“Make the world better.”
Last recorded words; said to her daughter. (October 1893)
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Lucy Stone 34
American abolitionist and suffragist 1818–1893Related quotes
Source: As remembered by Don Redelmeir, Michael Lewis, "The Undoing Project: A Friendship that Changed the World". Penguin, 2016 (ISBN 9780141983035).
“I lack only $1 billion to make the world a better world.”
Quoted from Larry King Weekend, Interview With Maharishi Mahesh Yogi (2002-05-12) http://transcripts.cnn.com/TRANSCRIPTS/0205/12/lklw.00.html
Banksyhttp://newsvote.bbc.co.uk/1/hi/entertainment/arts/2018739.stm
Variant: Some people want to make the world a better place. I just wanna make the world a better-looking place. If you don't like it, you can paint over it!
Source: Wall and Piece (2005)

“I have not come into this world to make men better, but to make use of their weaknesses.”
Disputed, (1941-1944) (published 1953)

“If you want to make the world a better place
Take a look at yourself, and then make a change.”
Source: Song Man in the Mirror
Context: I'm starting with the man in the mirror
I'm asking him to change his ways
And no message could have been any clearer
If you want to make the world a better place
Take a look at yourself, and then make a change

Investigations have failed to confirm this in Emerson's writings (John H. Lienhard. "A better moustrap" http://www.uh.edu/engines/epi1163.htm, Engines of our Ingenuity). Also reported as a misattribution in Paul F. Boller, Jr., and John George, They Never Said It: A Book of Fake Quotes, Misquotes, & Misleading Attributions (1989), p. 25. Note that Emerson did say, as noted above, "I trust a good deal to common fame, as we all must. If a man has good corn, or wood, or boards, or pigs, to sell, or can make better chairs or knives, crucibles or church organs, than anybody else, you will find a broad hard-beaten road to his house, though it be in the woods".
Misattributed

“You might not believe it… but you make the world a better place when you smile.”
Variant: The world is a better place when you smile
Source: The Guardian

“The point of life was to press on, to do the best you can, to make the world a better place.”
Source: Clear and Present Danger