When to skip the maths

You do not need to follow every line of every proof. But skipping has a cost. Knowing what you can skip is a skill.

Usually safe to skip on a first or second read

• Long proofs in an appendix, if you trust the venue and the result is not the main claim.
• Derivations that only rearrange a known formula.
• Standard parts you already know, like a usual loss function.

Never skip

• The definition of what is measured. If you do not know exactly what "accuracy" or "error" means here, you cannot judge the results.
• The assumptions. "Assume the data is independent" or "assume the function is smooth" tell you where the result can fail.
• The main equation of the method. It is the claim in symbols.

Assumptions are where results break

A theorem is only as true as its assumptions. Many methods that work beautifully "in theory" fail in practice because an assumption does not hold in real data.

ExampleA paper proves its method converges, assuming the data points are independent. Your data is sensor readings over time, where each reading depends on the last. The proof says nothing about your case.

A useful middle path

If a section is too hard, read only the first and last sentence of each paragraph, and every sentence near an equation that starts with "where" or "assume". You will usually catch the definitions and assumptions, which is what matters most.

RememberSkip derivations if you must. Never skip definitions, assumptions or the main equation.