How and where did the mathematicians and philosophers before, get the equations and formulas in math?

Question

Everytime I attend my math class, i get awestruck at the equations and formulas that my teacher shows and explains to us. I was just wondering how the mathematicians and philosophers came up with these equations and formulas that are connected to each other. How long and how did they do it???

Answer 1

They had way too much time on their hands. Yahoo! Answers didn't exist back then.

Answer 2

Some people had a lot of time on their hands. Throughout history, there have been some incredibly bright people. Archimedes, Newton, Fermat, Pythagorus, and so on. Such an intuitively bright person comes about every few hundred years and spurs centuries more of thought.

Geometry, like physics, can be observed. Algebra is a regulated problem-solving strategy, that has grown over the years. What's spectacular is the less-obvious equations and theorems that come out of linear algebra and number theory and whatnot, which are a century or more old.

Answer 3

A lot of it I'm sure depended on the ingenuity of the individual. Even creative and inventive individuals like Thomas Edison had to make many mistakes through trial and error before he hit upon the right combination to make the light bulb filament work.

The English genius Sir Isaac Newton is quoted as saying, "If I have seen farther than other men, it has been because I have stood upon the shoulders of giants." In other words, they planted the seed, he simply nourished it and helped it grow by expounding upon their work. Newton is also purported to have said, and I paraphrase here. "If I have succeeded, it has been because I continually hold the object of my curiosity before my minds eye." In other words, even though he might not come up with an answer immediately, he persisted until a flash of insight provided the solution.

Answer 4

I used to think that way too...still do, sometimes. The funny thing is, the equations are the easy part. It's the original ideas that are tough. A lot of physics equations just pop out easily from the ideas...even some of the fairly complicated ones. The trick is to observe reality and concisely and completely describe what you see.

Answer 5

Perseverance and ingenuity.