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The Myth and Magic of Generating New Ideas

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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

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...


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 pa...


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 ke...


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 understandin...



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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Insights of Albert Einstein

Insights of Albert Einstein

Many insights of Albert Einstein are now part of popular imagination: black holes, time warps, and wormholes show up in movies and books.

Less famous, but probably the most revolutionary pa...

Some changes don't change anything

The most fundamental aspects of nature stay the same.

For example, Einstein's papers on relativity show that the relationship between energy and mass is invariant, even though energy and mass can take on many different forms.

Even though matter produces energy, the energy-matter content of the universe never changes. Matter and energy are less fundamental than the underlying relationship between them.

Relationships over things

We often think of things as the heart of reality. But most often the relationship is more important, not the stuff.

We may think "stuff" like space and time are unchangeable aspects of nature. In reality, the relationship between space and time stays the same.

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Multiple Intelligences

Multiple Intelligences

Harvard psychologist Howard Gardner described nine different types of intelligence in his book Frames Of Mind: The Theory Of Multiple Intelligences.

Each ‘type’ of intellig...

Naturist - Nature Smart

There are people who find nature to be meditative and feel closely connected to trees, rivers and flowers. The natural elements around them like the clouds and the universe attracts them.

They make great astronomers, botanists, geologists and landscape architects.

Interpersonal - People Smart

Some people love interacting with friends, family and colleagues. They understand body language, and communicate better and are sensitive to others feelings, perspectives and viewpoints. This super-important intelligence type can be applied to most careers.

Interpersonal Intelligence types can have great careers as managers, psychologists, teachers and social workers.

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The One Big Thing

Instead of checking off a list of tasks, concentrating on one big thing in a day turns out to be a lot more fruitful and gratifying.

To-Do Vs Might-Do

  • A To-Do list is composed of your routine activities that continue to come up daily.
  • A Might-Do list is composed of the things you might do someday, things that are your goals and you will, in the course of time, schedule them in your calendar.

The Handy Calendar

The important, big things can be 'baked-in' your calendar, while you keep track of meetings and appointments.

The Might-Do list acts as your goals list that you will incorporate in your coming days while doing your routine work.

The difficulty of behavioral goals

The difficulty of behavioral goals

Behavioral goals are hard to reach because they usually roll around conflicting desires.

Something in you wants to achieve the goal, while something else in you wants to u...

Grit, determination and victory

The traditional approach to goal accomplishment revolves around the idea of winning most of our inner conflicts. Grit and determination are emphasized as the keys to victory and the positive side should always win.

This approach assumes that there is within us a stockpile of willpower that gives us the power we need to act constantly toward our long-term interests; if we can’t seem to do that, the failing is as much a moral one as a practical one.

Conventional striving doesn't always work

Striving isn’t the only strategy when it come to reaching your goals.

Try tracking your behavior without particularly striving to change it. This way, you commit only to tracking the relevant numbers (money spent, calories consumed, miles walked, pages read/written, etc.)

Chaos Theory

Chaos Theory

Chaos Theory is a mathematical toolkit that allows us to extract ordered structures from chaos. The theory can reveal the intricate workings of such diverse natural systems as the beating of the hu...

Tiny variations vastly affect the outcome

Order on a small scale can produce chaos on a larger scale. In systems that behave without chaotic effects, small differences could eventually increase in size until they produce large effects - the hallmark of a chaotic system.

Meteorologist Edward Lorenz made this profound discovery when he attempted to predict the weather more accurately using a mathematical model. He found that rounding numbers off to three decimal places significantly changed the course of his weather predictions. Lorenz famously illustrated this effect with the analogy of a butterfly flapping its wings, thereby causing a hurricane formation elsewhere.

Understanding the butterfly effect

A good way to see the butterfly effect is with a game of billiards. No matter how consistent you are with the first shot, the smallest of differences in the speed and angle with which you strike the white ball will cause the balls to scatter in different directions every time.

What at first appears to be random behavior is completely deterministic. It only seems random because changes that are hardly noticeable are making all the difference.

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The scientific revolution

Human history is often framed as a series of episodes, representing sudden bursts of knowledge. The Agricultural Revolution, the Renaissance, and the Industrial Revolution are a few examples where ...


Much of the knowledge about the natural world during the middle ages dates back to the teachings of the Greeks and Romans. Many did not question these ideas, despite the many flaws.

  • Aristotle taught everything beneath the moon was comprised of four elements: earth, air, water, and fire.
  • Greek astronomer Claudius Ptolemy thought that heavenly bodies such as the sun, moon, planets and various stars all revolved around the earth in perfect circles.
  • The ancient Greeks and Romans held to the idea that illnesses were the result of an imbalance of four basic substances and was related to the theory of the four elements.

Rebirth and Reformation

  • During the Renaissance, there was a renewed interest in the arts and literature. It led to a shift toward more independent thinking.
  • In 1517, Martin Luther nailed his 95 theses to the door of the Roman Catholic Church. Luther promoted his thoughts by printing and distributing them, encouraging churchgoers to read the Bible for themselves. This led to the Protestant Reformation.
  • In the process, the criticism and reform led to placing the burden of proof ahead in understanding the natural world, paving the way for the scientific revolution.

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Social Physics

Social Physics

Psychohistory is a fictional way to predict the future of humanity, using mathematical techniques.

Applying maths on human behaviour was initiated by Adolphe Quételet in the 19th centur...


This is an invaluable tool for the fields of biology, medicine, economics, arts and humanities and the administrative services of the government.

Statistics provides useful tools, but those calculations and assumptions are based on certain constants that can lead to serious mistakes if taken too literally or applied to a large size. These calculations provide usable figures in a ‘quick and dirty’ way.

Adolphe Quételet's Estimations

Quételet, the mathematician turned astronomer who was performing social physics miracles as the central figure of Belgium science, got better in his game by learning probability theory and making use of his polymath brain. His work included estimations and calculations using the available data and his mathematical and statistical skills. Instead of counting everyone to know the population, Quételet used some reasonable estimates and then multiplied the number of births per year with the ratio of the total population to the annual births.

The new methodology was published in Quételet’s books in the 19th century, like Social Physics (1835) and its newer editions, and caught the imagination of the public. Concepts like the Average Man and the Bell Curve (a normal probability of distribution) simplified complex statistics and made it accessible to the world while being easily quotable and comparable.

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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.