, and – as a summary – formal. Autonomous and isolated – because mathematical models can be investigated “on their own” in isolation from the modeled objects. And one can do this for many years without any external information flow. Stable – because any modification of a mathematical model is qualified explicitly as defining a new model. No implicit modifications are allowed. Self- contained – because all properties of a mathematical model must be formulated explicitly. The term “formal model” can be used to summarize all these features. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://scireprints.lu.lv/192/1/Interview_Podnieks_Tabak.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Discussion |
