Mad as a hatter is not from Alice in Wonderland like I once thought.
Mad as a Hatter comes from the fact that in the 18th and 19th centuries hat makers treated hats with mercury which became a hazardous occupation. This was known to have affected the nervous systems of hatters, causing them to tremble and appear insane. A neurotoxicologist correspondent informs me that “Mercury exposure can cause aggressiveness, mood swings, and anti-social behaviour.”, so that derivation is certainly plausible – although there’s only that circumstantial evidence to support it.
The use of mercury compounds in 19th century hat making and the resulting effects are well-established – mercury poisoning is still known today as ‘Mad Hatter’s disease’. That could be enough to convince us that this is the source of the phrase. The circumstantial evidence is rather against the millinery origin though and, beyond the fact that hatters often suffered trembling fits, there’s little to link hat making to the coining of ‘as mad as a hatter’.