The leap year is February 29, not December 32 due to a Roman calendar quirk

To expand on this: "sept-" is a prefix meaning 7, like septuplets. But September is the 9th month of the year. "oct-" means 8 like octagon, but October is the 10th month of the year. And so on for November and December.

"Historical" meaning going back to the Roman Republic:

> We can partly thank the Roman king Numa Pompilius. According to tradition, during his reign (c. 715–673 BCE) Numa revised the Roman republican calendar so that January replaced March as the first month. It was a fitting choice, since January was named after Janus, the Roman god of all beginnings; March celebrated Mars, the god of war. (Some sources claim that Numa also created the month of January.) However, there is evidence that January 1 was not made the official start of the Roman year until 153 BCE.

> In 46 BCE Julius Caesar introduced more changes, though the Julian calendar, as it became known, retained January 1 as the year’s opening date.

* https://www.britannica.com/story/why-does-the-new-year-start...

> The Romans did not have records of their early calendars but, like modern historians, assumed the year originally began in March on the basis of the names of the months following June. The consul M. Fulvius Nobilior (r. 189 BC) wrote a commentary on the calendar at his Temple of Hercules Musarum that claimed January had been named for Janus because the god faced both ways,[83][where?] suggesting it had been instituted as a first month.[citation needed] It was, however, usually said to have been instituted along with February, whose nature and festivals suggest it had originally been considered the last month of the year. The consuls' term of office—and thus the order of the years under the republic—seems to have changed several times. Their inaugurations were finally moved to January 1(Kal. Ian.) in 153 BC to allow Q. Fulvius Nobilior to attack Segeda in Spain during the Celtiberian Wars, before which they had occurred on March 15 (Eid. Mart.).[87] There is reason to believe the inauguration date had been May 1during the 3rd century BC until 222 BC[citation needed] and Livy mentions earlier inaugurations on May 15 (Eid. Mai.), July 1 (Kal. Qui.), August 1 (Kal. Sex.), October 1(Kal. Oct.), and December 15 (Eid. Dec.).[88][where?] Under the Julian calendar, the year began on January 1 but years of the Indiction cycle began on September 1.

* https://en.wikipedia.org/wiki/Roman_calendar#Years

Notably, I thought the accounting/tax year started in late March, and didn't change to January because figuring out a 10-month accounting/tax year would be a nightmare. But also, accountants didn't skip the days that everyone else did when moving from the Julian to the Gregorian calendar, because paying people 2/3 of a month's salary and charging 2/3 of a month's rent would also be a nightmare, which is why the accounting/tax year now starts on April 6th?

(Calendars are weird, yo!)

> Except that isn’t exactly true. The Romans did not add an extra day on February 29, but on February 24, which is where the more complicated answer begins. The Romans kept a calendar by counting backwards from specific set times of the month, the kalends (March 1), the nones (March 7) and the ides (March 15). Julius Caesar was famously told in Shakespeare’s play to: “Beware the ides of March,” also known as March 15, the day of his murder.

> If the Romans started counting on the first day of March, which they called the kalends and moved backwards, then their days would progress retrospectively like this: the kalends is March 1, second kalends is February 28, third kalends is February 27 and so on until February 24 is the sixth kalends of March. On a leap day, they added a second sixth kalends of March, which they called the “bissextile day”, that is the second sixth day. In older writings of various kinds, you will still see people call the leap day, February 29, the bissextile day.

What the article doesn't explain, and I don't know either, is why they chose the sixth calends of March specifically, because there are "higher" calends, so it's not really the natural place to stick it.

The Romans actually added January and February to the beginning of the year very early on, according to Livy, in the time of King Numa, second legendary king of Rome. The article doesn't mention this, but even during almost all of what we know as Rome, the months were numbered wrong!

ed: what a mess! the answer appears to be here: https://www.google.com/books/edition/Johnson_s_Universal_Cyc...

Basically, the last days of February were already "past" the end of the religious year and placed in a special intercalary period, so the sixths calends of February was the last day of the "real" religious year in his time, which did not end at the same time as the business or calendar year. I think. This source also claims Caesar put January at the beginning of the year, which I am fairly sure is not correct.

ed2: apparently authorities differ on month ordering timelines: Wikipedia cites Plutarch (not Livy) as saying it was King Numa who placed January at the begiining, Livy placing it centuries later during the late Republic, and others putting it in the time of the decemvirs, but I think it is still the case that even after the ordering was done the religious observances for the "end" of the year continued to take place in the beginning of the calendar year.

But I guess this idea is wrong ?

Actually, I think that's the only rule most people know. I think the "funny story" is actually the opposite: most people were treating 2000 as an ordinary every-4-year leap year, did not know about the 100 divisor, but were inadvertently saved by the 400 divisor.

The Wikipedia link does document some cases of what you say (yes on the 2nd rule, omitting the 3rd rule) but I think there were far, far more cases of simply assuming only the 1st rule applied.

Instead of showing rules as a linear list, I'd suggest it's easier to visualise it as a tree, or simpler still, as a series of nested ifs.

https://en.wikisource.org/wiki/Translation:Inter_gravissimas

"Next, so that the equinox will no longer recede in future from the twelfth day before the Kalends of April [i.e. 21 March], we decree:

    that the bissextile day every fourth year shall continue, as the custom is now, except in centurial years, although these were always bissextiles before, and we wish the year 1600 to be bissextile as well;
    after that, however, the centurial years that follow shall not all be bissextiles, only every fourth centurial year shall be bissextile, thus the years 1700, 1800 and 1900 shall not be bissextile. But in the year 2000, the bissextile day shall be added in the usual way, with February containing 29 days;
    and then the same order of leaving out and adding the bissextile day shall be observed in each period of 400 years ever after."

And you can have a "year day (or 2 on leap years) at the end to round the calendar out to 365 days.

It makes too much sense, that's why it will never happen. https://en.m.wikipedia.org/wiki/International_Fixed_Calendar

13 months of 29 days. The 29th of each month being imaginary with two exceptions, 1 annual and 1 leap.

Or more seriously, https://en.wikipedia.org/wiki/International_Fixed_Calendar

13 is a prime number.

There's a reason the number 12 comes back to often for these types of things.

And the current calender really isn't that much of a hassle.

Curious, how would you fix the leap year stuff?