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The Greatest Maths Mistakes
Even the most brilliant minds and advanced teams have made mathematical mistakes – and sometimes, those small errors have changed history. From lost spacecraft to financial chaos, these stories remind us that maths, though exact in theory, depends on the humans who use it.
Here are three of the greatest mathematical mistakes ever made – and what they can teach us about accuracy, attention, and humility in the face of numbers.
The Mars Climate Orbiter Disaster (1999)
In 1999, NASA lost a £100 million spacecraft because of one tiny mathematical mismatch. The Mars Climate Orbiter was meant to study the Martian atmosphere. Instead, it disintegrated as it entered orbit – all because two engineering teams used different units of measurement.
The spacecraft’s navigation software, written by Lockheed Martin, calculated thrust in pound-force seconds (imperial), while NASA’s team expected data in newton seconds (metric). The result? The probe descended 100 kilometres too low and burned up in the Martian atmosphere.
A simple unit conversion – something schoolchildren learn in physics – destroyed years of work. NASA’s official report called it a “failure of systems engineering,” but at its heart, it was a maths error: a reminder that units matter, especially in space.
The Patriot Missile Failure (1991)
During the Gulf War, the Patriot missile defence system was designed to intercept incoming Scud missiles. But on 25 February 1991, the system failed – resulting in the deaths of 28 soldiers in Dhahran, Saudi Arabia.
The cause was a tiny rounding error in the system’s clock calculation. The missile battery used a clock with binary arithmetic that approximated one-tenth of a second as a fraction (1/10 = 0.1). The number 0.1 can’t be perfectly represented in binary, creating a tiny rounding error of 0.000000095 seconds per cycle.
That sounds minuscule – but after 100 hours of continuous operation, the error accumulated to 0.34 seconds. In that time, a Scud missile travelling at Mach 5 moved over half a kilometre, enough for the system to miss.
It was a tragic reminder that small inaccuracies in time or measurement can have devastating consequences when scaled up.
The Spanish Armada’s Miscalculated Compass (1588)
Sometimes, mathematical mistakes don’t just lose machines – they lose empires. In 1588, when the Spanish Armada set sail to invade England, it carried the finest navigators of its time. But many of them didn’t realise that magnetic north and true north are not the same thing.
Sailors relied on compass readings without accounting for magnetic declination – the difference between magnetic north (where the compass points) and true geographic north (the Earth’s axis). This small angular difference, just a few degrees, was enough to send parts of the fleet wildly off course.
Combined with storms, poor planning, and English resistance, the navigational miscalculation helped doom the Armada. It became one of the earliest and most dramatic examples of how a mathematical misunderstanding of direction could alter the course of history.
The Lesson Behind the Errors
Each of these mistakes – from the skies above Mars to the seas around Britain – shares a common thread: tiny numerical errors with enormous consequences. They remind us that mathematics isn’t just an abstract subject; it’s the foundation of how we build, measure, and navigate our world.
Whether it’s converting units, rounding decimals, or aligning a compass, precision in maths isn’t just academic – it’s practical, essential, and deeply human.
As mathematician and physicist Henri Poincaré once said:
“To doubt everything or to believe everything are two equally convenient solutions; both dispense with the necessity of reflection.”
Numbers don’t make mistakes – but people do. And through those mistakes, we keep learning just how powerful mathematics really is.