What's more it's the only square-numbered year you and I will ever live in.
The last was 1936 (= 44 × 44), and you'd have to be over 88 to be alive back then.
The next will be 2116 (= 46 × 46), and that's in 91 years time.
So 2025 is all we're getting, square-wise.
2025 is extra-special, as square numbers go, because 20 + 25 = 45.
2025 = (20 + 25)2
2025 is also the square number of a triangular number.
(1+2+3+ ... +8+9)2 = 452 = 2025
This is rare.
The last time it happened was in 1296 = (1+2+3+ ... +8)².
Edward I was on the throne at the time.
It also helps explain an extraordinary fact about the standard 9×9 multiplication table...
If you add up all the numbers in the multiplication table the total is 2025!
The underlying reason is that the digits 1 to 9 add up to 45.
Thus each row totals a different multiple of 45 from 1×45 to 9×45.
Surprisingly 2025 is also the sum of the first nine cube numbers.
13+23+33+43+53+63+73+83+93 = 2025
This is equally rare - it last happened in 1296.
Mathematically it's always true that 1³+2³+3³+...+n³ = (1+2+3+...+n)²
One of the reasons 2025 is particularly special is because of its prime factorisation.
2025 = 34 × 52
It's rare that a year is the product of two single-digit prime factors.
This last happened in 2000 (= 2⁴ × 5³).
It will next happen in 2304 (= 2⁸ × 3²).
What's particularly unusual is that all the powers in the prime factorisation are even numbers.
This means 2025 is also the product of two square numbers.
32 × 152 = 2025
This last happened in 1936 (= 4² × 11²) and will next happen in 2116 (= 2² × 23²).
Even rarer, it's the product of three square numbers.
32 × 32 × 52 = 2025
2025 is also the sum of two square numbers.
272 + 362 = 2025
This last happened in 2020 (= 16² + 42²) (= 24² + 38²)
...and will next happen, trivially, in 2026 (= 45² + 1²)
2025 is also the sum of three square numbers in eleven different ways. (I invited readers to tell us what they are, one set each)
