lucid, adj. (3) of or relating to a period of normality between periods of insane or irresponsible behaviour

So it turns out that doing a mathematics degree makes you do at least two things other than learn to draw ξ, ζ and ℵ -

1. Understand how some really quite cool aspects of the world work, and want to share your newfound understanding with everybody!
2. Get really completely confused about stuff that doesn't make any damn sense, then spend ages worrying about it.

So I thought that it might be cool if I collected together some of the things I've come to worry about and/or understand which I think you might like to find out about too.

If you've any thoughts on anything I've written, I hope to at some point allow comments on the individual articles. For now, though, if you have a question or spot something that's not clear, or just plain not true, don't hestiate to get in touch!

What will it look like

Ideally, a typical article will begin with a discussion of the general concepts involved written so as to be accessible to someone with no mathematical background. (This isn't always applicable!) Then there will be some discussion of roughly what sort of maths you need to understand it the subject and how it helps. Then there will be a heavily mathematical discussion useful to people who are actively learning the maths relevant to the subject.

Of course, whenever you think one of these sections isn't as it should be, get in touch!

Stuff I have written

Popular topics

Technical topics

Stuff I'm planning to write

• Quantum theory
  • Differential cross sections: an idiot's guide
  • The Higgs mechanism and...
  • ... spontaneous symmetry breaking
  • Transition rates in QM
  • How to think about quantum mechanics
  • Wave-particle duality - from waves to fields
  • Decoherence and wavefunction collapse
  • What holds neutron stars apart?
  • The Standard Model
  • Baryon wavefunctions and proton stability
  • Gauge bosons & fields with mass
  • Feynman diagrams & virtual particles
  • Nonlinearity of QED - sticky light
  • Why quantum gravity is hard
  • What they actually do at particle colliders
  • Superconductivity: from Cooper pairs to Landau-Ginzburg and onward
  • Zitterbewegung
  • Surface acoustic waves and all that
  • Why quantum computing is better
  • Rarita-Schwinger (spin 3/2) fields
• General physics
  • Action principles: Why?!
  • A cross-section of reality: Physics from the big to the small
• Concepts in mathematical physics
  • Fibre bundles and all that
  • Representation theory and symmetries
  • Gauge symmetries
  • Wick rotations
  • AdS/CFT correspondence
  • What is spin anyway?
  • Spinors
  • Spin quantization, double covers and the Dirac cup trick
  • Differential forms & Lie derivatives
  • Tensors and tensor densities
  • Noether's theorem and field theory
  • Lie groups
  • Tensor (Direct) Products vs. Direct Sums
  • Renormalization groups
  • Vielbeins, metrics and curvature
• Relativity
  • Special relativity: Core ideas
  • Black holes: Perspectives in GR and coordinate time
  • Warped products and conformal rescalings
  • Frame dragging
• Statistical physics and bulk properties
  • Entropy & the second law of thermodynamics
  • Landau-Ginzburg theory
  • Fermi liquids
  • Why things are colours (inc. band theory)
• Continuum mechanics
  • Why waves approach beaches straight on
  • Types of seismic wave
  • Sailing faster than the wind, against the wind
• Probability and statistics
  • N mistakes you really shouldn't make with statistics
• General mathematics
  • Infinities
  • Separation of variables
  • Are there the same number of even numbers and odd numbers?
• Pure mathematics
  • More infinities
  • The Axiom of Choice and friends
• Puzzles
  • The blue-eyed islanders
  • Pirates and coins
  • Prisoners and boxes
  • Mathematicians and boxes (Stack Ex.)
• Meta-subjects
  • Why it's necessary to actually practise maths

We have a

The Elucidation Project

Things I wish someone had told me earlier, things I wish more people knew, and things that are pretty cool.