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Re: Philosophy of Mathematics

January 5th, 2021, 1:22 pm

Scope is important. Start with: which of  each of 1..5 has been terribly influential, a kind of big bang.

Example of 1 [$]e[$].
Example of 4. a^2 + b^2 = c^2

As an aside, I have nice little book called The Story of Mathematics, which covers math from a cultural perspective.  Thought the ages, some societies were focused on trade and accounting, others wanted to build fantastic structures and developed their math accordingly. Others looked at the skies and wanted to figure out what is happening out there.  More math needed!  Derivatives and quant finance came later, (but not as late as some people think!)

The books is not rigorous or laden with derivations, of course, but it is insightful and has many beautiful pictures of artifacts and mathematical art.

And to fill in another space in your list:

3. formula:
 Image

It will be fun to build the taxonomy and examples out in spare time this winter.
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Re: Philosophy of Mathematics

January 5th, 2021, 1:26 pm

If you are an AI pioneer in the mid-20th century, then more so to 3 and 4?
Most of stuff in AI was invented in 19th century or earlier, e.g. graph theory was invented by Euler.
AI is an application of math.

Image
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Re: Philosophy of Mathematics

January 5th, 2021, 1:32 pm

If you are an AI pioneer in the mid-20th century, then more so to 3 and 4?
Most of stuff in AI was invented in 19th century or earlier, e.g. graph theory was invented by Euler.
AI is an application of math.
Well, yes, long history but if we think about the field as a discipline, Turing machine is mid-1930s (I think maybe 1936) and AI as an academic field - mid-1950s.

But not taking anything away from Euler, or Lovelace, or...
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Re: Philosophy of Mathematics

January 5th, 2021, 3:13 pm

If you are an AI pioneer in the mid-20th century, then more so to 3 and 4?
Most of stuff in AI was invented in 19th century or earlier, e.g. graph theory was invented by Euler.
AI is an application of math.
Well, yes, long history but if we think about the field as a discipline, Turing machine is mid-1930s (I think maybe 1936) and AI as an academic field - mid-1950s.

But not taking anything away from Euler, or Lovelace, or...
Turing is over-rated. And Minsky is a visionary. (and a friend of Jeffrey E.)
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Re: Philosophy of Mathematics

January 10th, 2021, 12:42 pm

Probably #1 algorithm of 20th century Cooley-Tukey FFT

https://en.wikipedia.org/wiki/Cooley%E2 ... _algorithm
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Re: Philosophy of Mathematics

February 7th, 2021, 1:13 pm

Found on GitHub recently:

math genealogy thearn

"A python script to collect data from the mathematics genealogy project and generate genealogy graphs, combine graphs, etc."

Example:

Image
Always interesting how different lines of thought can affect others too - bouncing off each other and generating new ideas. In physics, think of Feynman, but also his PhD advisor, John Archibald Wheeler and all of his students and then down the path to their students.  

Here is a little summary of The doctoral students of Richard Feynman - Physics Today, May 11, 2017 and notes on their work, with links.
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Re: Philosophy of Mathematics

February 7th, 2021, 1:57 pm

Can you do my family tree? I used to have the T-shirt.
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Re: Philosophy of Mathematics

February 7th, 2021, 3:00 pm

Can you do my family tree? I used to have the T-shirt.
I am going out to look at many, many trees now, no laptop, no iPhones and definitely no fooling around with Python(s)!

Good to post this for the snake charmers here though - maybe it can be adapted for useful purposes in other disciplines - finance, economics, etc.
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Re: Philosophy of Mathematics

February 7th, 2021, 5:38 pm

BTW where you get your trees. I knew Prof Dahlquist, a famous numerical analysis.
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Re: Philosophy of Mathematics

February 7th, 2021, 8:12 pm

BTW where you get your trees. I knew Prof Dahlquist, a famous numerical analysis.
That tree was just one given as an example on the github site.  Code is there too, of course, only 59 lines of it!
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Re: Philosophy of Mathematics

February 7th, 2021, 11:32 pm

Hmm. Neither my advisor nor I are listed, but we roll up to the Leontief branch, and thus to Gauss, the proto-quant. I guess I could add some edits to the project...
 
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Re: Philosophy of Mathematics

February 8th, 2021, 3:55 pm

Hmm. Neither my advisor nor I are listed, but we roll up to the Leontief branch, and thus to Gauss, the proto-quant. I guess I could add some edits to the project...
I would have thought they would all be descendants of Lie or Abel.
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Re: Philosophy of Mathematics

February 8th, 2021, 8:29 pm

Hmm. Neither my advisor nor I are listed, but we roll up to the Leontief branch, and thus to Gauss, the proto-quant. I guess I could add some edits to the project...
I would have thought they would all be descendants of Lie or Abel.
You mean Cain or Abel?  :D
 
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Re: Philosophy of Mathematics

February 8th, 2021, 8:36 pm

Another representation - you can hover over to follow paths, or download a pdf (poster version).

The first entry here is Sharaf al-Din al-Tusi.

Mathematics Genealogy - Stony Brook University Math Department January 2021

Sharif al-Din al-Tusi - Iranian mathematician and astronomer (c. 1135- c. 1213)

If every university Math Department did this for their students, that would be a great data set for merging and further building out.
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Re: Philosophy of Mathematics

February 9th, 2021, 12:32 am

Hmm. Neither my advisor nor I are listed, but we roll up to the Leontief branch, and thus to Gauss, the proto-quant. I guess I could add some edits to the project...
I would have thought they would all be descendants of Lie or Abel.
Umm - given that Abel died at the tender age of 26, he did not leave any known descendants, either physical or intellectual. Lie, of course did, and I discovered Donald Knuth in his branch. But nobody close to me.