Supposedly geniuses make more connections and think "productively" rather than "reproductively" (using some logic someone explained). Ordinary smart people think reproductively but faster than ordinary people.

http://www.creativitypost.com/create/how_geniuses_thinkMost people of average intelligence, given data or some problem, can figure out the expected conventional response. For example, when asked, "What is one-half of 13?" most of us immediately answer six and one-half. You probably reached the answer in a few seconds and then turned your attention back to the text.

Typically, we think reproductively, that is on the basis of similar problems encountered in the past. When confronted with problems, we fixate on something in our past that has worked before. We ask, "What have I been taught in life, education or work on how to solve the problem?" Then we analytically select the most promising approach based on past experiences, excluding all other approaches, and work within a clearly defined direction towards the solution of the problem. Because of the soundness of the steps based on past experiences, we become arrogantly certain of the correctness of our conclusion.

In contrast, geniuses think productively, not reproductively. When confronted with a problem, they ask "How many different ways can I look at it?", "How can I rethink the way I see it?", and "How many different ways can I solve it?" instead of "What have I been taught by someone else on how to solve this?" They tend to come up with many different responses, some of which are unconventional and possibly unique. A productive thinker would say that there are many different ways to express "thirteen" and many different ways to halve something. Following are some examples.

6.5

13 = 1 and 3

THIR TEEN = 4

XIII = 11 and 2

XIII = 8

(Note: As you can see, in addition to six and one half, by expressing 13 in different ways and halving it in different ways, one could say one-half of thirteen is 6.5, or 1 and 3, or 4, or 11 and 2, or 8, and so on.)With productive thinking, one generates as many alternative approaches as one can. You consider the least obvious as well as the most likely approaches. It is the willingness to explore all approaches that is important, even after one has found a promising one. Einstein was once asked what the difference was between him and the average person. He said that if you asked the average person to find a needle in the haystack, the person would stop when he or she found a needle. He, on the other hand, would tear through the entire haystack looking for all the possible needles.)