The history of mathematics....help with resources


by harkkam
Tags: history, mathematicshelp, resources
harkkam
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#1
Jan10-14, 01:01 PM
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Hey guys I need help finding good resources to help me understand basic to advance math from a developmental point of view, the applied necessities of the inventors of math operations and concepts.

For example the addition operation was invented by a caveman who wanted to know how many bows he had etc.

Then the Babylonians square numbers, and take square roots. But what practical problem required the invention of squares?

I'm trying to think of a problem that would require me to invent the concept of squaring and taking square roots to solve a problem in ancient time.

For example if I saw a star and I wanted to calculate the distance between me and the star what was the thought process in the mind of the person who created the solution to the
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hddd123456789
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#2
Jan10-14, 01:14 PM
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As for square roots, isn't knowing the length of the diagonal of a square a good choice? A book I personally enjoyed on the history of zero is Zero by Charles Seife. It's a popular account though, not a rigorous one if that's what you're looking for.
1MileCrash
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Jan10-14, 01:56 PM
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I highly doubt a caveman invented the concept of addition. I don't think counting was even understood by humans until much later than that.

HallsofIvy
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Jan10-14, 02:35 PM
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The history of mathematics....help with resources


Quote Quote by 1MileCrash View Post
I highly doubt a caveman invented the concept of addition. I don't think counting was even understood by humans until much later than that.
What reason do you have to think that? Counting and basic addition of positive numbers can be done fairly objectively and there is no reason to think early Cro-Magnon (cavemen) were not as intelligent as us.
1MileCrash
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Jan10-14, 03:48 PM
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Quote Quote by HallsofIvy View Post
What reason do you have to think that? Counting d basic addition of positive numbers can be done fairly objectively and there is no reason to think early Cro-Magnon (cavemen) were not as intelligent as us.

I don't see how they'd have to be less intelligent than us to precede the notion of counting. Sure, it's easy to think now that it is such a trivial idea, but there is a lot we take for granted. I don't think the people of the dark ages were any less intelligent than us either.

Ancient languages had words for "one," "two,".. and then after a short while (3 or 4), one more, "many." The natives islanders of Torres Strait are a common example. There was no discerning of numbers over the initial few at all in their entire language, the concept was absent.

Additionally, other languages used different words for quantities of different things. The word for two goats bore no relation to the word for two oxen, and the idea of "two" on its own did not exist. Two oxen was just a common thing, so it had a word. These languages predate the notion of counting and cavemen predate all of these languages.

The realization of numbers as "things" in their own right seems natural to us today, but I'd wager that these simple things are much larger milestones than you realize.
harkkam
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Jan10-14, 06:30 PM
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Quote Quote by hddd123456789 View Post
As for square roots, isn't knowing the length of the diagonal of a square a good choice? A book I personally enjoyed on the history of zero is Zero by Charles Seife. It's a popular account though, not a rigorous one if that's what you're looking for.
Thank you for your response, yes the diagonal of a square is a good example.

But lets study that for a minute, to arrive at the diagonal you would need the pythagorean theorem and for that, somebody had to be curious enough to need a solution to a diagonal of a triangle.

We can say that perhaps ancient Egyptians wanted to measure the distance between two opposite corners of a square plot, or that a bridge at an angle needed to be built between two points, one higher than the other and thus to build a bridge of the right length the distance of the two points needed to be figured out.

This need would lead to mathematicians trying to develop the pythagorean theorem and squaring and square roots concepts.

Now are there books or resources that have higher math topics like logs and binomials etc and the study of their development for practical purposes.

For example I was reading an article on how pi was estimated, with a square circumscribed around a circle and a square inscribed in that same circle.

The definition of a derivative is usually well laid out in textbooks and the concept well defined that you can actually "invent" the derivative yourself. You can see how:

[f (a + h) - f ( h ) ]/h would be a natural conclusion to trying to take the slope of ever smaller segments

But what went through the mind of the individual that decided the need to create the notation, x variable to represent something that was unknown.

The reason I want to know this information is to better understand mathematical thinking for myself, the logical process of its creation. I believe that the way math is taught to most people that its a system of rules that exists, and are asked to perform functions and operations, is a disservice.

For example F=ma, how did newton arrive at that? If we can understand that, then we will become in my estimation much better at understanding force itself.

I want to basically reinvent the wheel in math, so that I understand the tools I'm working with.

Sorry for the long post just need some resources for this kind of work
mesa
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#7
Jan10-14, 07:44 PM
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Quote Quote by 1MileCrash View Post
I don't see how they'd have to be less intelligent than us to precede the notion of counting. Sure, it's easy to think now that it is such a trivial idea, but there is a lot we take for granted. I don't think the people of the dark ages were any less intelligent than us either...

...The realization of numbers as "things" in their own right seems natural to us today, but I'd wager that these simple things are much larger milestones than you realize.
I can see your point, much like the concept of negative numbers took a VERY long time to come to fruition although counting is pretty basic.

Back on the farm when pulling eggs from the coop we always had to leave '3' in place because some of the 'smarter' chickens would notice if there were less and would have a fit. I bet 'uncivilized' humans managed to do at least as well :)
1MileCrash
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Jan10-14, 08:03 PM
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Quote Quote by mesa View Post
I can see your point, much like the concept of negative numbers took a VERY long time to come to fruition although counting is pretty basic.

Back on the farm when pulling eggs from the coop we always had to leave '3' in place because some of the 'smarter' chickens would notice if there were less and would have a fit. I bet 'uncivilized' humans managed to do at least as well :)
It is easy for us to call counting "basic" now, just like negative numbers are basic now.

There is an enormous gap between recognizing someone took eggs, and counting in a way that would allow addition to exist. I would argue that 3 was this number not because the chickens wanted 3 eggs or knew what '3' was, but that 3 was just number simply because it may be hard for them to see a difference between a group of 3 eggs and a group of 4, 5, 6, or 7 eggs.

I know without the ability to count, I could not visually see the difference between a group of 7 and 8, or 9 and 10. The number is probably considerably lower than that, but it's hard to imagine not being able to count, so it's hard for me to think about.
mesa
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Jan10-14, 08:09 PM
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Quote Quote by 1MileCrash View Post
It is easy for us to call counting "basic" now, just like negative numbers are basic now.

There is an enormous gap between recognizing someone took eggs, and counting in a way that would allow addition to exist. I would argue that 3 was this number not because the chickens wanted 3 eggs or knew what '3' was, but that 3 was just number simply because it may be hard for them to see a difference between a group of 3 eggs and a group of 4, 5, 6, or 7 eggs.

I know without the ability to count, I could not visually see the difference between a group of 7 and 8, or 9 and 10. The number is probably considerably lower than that, but it's hard to imagine not being able to count, so it's hard for me to think about.
Yup, no doubt there are many 'simple' things we use today that took a massive leap in our thinking in the past. Imagine what the old timers would think of imaginary's
SteamKing
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#10
Jan10-14, 08:24 PM
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A good introduction to the history and development of mathematics is Morris Kline, "Mathematical Thought from Ancient to Modern Times", 3 volumes. This work covers math development from the Babylonians and Egyptians up to about the middle of the TwenCen.

If you go to Amazon.com, there are several other titles by Kline which might also be of interest for a particular topic in math.
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Jan10-14, 09:28 PM
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Quote Quote by 1MileCrash View Post
It is easy for us to call counting "basic" now, just like negative numbers are basic now.

There is an enormous gap between recognizing someone took eggs, and counting in a way that would allow addition to exist. I would argue that 3 was this number not because the chickens wanted 3 eggs or knew what '3' was, but that 3 was just number simply because it may be hard for them to see a difference between a group of 3 eggs and a group of 4, 5, 6, or 7 eggs.

I know without the ability to count, I could not visually see the difference between a group of 7 and 8, or 9 and 10. The number is probably considerably lower than that, but it's hard to imagine not being able to count, so it's hard for me to think about.
You may want to look at the Ishango bone.
harkkam
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#12
Jan11-14, 03:24 AM
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Quote Quote by SteamKing View Post
A good introduction to the history and development of mathematics is Morris Kline, "Mathematical Thought from Ancient to Modern Times", 3 volumes. This work covers math development from the Babylonians and Egyptians up to about the middle of the TwenCen.

If you go to Amazon.com, there are several other titles by Kline which might also be of interest for a particular topic in math.

Thx, looks like my thread got hijacked lol

EDIT: Thank you again, i think this is what I was looking for, great resources


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