This probably doesn't count, but Sosigenes of Alexandria was an Ancient Greek astronomer who designed the Julian calendar in 45 BC. This was replaced in 1582 AD with the Gregorian calendar (named after Pope Gregory XIII) and is still in use today. Of course both were found by science, but it took the weight of the Catholic Church to push for the more accurate calendar.
The Gregorian calendar is pretty solid actually. Other than a leap second every few years, it'll stay in sync for a few thousand years. You can easily calculate all leap days in a one-liner.
365 is semi prime, so we could do a 5 day week, but that's pretty minor in the grand scheme of things. There isn't a lot to improve on the Gregorian calendar
Time zones are an abomination of legacy design features that should be taken out back and put out of their misery... And then a functionally similar but way simpler system put in place.
And that's the way science should be, with more data and better tools, you adjust and make things more accurate. I'm not sure what the efficacy issues are, but it's my understanding that current UTC leap seconds are put in place to reflect slight variation in the rotation of the earth. It is done in reaction to the earth's movement, so not something that could be predicted 450 years ago.
but 13 weeks doesn't divide nicely into the equinoxes, so seasons will start at weird times in the weeks. 12 Months is divisible by 4 so seasons can begin at the same day every 3 months.
I don't understand, the same ±1 day variation we have each year will stay the same? Do you mean the day of month? These are already spread out (20th, 21st, 22nd, and 21st, ±2).
So instead of the summer solstice being 21 June ±1, it will be month 6, day 4 ± 1 every year. (Assuming the year starts on what is now 1 Jan. (Spring is month 3 day 23, fall month 9, day 13, winter month 13 day 1).
Seasons are still 91.25 days, or ~13 weeks. That just now means 3 months one week instead of 3ish months.
The moon phase of 29.54 days won't align, but it doesn't now anyways. So instead of months with 2 moons, we'd get months with no moon. Might have to change "one in a blue moon" to "on a moonless occassion". And imagine the killer party when day 0 or day 00 aligns with a full moon!
I shouldn't have said tricky initially, I should have said annoying and clunky.
Make your year 12 metric weeks, and have the seasons start on the 1st of every third week. Way less clunky than the 1st of the 1st week, the second subweek of the third week, the third subweek of the 6th week, and 4th subweek of the 9th week.
It drives me nuts. Whenever possible, I use the 4-4-5 or 13-month calendars so I can better forecast or compare historical data. Gregorian is useless on month scale or lower. I honestly can't think of any practical use for it except to make things harder.