The specific question you're objecting to appears to be this: "…most mathematicians in the middle of the 20th century did not think much of probability, which was at the bottom in the hierarchy of mathematics, below number theory, algebra and differential geometry."
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Ok, blame me. He meant the hierarchy of the “difficulty” or prestige of the different areas, e.g. theoretical particle physicists think they do the most pure physics, followed by condensed matter, etc. That doesn’t imply solid state physics (and all the tech) is insignificant.
And thus for many of the top people in the field, these other areas are not worth their personal time and attention. Many theoretical physicists have this view even though the March APS meeting is huge.
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I don't think mathematicians generally thought what Kolmogorov, Levy, Feller, Tukey, etc. were doing was not difficult or worth attention relative to work in other fields, at least judging by their recognitions, involvement in organisations, etc.
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Again, Labourie’s point was not that they thought the work was not difficult or that it wasn’t useful. He meant they thought it wasn’t relevant, in the same way a particle theorist might likely think the latest solid state idea has no implications for a unified theory.
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