What qualities do all people who do great work share? Your first guess might be luck. Certainly, no one who achieves greatness lets a lucky break pass them by unused, but psychology actually shows luck is mostly a function of mindset. People who find opportunities are people who look for and are prepared to take advantage of them.

How about IQ then? A great brain also helps, but as many famous examples show -- from Steve Jobs to Richard Branson -- academic performance isn't required for an amazing life.

So what then do all ultra high achievers, from groundbreaking scientists to world-changing entrepreneurs to best-selling authors, have in common? To find the answer, Farnam Street blogger Shane Parrish recently turned to mathematician Richard Hamming and his book Art of Doing Science and Engineering: Learning to Learn.

In the course of a long post on the underpinnings of greatness (well worth a read in full), Parrish pulls eight essentials of high achievement from Hamming's book.

1. You need to believe that you are capable of doing great work.

This is simple but fundamental. "If you do not work on important problems, how can you expect to do important work? Yet direct observation, and direct questioning of people, shows most scientists spend most of their time working on things they believe are not important nor are they likely to lead to important things," Parrish quotes Hamming's book as saying.

The same can be said of a lot of folks in other occupations. What's holding them back?Sometimes circumstance, confusion, or inertia play a role, but in a lot of cases the biggest problem is probably a deep-seated fear they don't have what it takes to do the work that really matters.

2. You need to be willing to look like an idiot.

The only way to avoid occasional embarrassing failure is not to try anything difficult. Hamming uses his fellow mathematician Claude Shannon for an example of the opposite, fearless approach.

"While playing chess, Shannon would often advance his queen boldly into the fray and say, 'I ain't scared of nothing.' I learned to repeat it to myself when stuck, and at times it has enabled me to go on to a success ... The courage to continue is essential since great research often has long periods with no success and many discouragements," Hamming writes.

3. You need to strive for excellence.

Again, this is obvious but still somehow often forgotten. If you're not aiming for excellence, surprise surprise, you're not going to get there. "Without such a goal, you will tend to wander like a drunken sailor" is Hamming's memorable way of putting it.

4. You need to stay hungry. 

Why strive if you've already gotten to a comfortable place? Hamming observed that when scientists achieved global renown, the quality of their work nearly always suffered. Why? Their egos and the trappings of success got in the way of great (and therefore messy and unsure) work.

"Fame in science is a curse to quality productivity," Hamming claims. "Most famous people, sooner or later, tend to think they can only work on important problems -- hence they fail to plant the little acorns which grow into the mighty oak trees."

He adds, "In my opinion, the Institute for Advanced Study at Princeton, New Jersey, has ruined more great scientists than any other place has created--considering what they did before and what they did after going there ... most remained there and continued to work on the same problems which got them there but which were generally no longer of great importance to society." 

5. You need to work hard.

There's no way around this simple truth. Here's Hamming's fun story illustrating the point: "I had worked with [fellow mathematician] John Tukey for some years before I found he was essentially my age, so I went to our mutual boss and asked him, 'How can anyone my age know as much as John Tukey does?' He leaned back, grinned, and said, 'You would be surprised how much you would know if you had worked as hard as he has for as many years.' There was nothing for me to do but slink out of his office, which I did."

6. You need to invest in continual, lifelong learning.  

Learning isn't ever over if you want to do great things. "Intelligent preparation is like compound interest," Parrish explains. "The more you invest, the more situations you can handle, the more you learn how to do, so the more you can do, etc." Hamming, for instance, set aside every Friday afternoon for thinking "great thoughts."

7. You need to be OK with ambiguity.

If you can't handle doubt, contradiction, and messiness, you're not going to do great things, Hamming insists. "You must be able to believe your organization and field of research is the best there is, but also there is much room for improvement!" he writes. Unfortunately he also admits, "I have not the faintest idea of how to teach the tolerance of ambiguity, both belief and disbelief at the same time, but great people do it all the time."

8. You need to work with an open door (metaphorically or literally).

Yes, collaboration and contact with other people will knock your productivity down a notch, but it is also the most likely source of inspiration out there. The tradeoff of a little output for a lot more serendipity and insight is worth it, according to Hamming.

"Working with one's door closed lets you get more work done per year than if you had an open door, but I have observed repeatedly later those with the closed doors, while working just as hard as others, seem to work on slightly the wrong problems, while those who have let their door stay open get less work done but tend to work on the right problems!" he writes. "I suspect the open mind leads to the open door, and the open door tends to lead to the open mind; they reinforce each other."