2025 is remarkable

January 1, 2025 5:34 AM

A Banner Year

Next year’s date, 2025, is remarkable:

It’s a square (45²), the sum of two squares (27² + 36²), the product of two squares (9² × 5²), and 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.

Plus: Crazy Facts About the Number 2025

posted by chavenet (14 comments total)

Very nice. But isn't point 7 just a restatement of point 3?
posted by Panthalassa at 5:44 AM on January 1 [2 favorites]

To keep someone else from staring as long as I was staring: in the second line, all the 3s should be superscript, as should the 2 after the close-parenthesis in the third line.
posted by humbug at 5:44 AM on January 1 [3 favorites]

d'oh. yes, it's all properly formatted in the link. sorry about that
posted by chavenet at 5:47 AM on January 1

Augustus De Morgan used to say, “I was x years of age in the year x2.”

I remember my boyhood frisson upon realizing that I would be 33 and my father 66 in the year 2000.
posted by Lemkin at 6:14 AM on January 1 [3 favorites]

I got a similar shiver a few years ago when I, born in 1974, turned 47 and my dad, born in 1947, turned 74.

That's numberwang.
posted by emelenjr at 6:39 AM on January 1 [20 favorites]

Mod note: Posted edited to correct superscript formatting.
posted by Brandon Blatcher (staff) at 6:46 AM on January 1 [7 favorites]

It’s also the product of the proper divisors of its square root.
posted by madcaptenor at 7:04 AM on January 1 [3 favorites]

Mod note: [#HappyNewYear! We've added this to the New Year's roundup on the sidebar and Best Of blog!]
posted by taz (staff) at 8:56 AM on January 1 [1 favorite]

The Penguin Dictionary of Curious and Interesting Numbers is a book of these kind of facts. Makes a great bathroom book.
posted by neuron at 10:52 AM on January 1 [6 favorites]

And yet no songs written about it...
I guess we'll have to wait another 500 years
SLYT Zager & Evans - In the Year 2525
(I've no ideas what mathematical implications can be drawn from that year)
posted by Dub at 2:29 PM on January 1 [1 favorite]

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.)


What am I missing... 1849 squared is over 3,000,000, which is not an age.
posted by rebent at 6:26 PM on January 1 [1 favorite]

What am I missing... 1849 squared is over 3,000,000, which is not an age.

43 squared is 1849
posted by waving at 7:35 PM on January 1 [3 favorites]

My mathematician dad has been happily sharing these facts since yesterday!
posted by ellieBOA at 2:47 AM on January 2 [3 favorites]

Also (according to the Penguin Dictionary mentioned above) if you add 1 to all the digits you get 3136 which is also a perfect square!
posted by Ishbadiddle at 7:10 AM on January 2 [1 favorite]