Anna Lemańska
Truth and mathematics
Summary
In the article the problem of truth in mathematics is presented by the example of the six following statements:
1. The continuum hypothesis.
2. The sum of angles in any triangle is equal to the sum of two right angles.
3. For n>2 there isn’t a natural solution of the equation: x^{n} + y^{n} = z^{n}.
4. Every even natural number greater than 2 is the sum of two primes.
5. Every map could be coloured with four colours.
6. 2+2=4.
The analyses carried out in the article show that in mathematics truth can be understood in various manners. We can use different criteria of truth: classical, coherence, pragmatic and others, so in mathematics truth is revealing different faces. Certain sentences are true only in a sense of coherence, but there exist such sentences, as for example truths of arithmetic, which are true independently of axiomatic systems, culture or any other factors.
