How can we develop transformative tools for thought?

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• The typical modern design practice
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• The typical modern design practice

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  would not cause you to discover any deep insights about the field
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• you'd interview domain experts (in this case, mathematicians),
• and read any relevant literature.
• In short, you'd do what people in the design community refer to as immersing themselves in the target field.
• $$\color{red}24.$$ Of course, a designer who spoke to an expert on, say, Babylonian mathematics, might well have come across some of these ideas. We'll ignore that, since it depends on the oddity that many excellent prior ideas about numeral systems had been displaced in Roman culture.)