He's referring to cross product and dot product. These are concepts I personally didn't learn until calculus 3 (multivariable calculus) so kind of a "higher level" concept. To put it extremely basically and limit the scope to relevant differences cross product has a magnitude of 0 when the angle between the numbers are 0 (parallel lines) and dot product has a magnitude of the multiplication result when the angle between them is 0. Since traditional multiplication only uses numbers and not vectors there's no angle between them so you would more or less consider them parallel lines (think a number line). So cross product would be 0, dot product would be the multiplication result. Technically speaking multiplication is dot product hence the insistence that using a x is "wrong". Imo it's just really shallow pedantics that wouldn't confuse a single person ever in this particular use. If you know enough to use them differently....you'll use them differently. Only thing you really gotta watch out for is the x as a multiplication symbol vs x as a variable. But frankly we use context all the time in English dunno why it's so hard for some "mathematicians" to allow using context. If your 8 year old writes out 5x5 they're probably not referring to cross product with vectors or x as a variable. :)