“It is not true that people stop pursuing dreams because they grow old, they grow old because they stop pursuing dreams.”

Dream it. Wish it. Do it. http://www.storypick.com/quotes-by-tendulkar/

Source: The Dying Animal

Variant: I would prove to the men how mistaken they are in thinking that they no longer
fall in love when they grow old--not knowing that they grow old when they stop
falling in love.

Source: Born to Run: A Hidden Tribe, Superathletes, and the Greatest Race the World Has Never Seen

Source: The Alchemist

"The Old Player" (1861), in Songs in Many Keys (1862).
Context: Dream on! Though Heaven may woo our open eyes,
Through their closed lids we look on fairer skies;
Truth is for other worlds, and hope for this;
The cheating future lends the present's bliss;
Life is a running shade, with fettered hands,
That chases phantoms over shifting sands;
Death a still spectre on a marble seat,
With ever clutching palms and shackled feet;
The airy shapes that mock life's slender chain,
The flying joys he strives to clasp in vain,
Death only grasps; to live is to pursue, —
Dream on! there 's nothing but illusion true!

2016, Remarks to the People of Cuba (March 2016)
Context: There’s still enormous problems in our society. But democracy is the way that we solve them. That's how we got health care for more of our people. That's how we made enormous gains in women’s rights and gay rights. That's how we address the inequality that concentrates so much wealth at the top of our society. Because workers can organize and ordinary people have a voice, American democracy has given our people the opportunity to pursue their dreams and enjoy a high standard of living.

Source: How to Be Like Walt : Capturing the Magic Every Day of Your Life (2004), Ch. 3 : Imagination Unlimited, p. 63; Unsourced variant: All your dreams can come true if you have the courage to pursue them.

1980s, A Dream Deferred (1989)
Context: During the era of segregation a term was used to describe the racist separate system that was primarily intact in the South, although of course there were vestiges of it all across the rest of the country—it was called Jim Crow. Well, in 1989 I am pleased to say Jim Crow is dead, but as has been proven by incidents that happened in Forsyth County in Georgia, Howard Beach in New York, the community of Overton in Miami, just by cross burnings on college campuses, and by racial epithets being written on the walls of many of our college facilities. These incidents and so many more that are terrifying really, when we stop and think that they are still occurring in this country, point to the fact that while Jim Crow is dead his slightly more sophisticated first born son, J. Crow, Esquire, is alive and kicking. We as black people, we as women, we as humanity have not reached the promised land. We are still wandering around bumping into each other in the wilderness. The dream, that magnificent dream, pursued so fiercely by my father, is still only a dream. Racism, sexism, injustices, inequities of all shapes and sizes remain and we have to find a semblance of real peace, not the kind of peace where everything is wonderful on the surface but things are boiling underneath. I am talking about peace with justice. My father’s utterance rings persistently—either we will learn to live together as brothers and sisters or we will perish together as fools.