# Results that seem trivial, but are not [duplicate]

I saw the Cayley-Hamilton theorem

Let $\mathbf{A}$ be a $n\times n$-matrix, and $p(\lambda)=\det(\lambda \mathbf{I}_n-\mathbf{A})$ the characteristic polynomial of $\mathbf{A}$. Then $p(\mathbf{A})=\mathbf{0}$

and I thought it was trivial since $\det(\mathbf{A}-\mathbf{A})=0$. I checked with Wikipedia and learned that this didn't work because $\lambda$ is a scalar, and $\det(\mathbf{0})$ is also a scalar, and not a matrix. This brings me to my question:

Are there any other results that seem trivial, but aren't?

• Queen Dido's approach to the isoperimetric problem seems relevant. Richard Tapia wrote (2013), "When first introduced to this problem, even the less mathematically initiated individuals readily conjecture that the solution is the circle." However the history of attempts at a fully rigorous proof cover two thousand years. – hardmath Apr 9 '18 at 16:22
• – Arnaud D. Apr 10 '18 at 9:21

The weak Goldbach conjecture (a theorem now, it seems, proved by Harald Helfgott): Every odd integer $n>5$ is a sum of three primes. If you try yourself examples, this seems trivially true. There are millions of possibilities for a big odd $n$. Nevertheless, the proof is extremely complicated.
• Yes, there are $5$ arXiv papers, see wikipedia. However, an article with a proof has not been published in a journal yet. – Dietrich Burde Apr 9 '18 at 18:05