The use of base 60 for measuring time can be traced back to ancient Mesopotamia, specifically to the Sumerians, who lived around 4000 to 2000 BCE. The Sumerians developed a number system based on the sexagesimal (base 60) system, which they used for various calculations, including measuring time.
The choice of base 60 likely stemmed from the Sumerians' mathematical capabilities and the practicality of using 60 as a base. The number 60 has several divisors (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30), making it a highly divisible number. This divisibility allowed for easier fractions and calculations in daily life. For example, fractions such as 1/2, 1/3, 1/4, 1/5, 1/6, 1/10, 1/12, 1/15, 1/20, and 1/30 can be expressed as finite decimal fractions in base 60.
The sexagesimal system used by the Sumerians was later adopted and developed further by subsequent civilizations in the region, such as the Babylonians. The Babylonians extended the use of base 60 to the measurement of time, dividing an hour into 60 minutes and a minute into 60 seconds. This division of time into 60 units allowed for finer and more precise measurements than using a smaller base.
Over time, this sexagesimal system of time measurement persisted and was inherited by various subsequent cultures, including the ancient Greeks and later the Western world. Despite the prevalence of decimal-based systems in many other areas of mathematics and science, the division of time into 60 units has remained largely unchanged.
It's worth noting that the choice of base 60 for measuring time is a historical convention and doesn't necessarily have a direct mathematical or scientific rationale in the present day. However, it has persisted due to cultural and historical reasons, and our modern systems of timekeeping continue to employ this sexagesimal division.