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Mathematical Chronology

www-history.mcs.st-andrews.ac.uk

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Re: Mathematical Chronology

#41

Post by ice109 »

mrkgnao wrote: post #34

> 1964 > Hironaka solves a major problem concerning the resolution of singularities on an algebraic variety. Essentially, sometimes the varieties (which are geometric objects like curves, surfaces, etc.) studied in algebraic geometry are singular : they might have singularities , like nasty self-crossings or sharp edges. Hironaka's result lets you take a "bad" variety and "resolve its singularities", giving you a goo…

>can work with instead

what can you actually do with these "smoother" varieties?

Re: Mathematical Chronology

#42

Post by mrkgnao »

ice109 wrote: post #41
mrkgnao wrote: post #34

> 1964 > Hironaka solves a major problem concerning the resolution of singularities on an algebraic variety. Essentially, sometimes the varieties (which are geometric objects like curves, surfaces, etc.) studied in algebraic geometry are singular : they might have singularities , like nasty self-crossings or sharp edges. Hironaka's result lets you take a "bad" variety and "resolve its singularities", giving you a goo…

>can work with instead what can you actually do with these "smoother" varieties?

They are much closer to the curves and solids we're familiar with from everyday experience. For example: you have well-defined tangents at every point for a smooth curve, but a self-intersecting curve doesn't. So many techniques and a lot of intuition carries over into the abstract algebraic setting.

More generally, algebraic geometry is a central field of math because it is, basically, about solving polynomial equations. It's one of the most "well-connected" fields of mathematics today. Number theory, differential geometry, complex geometry, even differential equations: all these fields benefit from their interactions with modern algebraic geometry. (Also biology, I've heard. Lior Pachter is a name I remember in this connection.)

Re: Mathematical Chronology

#43

Post by kevinwang »

williamblake wrote: post #24
pluteoid wrote: post #17

Earlier quoted context omitted.

The qualities of the Saqqara boxes are entirely consistent with what we know about the mathematical and engineering sophistication of ancient Egyptians. There is nothing well-verified "not in the books" that upends the "conventional timeline". The only people claiming otherwise are Discovery Channel nutcase types who want you to believe, without real evidence, often with fake evidence, and always with fatuous reasoni…

I'm sorry that I have given you the impression that I or others like myself who discuss these questions believe in ancient aliens. I realize that this is a topic of confusion for many "debunkers". I don't accept belief as a valuable tool the process of discovering the truth, nor do I deem it necessary in the practice of science. Unbiased observation, free from belief is important. And denotative language seems to be…

Well the linked page says:

It’s also not surprising that they could create a flat surface or angles that are exactly-ish 90 degrees. The Egyptians boast some of the earliest known texts on geometry, like the Rhind Papyrus (from around 1650 BCE) and the Moscow papyrus (from about 1850 BCE). The latter papyrus indicates that the Egyptians could approximate pi (as 3.16049) and find the volume of a truncated pyramid. It stands to reason that 500 years later, they would be able to carve a flat surface and make a corner of exactly-ish 90 degrees.

Re: Mathematical Chronology

#44

Post by drio »

This is great. Thank you for sharing.

These days I am working on trying to understand the Fourier transform (1807). It is great fun. I finally understand the equation and how it works. Pure beauty. Now I am in the process to use it in practice. I am planning to write about it and perhaps write some visualizations to help others understand.

This post made me think about a crazy idea I had. I wanted to write periodic posts to talk about the work of all these great mathematicians. I also wanted to have a place where people could buy gear (t-shirts). The same way people is very proud of wearing a sports guy t-shirt (Lebron 23), I'd love to see people wearing t-shirts with mathematicians names (Fourier 10). It's crazy I know.

Re: Mathematical Chronology

#45

Post by drio »

drio wrote: post #44

This is great. Thank you for sharing. These days I am working on trying to understand the Fourier transform (1807). It is great fun. I finally understand the equation and how it works. Pure beauty. Now I am in the process to use it in practice. I am planning to write about it and perhaps write some visualizations to help others understand. This post made me think about a crazy idea I had. I wanted to write periodic p…

Also, what are your favorite books/resources about the history of Mathematics? Something with similar contents to this resource but perhaps connecting the different discoveries.

Re: Mathematical Chronology

#46

Post by iamandoni »

> Adleman, Rivest, and Shamir introduce public-key codes, a system for passing secret messages using large primes and a key which can be published.

My OCD wishes they would have said Rivest, Shamir, and Adleman like the algorithm is named after

Re: Mathematical Chronology

#48

Post by posterboy »

kevinwang wrote: post #43
williamblake wrote: post #24

Earlier quoted context omitted.

I'm sorry that I have given you the impression that I or others like myself who discuss these questions believe in ancient aliens. I realize that this is a topic of confusion for many "debunkers". I don't accept belief as a valuable tool the process of discovering the truth, nor do I deem it necessary in the practice of science. Unbiased observation, free from belief is important. And denotative language seems to be…

Well the linked page says: It’s also not surprising that they could create a flat surface or angles that are exactly-ish 90 degrees. The Egyptians boast some of the earliest known texts on geometry, like the Rhind Papyrus (from around 1650 BCE) and the Moscow papyrus (from about 1850 BCE). The latter papyrus indicates that the Egyptians could approximate pi (as 3.16049) and find the volume of a truncated pyramid. It…

If you look at marble statues, a square box is hardly amazing in comparison. "a few ten-thousandths of an inch" - close to micro meter precision - sounds almost like exaggeration, but some type of stone might just split in a very planar way.

Re: Mathematical Chronology

#49

Post by posterboy »

jordigh wrote: post #5

A guy I knew used to say that this is why computer science is so much easier to learn than number theory. It's thousands of years of number theory to learn vs a few dozen years of computer science. On top of that, the recent historical explosion of computer science is also accompanied by perhaps an even larger explosion of number theory.

Also, mathematics has to be discovered and remembered, whereas half the internet seemingly consists only of programming tutorials and documentation.

Edit: In the end there is no difference, however. Both are structural sciences. I guess you meant the maths in a CS degree.

Re: Mathematical Chronology

#50

Post by sedachv »

posterboy wrote: post #48
kevinwang wrote: post #43

Earlier quoted context omitted.

Well the linked page says: It’s also not surprising that they could create a flat surface or angles that are exactly-ish 90 degrees. The Egyptians boast some of the earliest known texts on geometry, like the Rhind Papyrus (from around 1650 BCE) and the Moscow papyrus (from about 1850 BCE). The latter papyrus indicates that the Egyptians could approximate pi (as 3.16049) and find the volume of a truncated pyramid. It…

If you look at marble statues, a square box is hardly amazing in comparison. "a few ten-thousandths of an inch" - close to micro meter precision - sounds almost like exaggeration, but some type of stone might just split in a very planar way.

> "a few ten-thousandths of an inch" - close to micro meter precision - sounds almost like exaggeration, but some type of stone might just split in a very planar way.

Not an exaggeration, just an extremely long time spent hand grinding/polishing with fine grit tools/paste.

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