There is a common expression in the US that goes
You learn something new every day.
The usage goes back to at least the mid 1800s and has risen in popularity since the later 20th century.
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I've found a saying that seems to be related to the meaning described by you: Live and learn (Wiktionary): An exhortation to gain knowledge from living experiences.
Commonly used after an accident or misfortune to indicate a moral lesson.
It is also mentioned as You live and learn
(The Free Dictionary)
: something that you say when you have just discovered something that you did not know.
There's a sample sentence:
I had no idea they were related.
Oh well, you live and learn .
P.S.
In Russian, we have a saying "Live for a century and learn century through" (Век живи, век учись - Vek zhivi, vek uchis').
Or, "one lives through one's life and learns all through one's life", since the word век has an antique sense of 'human lifespan'.
It is used to be said exactly in the manner of "live and learn", after one has discovered something previously unknown.
Sometimes the contemplative ending ".. and still one dies a fool" is added.
ell.stackexchange.com/users/2127/CowperKettle
Similar to @PeterBagnall's answer, a related expression in English is: Even old dogs can learn new tricks.
Interestingly, there is a related, opposite expression in English: You can't teach an old dog new tricks.
This negative expression apparently dates back to 1534 - and started as a literal rather than figurative assertion, also one that underscored difficulty rather than impossibility .
Both expressions have many modern variants, but all with which I am familiar include "old dog(s)" and "new trick(s)".
Using the positive or negative (variants of these)
expression(s) reflects a speaker's general optimism or pessimism about learning as people (figuratively) or dogs (literally) age.
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You're never too old to learn Which also has a connotation that you're never too old to start something new.
ell.stackexchange.com/users/4786/Peter Bagnall
An oft-heard sentiment at commencement ceremonies is: Graduation is not an end, but a beginning.
Then there's:
The more I learn, the less I know.
That ageless paradox goes back a long time.
I've found these quotes online, attibuted to Socrates:
“The only true wisdom is in knowing you know nothing.”
“The more I learn, the more I learn how little I know.”
Einstein is said to have said: “The more I learn, the more I realize how much I don't know.” while the music group Kansas famously sang: “
And if I claim to be a wise man, it surely means that I don't know.”
My dad was fond of quoting this Dutch proverb:
We grow too soon old and too late smart.
These three are not necessarily well-known sayings, but they are related quotes worth mentioning:
“You'll never know everything about anything, especially something you love.”
(Julia Child)
“I am learning all the time.
The tombstone will be my diploma.”
(Eartha Kitt)
“Anyone who stops learning is old, whether at 20 or 80.
Anyone who keeps learning stays young.”
(Henry Ford)
ell.stackexchange.com/users/113/J.R.
A saying in my language would literally translate like this: ‘As long as one lives one is learning!’    I would like to know whether there is an equivalent in English for this saying.
The English equivalent of a saying
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<phrase-request>
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ell.stackexchange.com/users/3223/Lucian Sava
Suggestions for equivalent sayings include: You're never too old to learn; The more I learn, the less I know; You learn something new every day; Live and learn; and The only true wisdom is in knowing you know nothing. Live and learn, the more I learn the less I know, the more I learn the more I learn how little I know, you learn something new every day are all possible phrases.
Live and learn, the more I learn the less I know, the more I learn the more I learn how little I know, you learn something new every day are all possible phrases.