Reddit mentions of Science: A History

A bit of a follow up: your observation that only the wealthy could afford the luxury of science is pretty much dead on, up until the late 19th century. Nearly all the famous scientists you encounter to that point were either aristocrats doing their own thing, or employed by wealthy aristocrats and merchants doing science to drive innovation and technology for their patrons.

I'd highly recommend John Gribbin's Science: A History http://www.amazon.com/Science-A-History-John-Gribbin/dp/0140297413#

To understand the general history of math, you won't need to understand what you most likely consider to be math. You will, however, need to understand how to put yourself in the shoes of those who came before and see the problems as they saw them, which is a rather different kind of thinking.

But anyway, the history of math is long and complicated. It would take years to understand everything and much of it was work done on paths that are now basically dead ends. Nevertheless, here are some other resources:

• In Pursuit of the Unknown: 17 Equations That Changed the World - In general, Ian Stewart is very good for introductory explanations to math.
  
  
• Gödel, Escher, Bach: An Eternal Golden Braid - Perhaps the only explanation of Gödel's work that I would consider "good." It's notoriously lengthy and can be difficult to read, but it doesn't assume much about the reader.
  
  
• Thinking about Mathematics: The Philosophy of Mathematics
  
  
• Philosophy of Mathematics: Selected Readings
  
  
• Stanford Encyclopedia of Philosophy
  
  
• Science: A History - Math did not evolve in an intellectual bubble and much of the mathematics we use today evolved out of a sort of feedback loop between scientists and mathematicians.
  
  Of course, let's not forget what is possibly the most complete single resource available today:
  
  
• Wikipedia
  
  This is a huge area and I applaud you for being interested in it. If you decide to look into it seriously, you WILL find yourself confused, bored, and annoyed at times. Yet it's a beautiful history and one that will illuminate much of the apparently meaningless gibberish in calculus, as well as many other areas.
  

The Baroque Cycle is brilliant http://en.wikipedia.org/wiki/The_Baroque_Cycle (as is the related Cryptonomicon).

They are Alt History in a way, but they are also Science fiction (that is the genre the author himself uses).

I was quite lucky in that i read a history of science just before reading this series, so i had knowledge of some of the historical characters used fresh in my mind. (this was the science history book: http://www.amazon.co.uk/Science-History-1543-John-Gribbin/dp/0140297413 , a great read in its own right).