Every so often, I run across great stories of geniuses who show exceptional mental prowess, often while still young. I'm going to share some of my favorites.

The first is probably the most famous, featuring a young Carl Friedrich Gauss. It may or may not be true, but I'll pass it on anyway. Gauss' teacher needed to occupy the students with busy work (some versions of the story say it was to talk to other faculty members, others say it was to take a nap), so he assigned the students to add up all the numbers from 1 to 100. Young Gauss was able to produce the correct answer, 5050, in just a few seconds, and without writing anything down!

How was that possible? Gauss took a look at the problem first, and was able to find a pattern that made the problem far simpler. His aha! moment came when he realized 1+100=101, as did 2+99, 3+98, and so on, all the way up to 50+51! Thus the problem became a matter of multiplying 50 by 101, which is much easier and quicker to do mentally. The bloggers at Better Explained can not only help you better understand how problems like this are solved, but also help you realize that one problem doesn't mean only one approach.

This next story is far more recent, and concerns Arthur Benjamin, whom many of you probably know from his TED video. In his book Secrets of Mental Math, Dr. Benjamin tells of a time when he was only 13, his teacher demonstrated how to work out a problem, and concluded with an answer of 108². Apparently unhappy with what he saw as an unfinished problem, he blurted out that 108² was simply 11,664!

The teacher was amazed that a 13-year-old could square a number like 108 in his head. The method he used, detailed in the above book, was roughly the same as this squaring method described on MathPath. When he explained his approach, and the teacher commented that she'd never run across this method, thoughts of being famous for this new discovery ran through his mind! Unfortunately, when he ran across the very same method in Martin Gardner's Mathematical Carnival, he realized this was not to be. I suggest reading the full story in Secrets of Mental Math, not only for the method, but also to learn how he discovered it on his own.

Dr. Solomon Golomb, who is a respected mathematician, engineer, and puzzle expert, had his own great moment in his college freshman biology class. The teacher was explaining that human DNA has 24 chromosomes (as was believed at the time), so the number of possible cells was 2²⁴. The instructor jokingly added that everyone in the class knew what number that was. Golomb immediately responded that it was 16,777,216. When the instructor didn't believe the number was right, and looked through his noted to find the correct number, he was stunned to find that Golomb was exactly right! Not surprisingly, Golomb instantly the nickname, “Einstein” from his fellow students.

But how did he know the answer? As it happened, Golomb had memorized the answers to all the exponential expressions from 1¹ up to 10¹⁰ as a personal challenge. While he hadn't didn't know the answer to 2²⁴ itself, he did realize that it was the same as 8⁸, which he did know!

Learning the answers for exponential expressions up to 10¹⁰ is akin to learning the multiplication tables, but since the results go up into the billions, it seems much more impressive. You can learn to do this yourself in the brand new Exponential Expressions section of Grey Matters' Mental Gym.

Dr. Golomb's ability to stun his college instructor using memorized information reminds me of one of my own college experiences. In my case, I stunned my art history teacher with my ability to perfectly recall the names of 60 paintings, their respective artists, and the exact year each one was painted. Was I instantly regarded as an art genius? No, I was accused of cheating (click that link for the full story).

I'll wrap this post up with a story of memory skill that happened back in Ancient Greece in the 5th or 6th century BC, yet still resonates to this day. Simonides of Ceos, a respected Greek poet, was attending a well-attended banquet dinner. Like all orators of the time, Simonides possessed a great memory as a tool of his trade. After giving his speech toasting the guest of honor, Simonides went outside for a break. While he was there, the roof of the structure collapsed, killing everyone who was inside. As the excavation happened, city officials called for Simonides' help to identify the bodies.

Incredibly, Simonides was able to identify every body from the banquet dinner! He later realized that he was able to do this because he knew the people by where they were sitting. It was this experience that inspired him to create a formal memory system based on locations. This system is still used today, and is known as the Journey System. It involves visualizing something that represents the first point of your presentation in the first location of some familiar place (say, the bedroom where you wake up). To recall your second point, you mentally travel to the second point in your journey (say, the hall outside your bedroom), and see a different image there. In this way, it's possible to remember hundreds of different points without any notes.

The memory system itself isn't all that survives to this day. As orators throughout the ages used this same technique, it wasn't uncommon for them to refer to the journey through their mental structures as the speech was given. This tradition of references to mental journey stayed around long enough that it eventually came into the English language as, “In the first place . . . ,” “In the second place . . . ,” and so on.