Tag Archives: number theory

The Numerology about Mr. Lee Kuan Yew

In the aftermath of the death of Singapore’s founding father, Mr. Lee Kuan Yew (1923–2015), a number of numerological tidbits (or numerical curiosities, to put it mildly) floated on social media, which got a number of apparently self-professed innumerates pretty excited. Here are three such postings that I saw in my Facebook feed and on WhatsApp.

RIP: Lee Kuan Yew (1923–2015)

A numerological message that was circulated among WhatsApp users in Singapore
(© Unknown)—A numerological message that was shared among Singapore WhatsApp users

The WhatsApp message gives the impression that it was the works of some “pseudo-mathematician,” but it could very well have been the digital footprints of a “mathematical crank” or an amateur-numerologist, who wanted to tickle mathophobics with such numerical coincidences.

Did Singapore’s numerologists (or pseudo-mathematicians) fail to point out some of the following numerological absurdities?

The digital root of Mr. Lee’s birth year is 1 + 9 + 2 + 3 = 15, which stands for the last two digits of the year he experienced his last heartbeat.

The pollution index for that week was in an unhealthy range, and the average PSI for the six-day mourning period was about 91.

Or, were there exactly 91 priests on vigil at an undisclosed Roman Catholic Church, who were interceding for Mr. Lee to ensure that his heavenly destination is 100% secured, although his manifold deeds to the nation inarguably exceeds the number of his political faux pas, especially vis-à-vis his political enemies or opponents?

Or, did 91 senior monks and nuns (or did I mistake them for disciples of Shintoism?) resort to “synchronized chanting” to ensure that the highest level of enlightenment be bestowed on the late Mr. Lee, who might be reincarnated as a future Buddha for his numerous selfish deeds towards his oft-ungrateful and unappreciative fellow citizens?

And did any police personnel verify whether there were 91,000 odd mourners in black attire on that Black Sunday, not to say, 91 VIPs or Heads of States who attended the eulogy, depending on one’s definition of a VIP?


The Numerology of the Old Guard

One Facebook numerological factoid that circulated in the first post-LKY week was the following:

Singapore’s political fathers who outlived the biblical three-scores-and-ten lifespan

At face value, these nonagenarians had their blessed lives prolonged up to “four scores and ten and one” years. Sounds like their good earthly or political deeds were good karma for their longetivity? Are they the recipients of the following success equation?

Sacrifice + Service + Incorruptibility + Risk  = Political Success + Longevity

Observe that simply taking the difference between the birth year and the death year of Mr. S Rajaratnam suggests that he died at the age of 91; however, if we look closely at the month dates (Feb. 25, 1915 – Feb. 22, 2006), he was still 90 years old, when he passed away. The same argument goes for Dr. Toh Chin Chye (Dec. 10, 1921 – Feb. 3, 2012), who wasn’t yet 91, when he died. So, always take the pseudoscience of numerology with a grain of salt. As with fengshui charlatans, a degree of skepticism towards numerologists of all sizes and shapes isn’t an option—wear your critical-thinking cap when meeting, or reading about, these paranormal folks!


Fortune via Misfortune—From 4D to 5C

(© Unknown) Punters used combinations of the digits related to Mr. Lee death date to lure Lady Luck.

To rational non-punters or non-gamblers, betting on someone’s death date, whether he or she was poor or rich on this side of eternity, seems like an extreme case of bad taste,  or simply showing zero respect for the deceased and their family members. However, in superstitious circles, that practice isn’t uncommon among mathematically challenged or superstitious punters, who think that bad luck paranormally translates into good omen, if they bet on the digits derived from the death date or age of a recently deceased person.

In fact, during the nation’s six-day mourning period for its founder, besides the long queues of those who wanted to pay their last respects to Mr. Lee at the Parliament House, another common sight islandwide were meters-long lines of 4D or TOTO punters, who wanted to cash in on the “lucky digits” to retire prematurely, hoping to lay hold of the traditional 5Cs (cash, car, condo, credit cardcountry club), coveted by hundreds of thousands of materialistic Singaporeans.


Number Theory over Numerology

Fengshui in the Gym
(© BBC) Chinese numerology in the gym? Or, is it just a mild form of deification of a political figure?

Instead of promoting a numerological or pseudoscientific gospel based on Mr. Kuan Yew’s death date or age, which only helps to propagate superstition and pseudoscience, perhaps a “mathematically healthy” exercise would be to leverage on the D-day to teach our students and their parents some basic numerical properties—for example, conducting a recreational math session on “Number Theory 101” for secondary  1–4 (or grades 7–10) students might prove more meaningful or fruitful than dabbling in some numerological prestidigitation, or unhealthy divination.

A Search for Patterns

91  is the product of two primes: 91 = 7 × 13

91 = 1² + 2² + 3² + 4² + 5² + 6²

91 is also the sum of three squares: 1² + 3² + 9²

Are there other ways of writing the number 91 as a sum of squares?

91 = 33 + 43


Non-Numerological Questions to Promote Problem-Solving Skills

Let’s look at an “inauspicious number” of elementary- and middle-school (primary 5–secondary 4) math questions, which could help promote numeracy rather than numerology among students and teachers.

1. Sum of Integers

Show that the number 91 may be represented as the sum of consecutive whole numbers. In how many ways can this be done?

2. The Recurring Decimal

What fraction represents the recurring decimal 0.919191…?

3. Palindromic in Base n

For what base(s) will the decimal number 91 be a palindromic number (a number that reads the same when its digits are reversed)? For example, 91 = 101013.

4. The Billion Heartbeat

Does a 91-year-lifespan last less or more than a billion heartbeats?

5. Day of the Week

Mr. Lee Kuan Yew (September 16, 1923–March 23, 2015) died on a Monday. Using the 28-year cycle of the Gregorian calendar, which day of the week was he born?

6. One Equation, Two Variables

If x and y are integers, how many solutions does the equation x² – y² = 91 have?

7. Singapore’s New Orchid

A new orchid—Singapore’s national flower—had been named after Mr. Lee: Aranda Lee Kuan YewUsing the code A = x, B = x + 1, C = x + 2, …, , does there exist an integer x such that ARANDA sums up to 91? In other words, does there exist a numerological system such that  A + R + A + N + D + A = 91?

8. Singapore’s Coin Goes Octal

Singapore's "lucky" octagonal one-dollar coin
The alleged involvement of Mr. Lee in Singapore’s “lucky” octagonal one-dollar coin

There is an apocryphal story that had circulated for many years linking Mr. Lee Kuan Yew with Singapore’s octagonal one-dollar coin. A high-ranking monk had apparently told Mr. Lee that Singapore’s fortune would continue to rise only if Singaporeans were to carry a bagua—the eight-sided fengshui symbol. That prediction allegedly prompted the Monetary Authority of Singapore to issue the octagonal shape of the nation’s one-dollar coin.

That rumor was later put to rest by no other than self-declared agnostic Mr. Lee himself in one of his books, Hard Truths. He remarked that he had zero faith in horoscopes, much less the pseudoscience of fengshui.

What is the sum of the interior angles of the Singapore’s eight-sided coin?

9. Show that the largest number k for which the decimal expansion of 2k does not contain the digit 1 is 91.

© Yan Kow Cheong, April 26, 2015.

Resurrection isn't an option in Singapore!
Resurrection isn’t an option in Singapore!

Selected Answers/Hints

1. One example is 91 = 1 + 2 + 3 +⋯+ 13.
2. 91/99.
5. Mr. Lee was born on a Sunday.
6. Hint: Show that x² – y² = 91 has 8 integer solutions.
9. Hint: Use a computer to verify the result.

Mathematical Fiction Is Not Optional


“The Parrot’s Theorem” (translated from “Le Théorème du Perroquet”) was an instant bestseller in France when it was published in 1998.

Sylvia Nasar’s A Beautiful Mind and G. H. Hardy’s A Mathematician Apology are two nonfiction mathematical classics for both mathematicians and mathematics educators. Lesser known are the mathematical novels which often feature characters whose speciality is number theory, also known as higher arithmetic, and elevated as math’s purest abstract branch.

Mathematics à la Tom Clancy

Two novels that revolve around famous unsolved problems in mathematics are Philibert Schogt’s The Wild Numbers and Apostolis Doxiadis’s Uncle Petros & Goldbach’s Conjecture.

If you’re looking for math, women, sex, and back-stabbing, The Wild Numbers is a math melodrama unlikely to disappoint.


Winner of the New South Wales Premier’s Prize


Fictional math

Who are these mathematical fiction books targeted? Math and science teachers? Educated laypersons? Pure mathematicians may like to read them, yet at the same time they may complain that the mathematics discussed in these books is anything but rigorous.

These books seldom fail to convey the following subtle messages:

• The thin line between mathematical genius and madness.

• The search for mathematical truth at all costs, and the heavy price of finding it.

• The arrogance and pride of pure mathematicians who look down on their peers, most of whom work as applied mathematicians and research scientists.

• The relatively high divorce rate among first-rate mathematicians as compared to their peers in other disciplines.

• Mathematics is apparently a young’s man game; one has past one’s prime if one hasn’t written one’s best paper by the age of 40.

• Mathematicians are from Mars; math educators are from Venus.

• Pure mathematicians (or number theorists) are first-rate mathematicians; applied mathematicians are second- or third-rate mathematicians. To the left of the “mathematical intelligence” bell curve are math educators from schools of education, and high-school math teachers.


“Reality Conditions” is collection of 16 short stories, which is ideal for leisure reading—it’s suitable for promoting quantitative literacy, or it’d serve as the basis for a creative course on “Mathematics in Fiction.”

The joy of reading mathematics

Let’s rekindle the joy of appreciating mathematics for mathematics’s sake. Let’s welcome poetry, design thinking, and creativity, whatever ingredient that may help to draw the community into recognizing and appreciating the language of science and of technology. These “pure-math-for-poets” titles have a place in our mathematics curriculum, as they could help promote the humanistic element of mathematics.

Here are ten titles you may wish to introduce to your students, as part of a mathematics appreciation or enrichment course.

The New York Times Book of Mathematics

The Best Writing on Mathematics 2010 

Clifton Fadiman’s Fantasia Mathematica

Clifton Fadiman’s The Mathematical Magpie

Don DeLillo’s Ratner’s Star

Edwin A. Abbott’s Flatland

Hiroshi Yuki’s Math Girls

John Green’s An Abundance of Katherines

Philip J. Davis’s The Thread: A Mathematical Yarn

Thomas Pynchon’s Gravity’s Rainbow


Juvenile fiction—A child prodigy and his friend tried to create a mathematical formula to explain his love relationships.


Green, J. (2006). An abundance of Katherines. New York: Dutton Books.

Guedj, D. (2000). The parrot’s theorem. London: Orion Books Ltd.

Kolata, G. & Hoffman, P. (eds.) (2013). The New York Times book of mathematics: More than 100 years of writing by the numbers. New York: Sterling.

Hiroshi, Y. (2011). Math girls. Austin, Texas: Bento Books.

Pitici, M. (ed.) (2011). The best writing on mathematics 2010. Princeton, New Jersey: Princeton University Press.

Wallace, D. F. (2012). Both flesh and not: Essays. New York: Little, Brown and Company.

Woolfe, S. (1996). Leaning towards infinity: A novel. NSW, Australia: Random House Australia Pty Ltd.

© Yan Kow Cheong, September 12, 2013.


Murderous math that doesn’t kill!