Man nearly falls off roof after ladder buckles - GIF

[tonyfoale]

It has always fascinated me how those early thinkers figured out all of these vitally important details. The mathematical concepts, relationships of the stars and the planets, etc.

They did all of this with their own minds, no computers to help them.

As Marv pointed out, they studied mathematics. The same is still true, there is still lots of scope for improving knowledge through purely theoretical mathematics in the fields of the large and small - the greater cosmos and the quantum arena. Much if not all of Einstein's contributions were a result of pure thinking and mathematics. Those people from centuries and millenia ago had similar intellects to those of today. They had less starting knowledge and less computational tools, but that is not a hinderance to analytical thought. Although some also had to content with religious doctrine which in some cases was a hinderance. The opposite is actually the case, with less starting knowledge they had more scope in which to apply some mathematics to both observed and unforeseen phenomenon.
My own meagre experience shows the value of mathematics as an aid to understanding the world. From the age of 8 my hobby was electronics and to understand more I had to study maths from books way ahead of classroom teaching. I studied and understood algebra, geometry, vectors etc. but I just could not get my head around the calculus from books. I lied and managed to get into university quite young, I was 15 and to pay my way I got a job as a lab technician at the university, that meant that I was exempt from tuition fees and had good access to the lecturers. Before going to my first lecture on the calculus I asked an engineering lecturer from the department where I worked to quickly explain differential calculus to me before the lecture. He explained that the derivative was a rate of change. Wow! That was what had alluded me through my book studies and the subsequent first lecture. Suddenly a whole new world of understanding opened before me. Stuff that I couldn't get beyond previously became crystal clear. A couple of years later I was involved in the simulation of various physical phenomena and I learnt the extraordinary power of mathematics to predict stuff that nobody had thought of previously.
It is a big mistake to think of our ancestors as being mentally less capable than ourselves, just because they rode horses instead of cars. The difference between those of earlier eras such as Euler, Newton, the Bernoullis, Galilao et al and their equals of today is that the ancients dealt with things that were within the human intellect to comprehend. Anyone could understand that apples fell to the ground. Today's smart chaps are dealing with things that even they themselves can understand only through the mathematics. Yet the predictive power has been amply demonstrated.