An example was given of a pair of knots
K_1, K_2 in the 3-sphere for which their unknotting numbers satisfy u(K_1\#K_2) < u(K_1) + u(K_2).Read the paper: Unknotting Number is Not Additive Under Connected Sum
And here's a video for you plebs who don't understand1
Footnotes
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Just in case anyone gets mad, i'm being sarcastic ↩
Footnotes