At the turn of the 1900s, the field of mathematics was changing. The old school relied of physical intuition as a means of proof. The new school found that an adherence to formal logic led to more reliable findings.
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In brief, traditionalists lost the battle in the professional community but won in education. The failure of “new math” in the 1960s and 70s is taken as further confirmation that modern mathematics is unsuitable for children. This was hardly a fair test of the methodology because it was very poorly conceived, and many traditionalists were determined that it would succeed only over their dead bodies. However, the experience reinforced preexisting antagonism, and opposition is now a deeply embedded article of faith.
Many scientists and engineers depend on mathematics, but its reliability makes it transparent rather than appreciated, and they often dismiss core mathematics as meaningless formalism and obsessive-compulsive about details. This is a cultural attitude that reflects feelings of power in their domains and world views that include little else, but it is encouraged by the opposition in elementary education and philosophy.
In fact, hostility to mathematics is endemic in our culture. Imagine a conversation:
A: What do you do?
B: I am a ———.
A: Oh, I hate that.from page 33-34.
Core methods such as completely precise definitions (via axioms) and careful logical arguments are well known, but many educators, philosophers, physicists, engineers, and many applied mathematicians reject them as not really necessary.
from page 34
Why It Matters:
The sciences are at risk in the reckless implementation of maths.
Education methods are weakened by the philosophical divide.