# PM Lee spending some vacation time on the Collatz conjecture: 5 things about the unsolved maths problem

SINGAPORE - Prime Minister Lee Hsien Loong announced on Friday (Dec 20) that he will be on leave from Dec 21 to Jan 3. During this time off, besides plans to spend time with family and "perhaps go #jalanjalan", he said he will also be looking at an unsolved mathematical problem called the Collatz conjecture and mathematician Terence Tao's method to prove this.

PM Lee wrote on Facebook: "It's something all of us can relate to: some challenges might stump us, but with persistence and by keeping an open mind, we might take a step or two closer to a solution."

The problem is also known as the 3n+1 problem.

It involves taking any number and if it is even, halve it. If it is odd, multiply it by three and then add one. Applying the rules repeatedly will eventually result in an infinite loop of the numbers 4, 2, 1, 4, 2, 1, ....

Here are some interesting facts about the Collatz conjecture:

#### 1. The problem is named after German mathematician Lothar Collatz

Collatz introduced the conjecture in 1937. He argued that no matter what number is chosen, the sequence will always reach 1. Mathematicians have tested quintillions (18 zeros) of examples without finding a single exception to Collatz's prediction.

#### 2. The mathematical problem comes with a warning

Amateurs beware: the Quanta Magazine article PM Lee referenced in his post says experienced mathematicians warn newbies to stay away: "It's a siren song, they say: Fall under its trance and you may never do meaningful work again."

This is largely because the Collatz conjecture might be the simplest unsolved problem in mathematics, making it "so treacherously alluring".

#### 3. Who comes closest to solving the problem?

Australian-American mathematician at University of California, Los Angeles, Terrence Tao has arguably come closest to solving it.

In September this year, Tao posted a 48-page document titled "Almost all Collatz orbits attain almost bounded values" on his blog, using advanced mathematics to find proof that the Collatz conjecture is "almost" true for "almost" all numbers. It is arguably the strongest result in the history of the conjecture.

#### 4. People have offered money to solve the problem

Though mathematicians agree that solving the conjecture would be reward enough, Hungarian mathematician Paul Erdos offered US\$500 for its solution and said: "Mathematics may not be ready for such problems."

Likewise, Sir Bryan Thwaites, after whom the problem is sometimes called the Thwaites' conjecture, offered £1000.

#### 5. There are Collatz calculators online

Want to test out the conjecture without having to do the work? There are several free Collatz calculators online that let you test various numbers up to the millions.

Spoiler: all the numbers you can test on these will bring you to back to 1 and the infinite loop of 4, 2, 1, ....

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