Should I mention a "math depression" I went through in my letter of motivation? I am a master student in mathematics studying in Europe and I am applying to several graduate schools in the USA. They aren't all Top 10 in these dubious rankings, but I am applying to Harvard, Northwestern and Rutgers. 

Currently, in the first paragraph of my letter of motivation (=letter of intent, statement of purpose, personal statement, ...) I explain how I overcame a big slump (=phase in which I had not much motivation to learn maths) which I went through after completing my bachelor, so roughly 1 year ago. 
I mention it because this was an important experience to me, and as a result I feel like a more mature mathematician, and I am now confident that I want to do maths in my life. 

However, I read that one should never put negative things about oneself in the letter of motivation, so right now I'm having doubts. 

Could people on the admission committee consider having gone through a slump a negative point? Do they only want to hear how awesome I was my entire life?
Actually, I kind of disagree with @TheHiary... I don't think you should put negative statements about yourself in your cover letter.
While they do not want to only here how awesome you would be, they do want to hear how, and why, you would be totally awesome working for/with them. You can look up some tips and guidelines about writing a cover letter here.
I also think that any half-page story has no place in your cover letter. It should be fairly short, clear and memorable/striking. I was suggested, two pages maximum. One page is better.
But, if it was an important experience for you as a potential researcher, there's definitely place for it in your cover letter, just not directly. What you should include, however, is:

what helped you get back your motivation
(you can say that e.g. a project made you &quot;rediscover your love of science&quot; without explicitly saying that you lost it for a while)

how your approach to research has changed in a positive manner
(e.g. working on the team project made me realize how important and helpful peer input, informal discussions and exchanging ideas was for my productivity)

how your vision of science/yourself changed after that
(e.g. working with Professor X. what made me secure in my opinion that I want a career as a researcher)

basically, any positive result of your experience is worth mentioning, but I would rather mention just what triggered the positive change of attitude instead of motivation-less period before