The difference between mathematicians and other people is not that they are specially clever, it is that they have learned to suffer the journey from misunderstanding to understanding. When encountering new mathematics, mathematicians accept that there will be a time that they are mystified, uncomprehending, in a foreign country where a language is spoken they barely understand. They also know that with persistence, understanding will come.

Of course they are better at this journey than non-mathematicians. How could it be otherwise? But this is not a matter of gift (though gift helps), it is that they have learned how to learn mathematics, how not to get stuck in misunderstanding, how to recognise misunderstanding. A few simple tricks are part of this, like writing out your own examples and trying to explain the new ideas to a friend. Other methods are elaborate, such as making complicated diagrams that relate old ideas to new, or that relate unsolved problems to each other in detail. Some people use humour and silliness, making up rude rhymes and diagrams with faces and tails. Or just lots of colours. Or court cases between conflicting claims, or epic dramas, or visual images of clouds and water and other indescribables. You have to learn to deceive your own tendency to accept misunderstanding.

It is not your fate to misunderstand, but it IS only human to think that partial understanding is good enough. And it is, in real life, almost all the time. But in mathematics, the opposite is true. Complete, detailed understanding is the goal, and it is a very personal goal.

Accept your misundertandings. And get rid of them. That is the heart of mathematics.

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