Importance of rigor I always have a hard time explaining the importance of rigor to my friends who are not mathematically minded. A lot of past mathematicians develop the foundations of today's mathematics without going through all the rigor but their work is still relevant now, e.g. Newton and Leibniz's calculus and Euler's work on infinite series. Is there a historical event where a wrong conclusion is derived due to lack of rigor and cause a harmful effect? **Edit** : Thanks so much for the lively discussion! I just want to point out that I'm not interested in counterintuitive results or paradoxes, instead I'm looking for instances where wrongly derived conclusion caused a _disastrous effect_.

Cauchy and Fourier had a famous dispute about whether Fourier's use of trigonometric series to solve the heat equation was valid. To a large extent, the basic rigorous notions of analysis were formalized in order to resolve this dispute. Along the way, Cauchy published a famous "wrong" theorem. (It wasn't really wrong; it just used a different definition than that which became standard.)

Here's another, more applied, example. I remember going to an joint meetings talk years ago in which the speaker described a situation in which engineers had employed widely-used software to numerically compute solutions to PDE's. But they had neglected to prove that, at the level of precision they were using, their methods would converge to the correct solution. The result was disastrous: a brand new 180 million dollar oil rig collapsed so thunderously that it registered a 3 on the Richter scale.

_EDIT:_ Thanks to Kcd here's the link to more details.