In 1882, French neurologist Jules Cotard described a strange new syndrome where patients insisted they didn't exist - regardless of all evidence to the contrary. 

And we're not talking about those cliched existential crises many of us will experience at some point in our lives - patients with Cotard's Syndrome believe, with all of their might, that they're either dead or non-existent, in a literal sense.

Also known as Cotard delusion, the condition is so rare, there are no formal estimates on the number of people affected, and the neurological processes behind it are poorly understood. But there are some well documented case studies.

To better grasp what the syndrome entails, take the case of Esmé Weijun Wang - a woman who suddenly developed Cotard's Syndrome back in 2013.

The first signs of the condition were reports that she was becoming more and more "scatter-brained", and slowly losing her grip on reality, reports Meeri Kim at The Washington Post.

After investigating her symptoms further, Wang pinpointed the start of them to a flight from London to San Francisco around a month earlier, when Wang lost consciousness off and on for four hours - an episode that even her doctors could not explain.

Wang was certain that she had died on that flight and now existed in some sort of fray between life and death, which was causing her new-found absent-mindedness.

"I was convinced that I had died on that flight, and I was in the afterlife and hadn't realised it until that moment," Wang explained to The Washington Post in 2015.

"That was the beginning of when I was convinced that I was dead. But I wasn't upset about it, because I thought that I could do things [in my life] over and do them better."

Those initial symptoms of anxiety and loss of reality seem to be common in the early stages of Cotard's Syndrome, but the delusions are unique and specific to each patient.

For example, a Scottish man who experienced brain damage during a motorcycle accident went on to think that a trip to South Africa was in fact a journey into Hell.

As the 1996 book chapter "Betwixt Life and Death: Case Studies of the Cotard Delusion" explains: 

[The patient's] symptoms occurred in the context of more general feelings of unreality and [of] being dead. In January 1990, after his discharge from hospital in Edinburgh, his mother took him to South Africa.

He was convinced that he had been taken to Hell (which was confirmed by the heat), and that he had died of septicaemia (which had been a risk early in his recovery), or perhaps from  AIDS (he had read a story in The Scotsman about someone with AIDS who died from septicaemia), or from an overdose of a yellow fever injection.

He thought he had "borrowed [his] mother's spirit to show [him] around Hell", and that she was asleep in Scotland.

Despite there being a few well-documented cases of people with Cotard's Syndrome, neuroscientists and psychologists still know very little about it - especially seeing as there isn't one particular type of injury or illness that seems to be associated with the syndrome.

But according to Olivia Goldhill at Quartz, a 2013 case study revealed that those with the syndrome had low activity in the areas of their brain associated with bodily awareness.

One hypothesis is that Cotard's Syndrome might be the result of a loss of emotionality towards everything, making a person's experience of the world withdrawn.

"It might be your favourite cat or your favourite food: if you don't have an emotional response, that would be really weird," cognitive scientist Max Coltheart from Macquarie University in Australia told The Washington Post.

"Here is something that looks like your favourite cat, but you aren't getting a buzz. If you were dead, you wouldn't be getting any emotional responses, and that's what may prompt this belief."

While understanding the neurological details of Cotard's Syndrome would dramatically improve the lives of those suffering from it, there's also a lot that the syndrome could tell us about normally functioning brains, too.

For example, understanding how the brain of a Cotard's Syndrome patient disassociates with the 'self' might help researchers understand how self-awareness forms in the brain, which, in turn, might have a serious impact on how we create artificially intelligent programs and robots.

In robotics, it could specifically help artificially intelligent systems to understand contradictions, reports Goldhill.

For instance, consider the sentence, "This sentence is false". Known as a liar's paradox, this sentence is nonsense to a logical machine, but understanding how human brains make sense of these contractions might help machines overcome this barrier.

"It seems to me, that if one took this seriously within my paradigm, it could serve as a guide for how to deal with contradictions and inconsistencies in a computing machine and in a robot," cognitive and computer science professor Selmer Bringsjord, from the Rensselaer Polytechnic Institute in New York, told Quartz.

Cotard's Syndrome is full of contradictions like the one's AI might face one day. For example, how can someone not exist if they are cognitively aware of their nonexistence? Doesn't Descartes' famous line "I think, therefore I am," mean that the thought of non-existence provides proof of existence?

These inconsistencies make Cotard's Syndrome all the more interesting and - as any researcher studying it can tell you - more confusing.

Hopefully, one day we'll have a better understanding of how the syndrome develops, because it wouldn't just help improve the lives of people with this rare condition - it might also help solve a major philosophical and technological dilemma.