Is it actually helpful to write todo lists? I've watched these two videos recently


How to Get things done which contains some tips from David Allen's book, "Getting Things Done", and the other video
How to hack your todo list which also contains some parts from the above mentioned book.


What this author suggests is writing down your tasks instead of keeping it in your prefrontal cortex, therefore you'll be more free to think about task at hand. I think I've read the book long time ago and there is some research mentioned (as in most books alike). 

Except for complex tasks that need to be broken down, I almost never had the benefit of writing task to a to do list. I actually found it terrible that my brain seemed to partially forget things while relying on the list [ which I didn't bring with me or I was in the hurry and forgot to look into my phone app]. I don't know if I was biased by the content of the book or if there is some science behind forgetting tasks that you jot down on the piece of paper. 

I understand that some people have a more complex day than me and need todo list for not-so-related things, but I find it somewhat scary that so many people so easily rely on something else remembering things for them.

I tried using lists because I was afraid I'll forget what I need to do. When it started bothering me, I decided not to write anything but longer grocery lists. And it's interesting how my brain started remembering things and recalling them exactly when I need them. I didn't feel my brain was cluttered, because I remembered tasks at the right time and right place[ I never thought about grocery list during working hours and vice versa].

I don't know it there is any well known research behind this "write things down to unclutter your brain"-thing, or it all boils down to poor memory or lack of commitment to remember something important ?

Side question, but related :  is it even possible to quickly forget the task and leave it written on the piece of paper ? 

I just want to know if this thing really works or it just sells similar books for time management.
There is some research that suggests writing a to-do list will help "unclutter your brain." The research is related to the phenomenon known as the Zeigarnik effect. 

The basic observation behind the Zeigarnik effect is that we tend to think more about tasks and goals that are incomplete. This leads to, among other things, increased priming for concepts related to a unfinished goal relative to a finished one (Förster, Liberman, &amp; Higgins, 2005).

Masicampo &amp; Baumeister (2011) investigated whether making a plan to finish a goal, as opposed to actually finishing the goal, could lead to a similar reduction in intrusive thoughts about the goal. They report:


  In several studies, we activated unfulfilled goals
  and demonstrated persistent goal activation over time. Unfinished goals caused intrusive thoughts during
  an unrelated reading task (Studies 1 and 5B), high mental accessibility of goal-related words (Studies 2
  and 3), and poor performance on an unrelated anagram task (Study 4). Allowing participants to formulate
  specific plans for their unfulfilled goals eliminated the various activation and interference effects.
  Reduction of the effects was mediated by the earnestness of participants’ plans: Those who ultimately
  executed their plans were those who also exhibited no more intrusions (Study 4). Moreover, changes in
  goal-related emotions did not appear to be a necessary component of the observed cognitive effects
  (Studies 5A and 5B). Committing to a specific plan for a goal may therefore not only facilitate attainment
  of the goal but may also free cognitive resources for other pursuits. Once a plan is made, the drive to
  attain a goal is suspended—allowing goal-related cognitive activity to cease—and is resumed at the
  specified later time.


In sum, there seems to be some evidence that uncompleted tasks do lead to intrusive thoughts, and that finishing the tasks reduces intrusive thoughts. Alternatively, making and committing to a plan to finish the tasks can reduce the instrusive thoughts even in the absence of finishing the task.

References

Förster, J., Liberman, N., &amp; Higgins, E. T. (2005). Accessibility from active and fulfilled goals. Journal of Experimental Social Psychology, 41(3), 220-239.

Masicampo, E. J., &amp; Baumeister, R. F. (2011). Consider it done! Plan making can eliminate the cognitive effects of unfulfilled goals. Journal of Personality and Social Psychology, 101(4), 667.