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Mathematicians Bridge Finite-Infinite Divide

quantamagazine.org

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Re: Mathematicians Bridge Finite-Infinite Divide

#31

Post by auggierose »

Smaug123 wrote: post #30
auggierose wrote: post #29

Earlier quoted context omitted.

My point is that if you prove that 91 has as its prime factors 7 and 13, I don't care if you did that proof using infinite methods or not. In general, I am only proving theorems that are useful to me, so "a bit less useful" doesn't apply to these situations. If I needed that "bit more usefulness", I would go ahead and prove it (if I could). Your reasoning mostly only applies if you prove theorems for their own sake,…

It's only an analogy. The analogy is meant to be "prove that 91 has prime factors" using infinitistic methods, and "prove that 91's prime factors are 7 and 13" using finitistic ones.

I am aware of that. That's why analogies are usually not very useful.

Re: Mathematicians Bridge Finite-Infinite Divide

#33

Post by xviia »

robinhouston wrote: post #8

I love the fact there's a long popular article devoted to the proof “that RT^2_2 is Π^0_3 conservative over IΣ^0_1”, as the abstract of the paper summarises it. Reverse mathematics is a fairly niche area even within mathematical logic. Kudos to Natalie Wolchover for taking it on.

It makes me curious how Quanta is funded. The journal is very high quality and in a niche market: pure science journalism. I can't imagine they make enough subscription revenue; maybe it's funded mostly through the Simons Foundation?

Either way, glad it exists!

Re: Mathematicians Bridge Finite-Infinite Divide

#34

Post by Smaug123 »

auggierose wrote: post #31
Smaug123 wrote: post #30

Earlier quoted context omitted.

It's only an analogy. The analogy is meant to be "prove that 91 has prime factors" using infinitistic methods, and "prove that 91's prime factors are 7 and 13" using finitistic ones.

I am aware of that. That's why analogies are usually not very useful.

I have no idea how you learn, but analogies are basically the only way I use of absorbing new concepts.

Re: Mathematicians Bridge Finite-Infinite Divide

#35

Post by defen »

xviia wrote: post #33
robinhouston wrote: post #8

I love the fact there's a long popular article devoted to the proof “that RT^2_2 is Π^0_3 conservative over IΣ^0_1”, as the abstract of the paper summarises it. Reverse mathematics is a fairly niche area even within mathematical logic. Kudos to Natalie Wolchover for taking it on.

It makes me curious how Quanta is funded. The journal is very high quality and in a niche market: pure science journalism. I can't imagine they make enough subscription revenue; maybe it's funded mostly through the Simons Foundation? Either way, glad it exists!

I believe it's funded by James Simons

Re: Mathematicians Bridge Finite-Infinite Divide

#37

Post by pohl »

openasocket wrote: post #36

I'm having trouble imagining what finitism actually is, based on what I remember from set theory. Is it equivalent to Zermelo-Frankel set theory without the axiom of infinity?

I found this helpful:

"The main idea of finitistic mathematics is not accepting the existence of infinite objects such as infinite sets. While all natural numbers are accepted as existing, the set of all natural numbers is not considered to exist as a mathematical object. Therefore quantification over infinite domains is not considered meaningful."

https://en.wikipedia.org/wiki/Finitism

Re: Mathematicians Bridge Finite-Infinite Divide

#38

Post by xviia »

defen wrote: post #35
xviia wrote: post #33

Earlier quoted context omitted.

It makes me curious how Quanta is funded. The journal is very high quality and in a niche market: pure science journalism. I can't imagine they make enough subscription revenue; maybe it's funded mostly through the Simons Foundation? Either way, glad it exists!

I believe it's funded by James Simons

Ah, now I understand. For others:

Simons Foundations --> James Simons, who is a hedge fund mananger worth ~ $14billion.

Excellent interview with Numberphile here:

https://www.youtube.com/watch?v=QNznD9hMEh0

Re: Mathematicians Bridge Finite-Infinite Divide

#39

Post by antognini »

xviia wrote: post #38
defen wrote: post #35

Earlier quoted context omitted.

I believe it's funded by James Simons

Ah, now I understand. For others: Simons Foundations --> James Simons, who is a hedge fund mananger worth ~ $14billion. Excellent interview with Numberphile here: https://www.youtube.com/watch?v=QNznD9hMEh0

In addition, James Simons was a mathematician prior to his work in the finance industry, hence his partiality toward funding a magazine that often writes about pure mathematics.

Re: Mathematicians Bridge Finite-Infinite Divide

#40

Post by bradleyjg »

antognini wrote: post #39
xviia wrote: post #38

Earlier quoted context omitted.

Ah, now I understand. For others: Simons Foundations --> James Simons, who is a hedge fund mananger worth ~ $14billion. Excellent interview with Numberphile here: https://www.youtube.com/watch?v=QNznD9hMEh0

In addition, James Simons was a mathematician prior to his work in the finance industry, hence his partiality toward funding a magazine that often writes about pure mathematics.

I believe he is now back at Stony Brook in the mathematics department. Not full time, he has a lot going on, but some kind of affiliation.
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