There are quite a few prodigies who were prominent at younger age.
In the older days, there were people like William Sidis, who graduated from Harvard at the age of 16 but had a nervous breakdown at 23 and lived as basically a homeless for the rest of his life.
As times improved, prodigies were educated better. However, there is still the case of Ruth Lawrence (1971-), who graduated from Oxford at the age of 13 and was a Ph.D(mathematics) at the age of 21, but met a mathematician double her age when she was 27. He happened to be an Orthodox Jew, so she moved with him to Israel, had 4 children and although she now teaches in a University in Jerusalem, she did not achieve the fame which was expected on her.
There is the tale of Sho Yano. He entered Loyola Univ in Chicago at the age of 9 ,graduated at 12 and entered the Medical school in the same univ.
However, he did not go into the research as expected, and became a clinical pediatric neurologist. While no easy job, it was a big 'surprise' for those who watched him (his mother was Korean so he was also known in Korea too)
What he does now is not clear. A quick search shows he is now a clinical geneticist (those who specialize in genetic diseases) at Bethesda, Maryland. While , again, not a pushover, some people have reservations about the path he chose, considering the ability he had.
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Some people might say as long as these people are happy and do what they wanted to do it is good, but I personally think people should put their ability first , not their happiness.
People like Michael Jackson or Lady Gaga were also called prodigies.
In Korean Pop, there are two prodigies which everyone can kind of recall easily, one of KPop and one not. There might be more but they , in my opinion, are more prominent.
Born in 1986
Selected a trainee in 1998 , age 12, by Lee Sooman himself
At that time, it was rare for pre-teens to train to become an idol , so she went thru a lot of heat. A LOT.
She debuted on August 2000, and Lee Sooman did his best to promote her as a child prodigy. But her initial album didn't do too great, and her Japanese debut in 2001 was also buried.
But, on Jan 2002, when she was 16, "Listen to My Heart" became big in Japan.
And on the same year, No. 1 became big in Korea. She sold 560,000 copies with No.1 in K-O-R-E-A, a record the person I will mention next has NOT broken to this day.
She made the Kohaku in the same year, and won Grand Prizes from Seoul Music Awards, SBS and what later became MAMA at the age of 16.
The rest of her accomplishment are too long to list here. The more prominent ones are the first million seller (Valenti) in Japan at the age of 17, and on that year 2003 reached the singer who was #2 in income rankings (after Hamasaki Ayumi).
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There is one more prodigy most KPop fans will know, even though she is not part of KPop. Since I told her story about 1,343 times I will summarize it
Lee Jieun
Born 1993 (actually around 680)
trained for around 8 months
Debuted 2008, age 15
Break 2010 , age 17
First Gallup #1 song, age 18 (Good Day- 2011)
Lifetime Achievement Award from MAMA, age 21
Highest earning singer of all of Korean Pop , age 24 (2017)
(BoA reached #2 in Japan, but because of the crazy way Japan determines singer's incomes, even the top singers earn less than their equivalents in Korea. IU earned more than the highest earning singer in Japan on her peak year.)
First legitimate Grand Prize age 24 (Through the Night, 2018)
Company Owner, age 27 (forfeit 2022)
Ranked in the top 9 singers of the world, age 28 (Most Awarded Singers, after BTS, The Weeknd, Ed Sheeran, Taylor Swift, Olivia Rodrigo , Justin Bieber, Dua Lipa and Megan Thee Stallion - order not exact)
There might be more, like Jungkook, which I missed. However I think it is proper to call them as Prodigies, since in modern world pop is as prominent as science and tech.