A Revolution in Mathematics? What Really Happened a Century Ago and Why It Matters Today
A revolution in mathematics at the end of the 1800s through the early 1900s resulted in a split between applied/scientific mathematics "find an explanation and test it thoroughly" and core mathematics, "find an explanation without rule violations". In contrast to scientific revolutions, this mathematical revolution was more fundamental and much less visible. Core mathematics is now more accessible to new practitioners, wholly dependent on internal rules rather than authority or other external validation, but less accessible to non-mathematicians, lacking analogy to the physical world. But the new methods allow for finding non-intuitive outcomes that would be intuitively rejected.
"New math" in primary education was botched. Math educators appreciate proof methods of the 1800s; they don't misunderstand current methods so much as don't know aout them.
Theoretical and practical relevance:
Demand for applied mathematics and limited resources put core research at risk.
"The long-term consequence of mathematical osteoporosis is that science would have to go back to being a bug!"
Can any approaches accurately reflecting core mathematics be used with children? They appreciate rules: see games.