> (By contrast, non-mathematicians are unable to build anything larger than a small hut without help from mathematicians in the form of geometry.)
If being a mathematician requires this sort of arrogant attitude, then I am all for locking those people up in an ivory tower and willingly foregoing the fruits of their labor.
The idea of applying mathematics and science to the efforts of people doing things instead of thinking about things is actually quite recent--maybe 300-ish years ago. Medieval Europeans didn't need a deep understanding of geometry or physics to discover flying buttresses or build Gothic cathedrals. Go back further in time and look at the majesty of Stonehenge or the Pyramids; the people who built those had no concept of tangents or pi and yet built what they did.
> I think the downvoting of my "tirade" to -2 has shown that non-mathematicians hate and fear mathematicians
No. I like mathematicians quite a lot, but I think you have your head stuck up your own ass.
> Go back further in time and look at the majesty of Stonehenge or the Pyramids; the people who built those had no concept of tangents or pi and yet built what they did.
The Sumerians were doing geometry in 2450 BCE, and the Egyptians were in contact with them. Older Sumerian texts (from before 3100 BCE) don't have a lot of geometry but do contain numerical measurements and arithmetic used for accounting.
The Moscow Mathematical Papyrus, from Egypt, is from the 13th Dynasty (ended 1649 BCE), and it has a problem in it about the volume of the frustum of a pyramid. The Rhind Papyrus (around 1550 BCE) contains six problems about building pyramids, some problems about granary design, and a number of problems about real estate. The pyramids analyzed therein are building-sized. At this point the Egyptians had been building pyramids for a millennium, but no older mathematical texts have survived (aside from a diagram from 1000 years earlier showing how to measure off the slope of a mastaba), but few papyri last even the 4000 years of these papyri. Papyrus is fragile.
Nevertheless, it seems that the ancient Egyptians considered the knowledge of mathematics important to building pyramids, at least by the end of the pyramid-building period.
As for Stonehenge, we have no idea. The folks who built it didn't have a writing system, so we don't know much about how they thought. Still, it does seem pretty plausible that you could roll a big stone lintel up a hill of sand, or carefully balance it onto progressively higher stone pivots, without knowing the Pythagorean theorem. I guess Stonehenge is bigger than a small hut, so you've got me there.
There are Babylonian and Egyptian sources describing how to solve quadratic and some cubic equations from about 1600 BCE, but that is unfortunately at the end of the pyramid-building period. I think it's likely that they had this knowledge much earlier, but it's possible that they built the Pyramids, or most of them, before anyone had figured that out.
If being a mathematician requires this sort of arrogant attitude, then I am all for locking those people up in an ivory tower and willingly foregoing the fruits of their labor.
The idea of applying mathematics and science to the efforts of people doing things instead of thinking about things is actually quite recent--maybe 300-ish years ago. Medieval Europeans didn't need a deep understanding of geometry or physics to discover flying buttresses or build Gothic cathedrals. Go back further in time and look at the majesty of Stonehenge or the Pyramids; the people who built those had no concept of tangents or pi and yet built what they did.
> I think the downvoting of my "tirade" to -2 has shown that non-mathematicians hate and fear mathematicians
No. I like mathematicians quite a lot, but I think you have your head stuck up your own ass.