Month January February March April May June Doomsday 3/1 (or 4/1 on a leap year) 28/2 (or 29/2 on a leap year) 14/3 4/4 9/5 6/6 Month July August September October November December Doomsday 11/7 8/8 5/9 10/10 7/11 12/12 Table 2 A set of easily memorable doomsday that always fall on the same day of the week. (Can you spot some patterns? Any important date for the hungry mathematicians?) Still confused? Let’s go over a simple example together [5]. Here’s a tip: You can always refer to the cheat sheet at the end of the article for quick reference to any “unfamiliar numbers” you find in the next paragraph. Suppose we want to know the day of the week for December 26, 1937 (Guess what? It’s Conway’s birthday! [2]). First, let’s start from year 1900. The century code for the 1900s is 3, meaning that the doomsday of 1900 was Wednesday. Here’s a fact: The day of the week of the same date moves forward by one day in the next year, and by two days for a leap year. Conway has, again, analyzed the pattern of the results and developed a “year shortcut.” For the year 1936, we can add the year shortcut 3 to the century code, so 3 + 3 = 6. The doomsday of 1936 was Saturday. Then we may safely arrive at the conclusion that the doomsday of 1937 was Sunday, as there was no leap day after December 26, 1936 until the date of interest. The nearest doomsday date to December 26 is December 12, so we subtract 12 from 26 to get 14. Dividing 14 by 7 gives us a remainder of 0, meaning that December 26 falls on the same day of the week as the doomsday of 1937, i.e. Sunday. Voila! We now know that Conway was born on a Sunday. John Horton Conway For over half a century, the Game of Life has fascinated countless mathematicians, computer scientists, and hobbyists with its infinite possibilities. And its creator, British mathematician John Horton Conway (1937–2020), lived a life just as full of wonder and playfulness. Born in Liverpool in 1937, Conway’s career followed a familiar path of some of the greatest mathematicians of his time: He became interested in mathematics at an early age, went on to study mathematics at the University of Cambridge and received his doctorate there in 1964, then stayed on as a faculty member until moving to Princeton University in 1986 [2, 3]. Yet, on the other hand, Conway was very much an atypical academic [3, 4]. Instead of being confined to his office at Princeton, he enjoyed roaming around the departmental common room and the hallways of the mathematics building. As a teacher, he often brought pocket props (such as ropes, cards, dice, Slinkys, and even a toy bike!) to his classes and would sometimes even “throw a shoe at the window if he thought the students were asleep [4].” Perhaps most famously, he approached mathematics with games and puzzles. “I learned very quickly that playing games and working on mathematics were closely intertwined activities for him [John Conway], if not actually the same activity.” — Manjul Bhargava, Professor of Mathematics at Princeton University [3] Doomsday Algorithm Here's yet another mathematical trick invented by Conway that you will not only enjoy but also find useful: the Doomsday Algorithm [5]. By working out the “doomsdays,” or a set of easily memorable dates that always fall on the same day of the week in the same year (Table 2), you can quickly determine the day of the week for any given date. Before delving into how the algorithm works, let’s first clarify what we mean by the term “doomsday.” Here, doomsday is defined as the day of the week for any doomsday dates in a year. Let’s start from a basic fact – the doomsday of 2000 was Tuesday. Conceptually, by observing how the doomsday shifts across years and centuries, one can work out the doomsday of any year. We can then find the day of the week of a particular date by calculating the difference between the date and its nearest doomsday date.
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