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The Myth and Magic of Generating New Ideas

https://www.newyorker.com/culture/annals-of-inquiry/the-myth-and-magic-of-generating-new-ideas

newyorker.com

The Myth and Magic of Generating New Ideas
Where do ideas come from? That's a big question. Here's a smaller one: Where do mathematical ideas come from? I've wondered about this from the time I first contemplated being a mathematician until long after I officially became one. My earliest memory of anything like a mathematical idea comes from a childhood walk with my dad.

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Where ideas come from

Where ideas come from

Ideas come to us when we have a specific problem but we do not focus on solving the problem directly.

It’s not at all obvious how to go about thinking up some new twist on these things. A new idea can feel like a remarkable discovery

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Unconscious processing

Henri Poincaré, the father of chaos theory and the co-discoverer of special relativity, relates his own discovery. "the idea came to me, without anything in my former thoughts seeming to have paved the way for it.”

The Irish mathematician, Sir William Rowan Hamilton, had a similar epiphany while strolling by the Brougham Bridge. He was so delighted that he stopped and carved the defining algebraic equation into the bridge.

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Don't overthink

The first phase of solving can be described as “worrying” about a problem or idea. It evokes anxiety and gives the impression of productivity.

But, overthinking can lead to a dead end. The key to solving the problem is to take a break from worrying. Focus your attention on some other activity. Take a long hike or a long drive, to give your mind the space to have a good idea.

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Mundane work is necessary

Big ideas do not come only from leisure. The arduous, mundane work is a vital part of the process. You can't skip the worrying phase. You work, and work, and work some more to get some understanding.

The eureka moments will emerge once you have prepared your mind.

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SIMILAR ARTICLES & IDEAS:

Early History

The connection between genius and possible insanity was first documented in 1891 in the Italian physicians’ book The Man Of Genius.

In 1869, this was taken up by the cousin of Charles Darwi...

Genius and Heredity

In a 1904 study by English physician Havelock Ellis, a list was made of 1030 individuals through extensive research, examining thoroughly the intellectual distinction people had by the various factors like heredity, general health, and social class.


These works established that genius minds are often hereditary.

Genetic Studies Of Genius

A body of work of Stanford psychologist Lewis M. Terman, was an in-depth multi-decade study of gifted individuals, and an attempt to improve the measurement of genius and its association with the degradation of mental stability. This also included an enhanced version of the French IQ (Intelligence Quotient) test.

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Learning rate and limits to learning

Learning rate and limits to learning

Some people take longer to develop the relevant building-block insights to progress in deep subjects like math. The ability to acquire understanding may vary from person to person....

The learning barrier

An explanation for learning difficulty is that our motivation, moods, and interest play a large role in how difficult it is to keep learning math.

We have a psychological need for autonomy (doing maths because you want to), competence (you feel capable), and relatedness (your teacher or peers may praise you). Any behaviors that worsen these needs will demotivate you to learn.

Learning engagement and the need for rewards

The better we get at some things, the more we want to do it. Conversely, the worse we fare in other domains, the less we want to work at it.

If we see our engagement as a way of getting rewards (money, respect, achievement, or just fun) for the time we invest, it can create a trap. The better you get at some things, the narrower your set of interests and hobbies may become.

Creative genius and madness

Creative genius and madness

There are many so-called mad geniuses in history. Suicide victims include Vincent Van Gogh or Ernest Hemingway. Creative geniuses who have succumbed to alcoholism or other addictions are legio...

Cognitive disinhibition

The creative genius tends to pay attention to things that normally should be ignored or filtered out.

People with schizophrenia are bombarded with hallucinations and delusions that should also be filtered out. However, creative genius differs from them in that the genius can separate bizarre fantasies from realistic possibilities. 

Normal and abnormal

Many geniuses walk the line between the normal and the abnormal. The many impulses and ideas they perceive are a fountain of creativity. However, rational thought does impose a limit on a person's concept of his relation to the world.