Fear of trains fear about rail travel was heightened after British surgeon John Eric Erichsen described a post-traumatic diagnosis known as railway spine or "Erichsen's disease". People diagnosed with this had no obvious injury and were rejected as fake. Nowadays it is known that traffic accidents may cause posttraumatic stress disorder. It has been variously called as "train phobia", "railroad phobia", "dread of railway travel", etc. The German term "Eisenbahnangst" used, e.g., by Sigmund Freud was literally converted into Greek as "siderodromophobia" (Eisen = sideron = iron, Bahn = dromos = way, Angst = phobos = fear). In cases when this anxiety exceeds
Irrational number to show that π is irrational, whence it follows immediately that π is irrational also. The existence of transcendental numbers was first established by Liouville (1844, 1851). Later, Georg Cantor (1873) proved their existence by a different method, which showed that every interval in the reals contains transcendental numbers. Charles Hermite (1873) first proved "e" transcendental, and Ferdinand von Lindemann (1882), starting from Hermite's conclusions, showed the same for π. Lindemann's proof was much simplified by Weierstrass (1885), still further by David Hilbert (1893), and was finally made elementary by Adolf Hurwitz and Paul Gordan. The square root of 2