A magic square is a quadratic scheme of numbers which adds up vertically, horizontally and diagonally to the same sum.
Example: (sum is 15 for each row, column and diagonal)
There is no such thing like a record for finding the world's largest magic square. There are well-known algorithms for constructing an arbitrarily large magic square. Therefore, it is easy to compute very large magic squares. However, the records in this list are for printing or writing magic squares.
You can read more about magic squares at forum.swarthmore.edu/alejandre/magic.square.html.
Interesting records for multi-magic squares (not only the sum of
the numbers but also the sum of their squares, cubes, etc. must be
the same) can be found at www.multimagie.com.
The Games and Puzzles
Journal and the web site magictour.free.fr list
interesting Magic Knight Tour records.
105 x 105 Richard Suntag (Pomona, USA) 1975
501 x 501 Gerolf Lenz (Wuppertal, Germany) 1979
897 x 897 Frank Tast & Uli Schmidt
(Pforzheim, Germany) 1987
1000 x 1000 Christian Schaller (Munich, Germany) 1988
2001 x 2001 Sven Paulus, Ralph Bülling, Jörg Sutter
(Pforzheim, Germany) 1989
2121 x 2121 Ralf Laue (Leipzig, Germany) 1991
3001 x 3001 Louis Caya (Sainte-Foy, Canada) 1994
3559 x 3559 Peter Weber & Tassilo Herbig (Zittau, Germany) 2012
1111 x 1111 Norbert Behnke (Krefeld, Germany) 1990