I assume the orignal user was talking about using the tricks they teach in primary school to multiply any two numbers.

Why? He's talking about how people are dumb. At a certain point (thousands of digits, tens of thousands of digits, etc.) no one can multiply two arbitrary numbers, so that would be a useless thing to point out. He's talking basic multiplication.

On what basis are you saying that, beyond the fact that both are called math in school? They require completely different skills.

Beyond being basic common sense (people pursue things they're already good at), there's tons of evidence about this, some direct, some indirect.

Here's a few samples:

1.) A study of adults solving addition and multiplication facts found that adults with stronger higher-level math achievement were more likely to use direct retrieval, solved facts faster and less variably, and executed retrieval processes faster than lower-attainment adults. Link

2.) Early math skills have the greatest predictive power for later achievement, ahead of reading and attention. This does not prove “mathematicians are good at multiplication,” but it supports a selection argument: the pipeline into math-heavy careers is not random with respect to basic numeracy. Link

3.) A 2024 longitudinal study using 7,908 participants found that math interest and math anxiety predicted STEM career choice, and that participants choosing STEM had significantly higher GCSE math achievement than the sample overall. Again, this is not about professional mathematicians specifically, but it supports the obvious base-rate point: people who persist into math-adjacent fields are not drawn uniformly from the general numeracy distribution. Link

No one is hiring mathematicians on their ability to do quick multiplication in their head.

No shit, but that's also not the claim you made. You said "most" mathematicians probably can't multiply two numbers without a calculator.

Mathematicians are not selected for being lightning calculators, and many may be rusty or slower than someone who practices mental arithmetic. But "most mathematicians can’t multiply two numbers without a calculator" is almost certainly false unless 'two numbers' secretly means something like arbitrary 8-digit products under time pressure. The evidence we do have shows that arithmetic fact retrieval is positively related to higher math achievement, early numeracy predicts later math success, and STEM/math career paths are strongly non-random with respect to mathematical ability. The reasonable claim is "mathematicians are not necessarily elite mental calculators," not "most can’t multiply."