Ancient Algorithms: What Egyptian Fractions Teach Us About Computing

You might not realize it, but every time you write a recursive function, you're walking a path mathematicians tread millennia ago. Egyptian fractions—expressions made only from reciprocals of whole numbers—represent some of the oldest algorithmic thinking ever recorded, and they're far more clever than they seem at first glance.

The Puzzle Ancient Egyptians Had to Solve

We take modern fractions for granted: 3/7, 5/12, 17/23. These just feel natural to us. But this notation didn't become standard in Europe until the 1700s. Before that, if you wanted to write a fraction, you had to break it into a sum of unit fractions—those with 1 in the numerator.

So the Egyptians had a real problem on their hands: how do you fairly split 7 loaves among 8 people? Writing 7/8 wasn't an option. Instead, they'd break it down like this: 1/2 + 1/4 + 1/8. Seems almost too simple, but this approach demanded serious mathematical sophistication—and it birthed what we now recognize as the Egyptian fraction algorithm.

A Greedy Solution From Antiquity

Here's where it gets exciting for anyone who writes code. The technique Egyptians used to convert any fraction into this form is essentially a greedy algorithm—pick the largest possible unit fraction, subtract it, then do it again.

Let's look at 4/23. The algorithm asks: what's the smallest integer bigger than 23 divided by 4? That's 6. So we start with 1/6. Subtract that from 4/23 and we get 1/138. Done. So 4/23 equals 1/6 plus 1/138.

This method always works—a mathematical theorem proven in 1880, though Europeans had been using the technique since Fibonacci wrote about it in the 1200s.

Why This Should Matter to You

You might be thinking this is just cool trivia. But look closer at what's happening in that algorithm:

1. Recursive decomposition - You take a complex problem and break it into something simpler
2. Greedy selection - At each step, you make the best choice available right now
3. Termination proof - The remainder shrinks every time, so you know you'll finish

These aren't just abstract concepts. They're the foundation of how we think about algorithms today. When you write a recursive function, you're using the exact same logical framework those ancient mathematicians developed.

A Reckoning With History

There's an uncomfortable truth worth facing here. The Egyptian fraction method existed thousands of years before Greek mathematics even began. Yet when Europeans "rediscovered" the Rhind Papyrus in the 1800s, this technique often got credited to Greek scholars instead of its actual creators in ancient Egypt.

This isn't ancient history either. It's a pattern that continues today—contributions from African and non-European civilizations frequently get minimized or erased from mathematical and computer science narratives.

A Number Puzzle That Still Baffles Experts

One of the most intriguing mysteries involves what scholars sometimes call the "Egyptian triple": 13, 17, and 173. When you interpret these as 3 + 1/13 + 1/17 + 1/173, you get an approximation of π accurate to four decimal places—actually better than the commonly cited Egyptian value of 3.16.

Whether this was deliberate mathematical genius or just a happy accident? Historians still argue about it.

From Then to Now

Egyptian fractions have a direct link to continued fractions, a subject still actively studied in computer science and number theory. And that greedy algorithm approach? It shows up everywhere today—in resource allocation, scheduling problems, and optimization challenges.

So the next time you're untangling a recursive function or defending why a greedy approach makes sense, remember: you're part of a mathematical tradition nearly 4,000 years in the making.

Sometimes the oldest algorithms really are the best ones.