Looking at Tao’s table of contents for the 2014 pape

Looking at Tao’s table of contents for the 2014 paper I can see why his work is so highly regarded. Even without having followed this mathematically, even I can get the ‘gist’ of the process.

1. Introduction
1.1. Statement of main result
1.2. Overview of proof
1.3. A program for establishing blowup for the true Navier-Stokes equations?
1.4. Acknowledgments
2. Notation
3. Averaging the Euler bilinear operator
3.1. First step: complexification
3.2. Second step: frequency localisation
3.3. Third step: forcing frequency comparability
3.4. Fourth step: localising to a single frequency scale
3.5. Fifth step: extracting the symbol
3.6. Sixth step: simplifying the weights
3.7. Seventh step: restricting to rotations around fixed axes
3.8. Eighth step: parameterising in terms of rotation angles
3.9. Ninth step: Fourier inversion and checking a non-degeneracy condition
4. Reduction to an infinite-dimensional ODE
5. Quadratic circuits
5.1. The pump gate
5.2. Application: finite time blowup for an exogenously truncated dyadic model
5.3. The amplifier gate
5.4. The rotor gate
5.5. A delayed and abrupt energy transition
6. Blowup for the cascade ODE
6.1. First step: constructing the ODE
6.2. Second step: describing the blowup dynamics
6.3. Third step: setting up the induction
6.4. Fourth step: renormalising the dynamics
6.5. Fifth step: crude energy estimates for distant modes
6.6. Sixth step: eliminating the role of b1,c1,d1
6.7. Seventh step: dynamics at the zero scale

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3 − = zero

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