Is there a solution for parker's square?

Question

From wiki: Mathematician Matt Parker attempted to create a 3x3 magic square using square numbers in a YouTube video on the Numberphile channel. His failed attempt is known as the Parker Square.

I wonder , if there's a solution or proof that there is none?

Answer 1

This is an open problem. No example is known; nor is a proof that there is none.

Open Problem Garden says:

This question was first asked in 1984 by Martin LaBar and popularized in 1996 by Martin Gardner, who offered \$100 to the first person to construct such a square. In 2005 Christian Boyer offered €1,000 and a bottle of champagne for a solution to a somewhat easier problem. For a review of the history of research, see […]. For basic facts about the anticipated $ 3\times 3 $ magic square of squares, see […].

Some discussion is given on mathpages.com.