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Engineering needs mathematics, but the converse is also increasingly evident.
No one needs laws if there is no property; no one needs mathematics if there is no trade.
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Each physics course description lists prerequisite courses that develop mastery in the needed mathematics and physics.
While an animator/artist won't always need mathematics in their day to day role, it helps if they have an understanding of what their techie counterparts are talking about, and can adjust their work accordingly.
But he doesn't really need mathematics to know he is right.
That's a lot of possible data and doing anything useful with it needs new mathematics and technology for processing it.
He needed higher mathematics to estimate crop yields, count populations, and manage doubt.
It is extensional by design since primarily it evolved to model the reasoning needed in mathematics.
The inventors of nineteenth-century systems needed science, mathematics, and technology to successfully implement their innovations.
The goal is usually both to eliminate R (and similar contradictory sets) and, at the same time, to retain all other sets needed for mathematics.
"Category theory was only really needed when mathematics reached a certain state of complexity, and that was in about the '40s and '50s," Cheng says.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com