What Sumerian advance in mathematics do we use every day when we look at a calendar?

Answer 1

It's not so much the calendar as time:

They rounded up the lunar month to 30 days making the year 360 days, or 6 x 60 days. This 360 was used to divide up the sky and is used today in dividing up a circle in a plane - in 360°.

Where we see Sumerian influence in in time which is measured using sexagesimal (base 60) numbers - there are 60 seconds in 1 minute, 60 minutes in 1 hour.

When writing numbers in different bases, those less than 10 use a subset of the digits 0-9, those over 10 (eg 16 - hexadecimal) use the letters of the alphabet (eg hexadecimal uses 0-9 and a-f). As there are only 26 letters, this limits the base to 10+26 = 36. It could be extended by prescribing use of capitals and lower case letters for higher bases, but instead decimals are used with a symbol to separate the different digits.

For base 60, we use decimal numbers separated by a colon for time, and digits followed by ° (degrees) ' (minutes) " (seconds) for angles.

Using the sexagesimal place value system, each column is 60 times the value of the column to its right, giving ... : 3600 : 60 : 1 as the place column values.

Using the 24 hour clock any time (to the nearest second) is actually the sexagesimal representation of the number of seconds since midnight: H:M:S, for example, 1 minute past midnight = 0:1:0 = 0 × 3600 + 1 × 60 + 0 = 60 seconds past midnight (which makes sense a 1 minute = 60 seconds). Similarly, 15 seconds past 20 minutes past 5 in the afternoon is 17:20:15 = 17 × 3600 + 20 × 60 + 15 = 62415 seconds since midnight.