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Math is a science of not being wrong about things, its techniques and habits hammered out by centuries of hard work and argument.
A mathematician is always asking, “What assumptions are you making? And are they justified?”
Mathematics is the study of things that come out a certain way because there is no other way they could possibly be.
Just because we can assign whatever meaning we like to a string of mathematical symbols doesn’t mean we should. In math, as in life, there are good choices and there are bad ones. In the mathematical context, the good choices are the ones that settle unnecessary perplexities without creating new ones.
An important rule of mathematical hygiene: when you’re field-testing a mathematical method, try computing the same thing several different ways. If you get several different answers, something’s wrong with your method.
That’s how the Law of Large Numbers works: not by balancing out what’s already happened, but by diluting what’s already happened with new data, until the past is so proportionally negligible that it can safely be forgotten.
Quick, think of a number from 1 to 20. Did you pick 17? Okay, that trick doesn’t always work—but if you ask people to pick a number between 1 and 20, 17 is the most common choice. And if you ask people for a number between 0 and 9, they most frequently pick 7. Numbers ending in 0 and 5, by contrast, are chosen much more rarely than chance would lead you to expect—they just seem less random to people.
Every single stimulus that greets you, no matter how ordinary, seems intensely meaningful
The late nineteenth century was a kind of golden age of data visualization. In 1869 Charles Minard made his famous chart showing the dwindling of Napoleon’s army on its path into Russia and its subsequent retreat, often called the greatest data graphic ever made; this, in turn, was a descendant of Florence Nightingale’s cox-comb graph† showing in stark visual terms that most of the British soldiers lost in the Crimean War had been killed by infections, not Russians.
Diagram of the causes of m,ortality
It’s not clear how much higher math Beckett knew, but in his late prose piece Worstward Ho, he sums up the value of failure in mathematical creation more succinctly than any professor ever has: Ever tried. Ever failed. No matter. Try again. Fail again. Fail better.
