Marjorie Rice discovered 4 new types of pentagon tessellations after reading a Scientific American article about tessellations and becoming interested in the subject.
Note that what happened in the movie was not an example of a brilliant but uneducated person having an unusual insight. We see Will devouring books of all sorts in his free time. It’s a case of a brilliant self-educated person solving an advanced problem. If you’re capable of learning by reading mathematics textbooks at a very accelerated rate, the educational value of sitting in a math class is limited. He even makes that point explicitly when he’s insulting the long-haired guy about dropping a hundred grand on an education he could get for free at the local library.
This is a point well worth noting. But it is also worth noting that taking math classes, and earning a degree in mathematics, involves more than just sitting in math class. It also involves having the style, substance, and logic of one’s own work checked by professional mathematicians.
Here’s an excerpt I found interesting in Robert Kanigel’s biography of Ramanujan:
Isn’t there a story about Subrahmanyan Chandrasekhar and his solving a problem at a young age while en route via steam ship to England? In reading his wiki-ography he is quite well educated, but I do recall something of a story about his solving some incredible equation/thought experiment before hitting the Big Time education and recognition.
Terence Tao had no maths education beyond Sesame Street and some fridge magnets when he independently discovered how to do basic arithmetic at the age of two. Unfortunately, he had plenty of education between then and winning the Fields Medal.
Jedediah Buxton kind of fits although was perhaps more of a savant. He was illiterate and may have had no maths education at all but was a prodigious mental calculator.
Buxton was clearly not a mathematical prodigy. He was a mental calculator:
There are some cases where a mental calculator was also a good mathematician (or some other type of scientist), but he’s not one of those cases. He showed lots of the symptoms of obsessive-compulsive behavior. Incidentally, that Wikipedia entry on him is pretty poor. It’s clearly based on just a few very old sources. For instance, at one point Buxton calculated in his head the 139th power of 2. It says that it can’t be verified that his calculation was completely correct, since the only way to check it was to use logarithms, and they don’t give a completely accurate answer. Of course, these days it’s easy to quickly get an accurate answer with a computer.
