no title gpt slop

[The Doctor]

That’s a beautifully layered question, and it touches on deep math history, philosophy of science, and even how intellectual progress actually works. Let's unpack it step by step — and yes, we’ll get to partial differentials.

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1. Why and How Were Partial Differentials Invented?​

The Motivation:​

Partial derivatives emerged when mathematicians realized that some functions depend on more than one variable.

• Example: Temperature at a point on a metal plate → depends on x and y.
• You want to know how temperature changes if you move only along x, keeping y fixed.
• So you differentiate with respect to x, holding y constant → that’s a partial derivative.

When and Who:​

• Formalized in the 1700s–1800s during the rise of:
  • Multivariable calculus
  • Fluid dynamics
  • Heat conduction (Fourier)
  • Lagrangian/Hamiltonian mechanics
• Big names:
  • Leonhard Euler
  • Joseph-Louis Lagrange
  • Pierre-Simon Laplace
  • Joseph Fourier
  • Later: Carl Gustav Jacobi, Riemann, Clairaut

So partial differentials weren’t “invented” in a single flash — they evolved as math followed the structure of physical reality.

They became vital for:

• PDEs (partial differential equations): heat equation, wave equation, Schrödinger’s equation, Einstein field equations.

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2. Does This Prove the Great Man Theory of History?​

Not entirely — but you're on to something.​

The Great Mind Spark:​

Yes, many major breakthroughs do come from lone geniuses:

• Newton with calculus and mechanics
• Gauss with number theory and magnetism
• Riemann with geometry that led to Einstein’s general relativity
• Galois with group theory as a teenager

Their insights open entirely new fields. It’s hard to overstate their originality.

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But They Don’t Work in a Vacuum​

Behind every "great man" is a scaffolding of earlier work, peers, translators, critics, and scribes.

• Newton had Descartes, Kepler, Galileo
• Gauss had Euler, Fermat, Lagrange
• Einstein stood on Maxwell, Lorentz, Riemann, and Mach

So genius is often a compression of what’s already fermenting in the culture.

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What About the “Midwits”?​

This is real too:

• Most people in any field extend, organize, teach, and polish what's already known.
• That’s not a flaw — it’s how science becomes a shared body of knowledge, not just flashes of insight.

In fact, even the “midwits”:

• Formalize notation
• Rigorously define terms
• Prove theorems carefully
• Make it usable and scalable

Without them, we’d still be writing calculus in prose like Newton.

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Summary: Is Math Progress Just Genius After Genius?​

• Yes: Some revolutions really do come from singular intellects.
• No: Those revolutions often synthesize existing ideas, and only become useful through community effort.
• Think of genius as a lightning strike, but the forest has to be ready to catch fire.

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TL;DR​

Partial derivatives arose as a natural tool for understanding multivariable change — especially in physics.
While great minds (Euler, Lagrange, Fourier) made the key leaps, they did so within a network of evolving thought.
The Great Man Theory explains the sparks, but not the fuel — genius ignites fields, but the “midwits” build them into civilizations.

Would you like a visual or story of how Euler or Gauss actually thought through one of these discoveries? Some of it is almost poetic.

 

[OccitaNEET]

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