> I think what is really being asked is: "What level of confidence is required?". That's something that varies from field to field. In physics, a new discovery

> I think what is really being asked is: "What level of confidence is required?". That's something that varies from field to field. In physics, a new discovery requires a five-sigma result, meaning a result that has a one in 3.5 million probability of arising by chance rather than the legitimate detection of a new particle or phenomenon. http://www.select-statistics.co.uk/blog/webmaster/one-sigma-or-five http://www.select-statistics.co.uk/blog/webmaster/one-sigma-... In psychology, by contrast, a p-value of 0.05 (i.e. 2 sigma) is accepted as statistically significant, which by itself may explain the sad state of the field. http://en.wikipedia.org/wiki/P-value http://en.wikipedia.org/wiki/P-value > I would assume you trust the hardware and only scrutinise the software? No, a scientist doesn't trust either hardware or software, but hardware can be checked and validated. In the case of Mathematica, the software cannot be checked and validated, it must be trusted. And for a scientist, trust cannot be distinguished from faith.