- The equation shown is $a^n + b^n = c^n$, which is the statement of Fermat's Last Theorem.
- This theorem, proposed by Pierre de Fermat in 1637, states that no three positive integers $a$, $b$, and $c$ can satisfy the equation for any integer value of $n$ greater than 2.
- Fermat claimed to have a proof but noted it was too large to fit in the margin of his book; no valid proof was found for centuries.
- The problem remained unsolved until 1994, when British mathematician Andrew Wiles, with assistance from Richard Taylor, published a complete proof after seven years of dedicated work.
- Wiles’ proof used advanced mathematical techniques from algebraic geometry and number theory, particularly involving elliptic curves and modular forms, far beyond the mathematics available in Fermat’s time.
- The solution confirms that for $n > 2$, there are no integer solutions $(a, b, c)$ where all are positive.
- Therefore, the “most difficult math problem in history” referenced here has been solved: there are no solutions for $n > 2$, and this was proven by Andrew Wiles.
Parent Tip: Review the logic above to help your child master the concept of hard math.
