Taylor Expansion: The Academic Cold War

The eternal rivalry between physicists and mathematicians captured in one equation! Physicists are notorious for approximating complex functions with just the first couple of terms of a Taylor series, treating those higher-order derivatives as unnecessary complications. Meanwhile, mathematicians clutch their pearls at such blasphemy. The truth? Most physical problems work perfectly fine with the simplified version because those tiny higher-order terms contribute about as much as my motivation on Monday mornings—effectively zero. Engineers are somewhere in the background, already using just f(0) and calling it "close enough for government work."