It would make sense for the most depressing day of the year to fall in January. Christmas is over and it's freezing but not festive, there is minimal daylight and everyone is broke. Most of us are suffering withdrawals from December's gluttony and excess, the bank holidays are months away and next thing to look forward to is Valentine's Day – which is arguably even more bleak. And so comes Blue Monday on 16 January, allegedly the most depressing day of 2017.

There is a scientific formula for Blue Monday, which although looks fairly legitimate – is actually nonsense. The formula is {[W + (D-d)] x T^Q} ÷ [M x N_a], and it is broken down as follows: W = weather, D = debt, d = monthly salary, M = low motivational levels, Na = the feeling of a need to take action.

But because it is not possible to quantify these factors, it is simply not possible to measure happiness using them. So really, we have no idea if Blue Monday is indeed the most depressing day of the year. There is one key flaw in Arnall's equation – it makes no mathematical sense, so the the date selected for Blue Monday is completely arbitrary.

So where did this formula come from? In short, it was a PR stunt. In 2005, the concept for a "Blue Monday" cropped up on a press release for Sky Travel's PR company, to encourage people with the January blues to book more holidays.

The fact that the theory and formula appeared under the same of a psychology academic called Cliff Arnall of Cardiff University only validated the pseudoscience further, and so it went mainstream.

According to Arnall, the date of Blue Monday – which takes place on the third Monday of January – could be easily calculated by the factors mentioned above. But a year after the first Blue Monday concept was launched, a Guardian article found out that the company behind the PR stunt had approached a handful of academics, offering them cash in exchange for their name on the paper.

But Blue Monday poses a bigger problem than popularising fake science and irritating mathematicians. Although some argue the concept starts an important conversation about mental health, leading charities have pointed out that it is dangerously misleading and threatens to trivialise depression and other mental health issues.

The charity Mind states that Blue Monday has "no foundation in scientific research" – and points out that those who live with depression know all too well that the feelings and symptoms aren't dictated by a date.

"Implying that they are perpetuates the myth that depression is just 'feeling a bit down', something that doesn't need to be taken seriously," the website reads. For this reason, Mind is asking people to use the hashtag #BlueAnyDay to raise awareness of the reality of depression.

The Mental Health Foundation holds a similar view, but tentatively highlights that there is a small element of truth to Blue Monday – that our mental health is affected by our environment and some studies have found seasonal variations in mental health problems. Overall, though, the charity is clear in pointing out the problems of designating one day as the most depressing day of the year.

"It is important to distinguish between temporarily feeling sad or anxious, which we all do from time to time, and mental health problems that can impact on our ability to take pleasure from day-to-day life," the foundation states. "Secondly, the idea that depression can somehow be calculated by formula is seen by many to trivialise their lived experience. Finally, there is an uncomfortableness at how people's mental health is being commodified in a way that physical health wound never be."