The Religious and Mathematical Origins of Our Leap Year

October 4th is normally followed by October 5th. In fact, it happens with such regularity that no one ever questions whether or not the 5th of the month occurs immediately after the 4th. It just does, as 5 always follows 4. However, Thursday, October 4, 1582 was followed immediately by Friday, October 15, 1582. That’s not a typo, and it makes 1582 the only year on record to contain 355-days.

So, how did that happen? Basically, because the Pope at the time said so, as the calendar used prior to that time did not suit the Roman Catholic Church’s agenda.

In the year 325 CE, the Council of Nicea decreed that Easter should be celebrated on the first full moon after the vernal equinox, which occurred on March 21 that year. However, the Julian calendar that was used at the time did not perfectly match the true length of the solar year (i.e., the time it takes for the sun to resume the exact same spot in the sky). The Julian year is 365 days and 6 hours, whereas the true solar year is approximately 11 minutes shorter.

This small discrepancy did not matter from year to year and would barely even be noticeable across any one person’s lifetime. However, by the 1570s, an error of 11 minutes over 1200 years meant that the vernal equinox had slipped to March 11. The date of Easter, arguably the most important feast in the Christian calendar, therefore slipped with it. If nothing were done, the date of the vernal equinox would continue to slip, with Easter slipping alongside it.

To solve this issue, Pope Gregory XIII convened a commission whose task was to: - One, determine the exact size of the errors in the previous calendars; - Two, create new lunar tables that were capable of predicting the future phases of the moon accurately; - Three, correct the cumulative “slippage” that had already occurred; and - Four, produce a new calendar that would prevent the error from occurring again in the future.

The first recommendation issued by the commission was that the Pope should decree an immediate one-time correction to the calendar that would eliminate 10 days.

The commission also proposed a series of adjustments to the Julian calendar to prevent the problem from reemerging in future centuries. As before, every year that was a Leap Year would last 366 days instead of 365 days. Unlike the old calendar, years that were divisible by 100 (i.e., 1600, 1700) would be standard 365-day years, but years that were divisible by 400 years would remain leap years (i.e., years with 366 days).

This combined effect reduced the average length of a year by 10 minutes and 48 seconds, effectively synchronizing the calendar year with the solar year. This reformed calendar ensured that the vernal equinox would always fall on March 21. The Pope therefore accepted the commission’s recommendations and decreed that Thursday, October 4, 1582 would be followed immediately by Friday, October 15, 1582.

This calendar is known as the Gregorian calendar, named after Pope Gregory XIII, and it is the one still used in the world today. Most European countries immediately adopted the reformed calendar, however it did not reign supreme in the British Isles until 1752, Sweden until 1753, and Russia until 1918. Greece, the last European nation to adopt the Gregorian calendar, did so in 1923.

So, why is this important?

First, it demonstrated the Pope’s enormous political power. Pope Gregory XIII was powerful enough to transform the year, the religious festivals, and the seasons for millions of people. This came during a time when the Catholic Church had lost much of its supremacy across Europe due to the Protestant Reformation, which began after Martin Luther posted his famous treatise, The Ninety-Five Theses, in the early 1500s. The decisive victory of the Roman Catholic Church in the matter of calendar reform solidified its power in much of Europe, particularly Italy.

Second, Christopher Clavius, a Jesuit scholar and member of the commission, provided mathematical and astronomical expertise that was critical in the development of the Gregorian calendar. Prior to this time, Clavius held little prestige among his Jesuit colleagues, as he was known for his radical views on Jesuit education and mathematics.

Jesuit schools at the time were well-known for providing excellent educations, with curriculums that offered a clear sequence of learning. Students first learned languages and the many branches of Aristotelian philosophy, followed by theology. Mathematics were rarely taught and used only to the extent that it was useful for understanding other, “higher” disciplines like theology.

Clavius had argued for several decades that mathematics should hold a central position in education, but he was continuously met with resistance. His position in the group commissioned to correct the calendar, however, gave him the esteem he needed among his colleagues to push forward mathematics, specifically Euclidean geometry, as a central discipline taught in Jesuit schools.

Clavius believed that Euclid’s The Elements had succeeded in imposing a true, eternal, and unchallengeable order upon a seemingly chaotic reality. He therefore saw these mathematical techniques as a means to succeed in doing what the Jesuits were struggling to accomplish in Europe: stifle the Protestant Reformation and establish a new Catholic order with a strict and unquestionable political, economic, and social hierarchy. As a core discipline taught in Jesuit schools, Euclid’s geometry became a key component in the education of Jesuits.

So, the Gregorian calendar demonstrated the power of the Catholic Church. It was also the impetus for Jesuit use of Euclidean geometry. This set the stage for the debates of the mid-17th century surrounding the use of infinitesimals in mathematics. I will be writing a post soon that describes this debate (i.e., the Jesuits vs. Cavalieri, Torricelli, and Galileo in Italy, and Thomas Hobbes vs. John Wallis in England) in detail, specifically its ramifications that helped shape the modern world and modern academic thought.


Alexander, A. (2014). Infinitesimal: How a dangerous mathematical theory shaped the modern world. New York, NY: Farrar, Straus, and Giroux.