Next year’s date, 2025, is remarkable:

• It’s a square (45²).
• It’s a product of squares (9² × 5²).
• It’s the sum of three squares (40² + 20² + 5²).
• It’s the sum of the cubes of the first nine positive integers (1³ + 2³ + 3³ + 4³ + 5³ + 6³ + 7³ + 8³ + 9³).
• Equivalently, it’s the square of the sum of those integers (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9)².
• It’s the second in a trio of square numbers in arithmetic progression (81, 2025, 3969).
• It’s one of only three four-digit numbers whose halves can be split, summed, and squared to produce the original number: (20 + 25)² = 2025.
• It’s the smallest square starting with 20 and the smallest number with exactly 15 odd factors (1, 3, 5, 9, 15, 25, 27, 45, 75, 81, 135, 225, 405, 675, 2025).
• It’s the sum of the entries in a 9×9 multiplication table.
• July 24, 7/24/25, will be a “Pythagorean day,” because 7² + 24² = 25².

When asked his age, Augustus De Morgan used to say, “I was x years of age in the year x².” (He was 43 in 1849.) People born in 1980 will be able to make the same cryptic response starting next year.

(Thanks to readers Chris Smith and Sam Householder.)