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In Search of Proofs from “The Book”

quantamagazine.org

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Re: In Search of Proofs from “The Book”

#11

Post by yantrams »

ggm wrote: post #9
tacomonstrous wrote: post #7

As a working mathematician, I'm uncomfortable with this apotheosis of 'the proof'. While there's always room for aesthetics, this might support the rather misleading premise that mathematics is about digging up chiseled beauties, when it is really about hours, days and months of flailing around, trying to understand one thing, or even what it means to understand that thing. And it's rarely pretty.

I think Davis and Hersh say this. Ruben Hersh "what is mathematics really" felt like it was opening the door to the sausage factory.

Brilliant book that. The way he explains how a polished rigorous proof hides the process(compared with frontend and kitchen views of a restaurant) by which a mathematician has arrived at it changed my perception of how mathematics is done.

I notice the same phenomena in programming too. The final piece of code that works doesn't reflect all the failed attempts at solving a problem. This is why I tend to not delete/clear cells at all from my jupyter notebooks. :) It is always informative/fun to refer to them at a later point in time to relive that problem solving experience.

PS: In case you haven't, you should try Proofs and Refutations by Lakatos.

Edit: Fixed name of the book mentioned and added some text.

Re: In Search of Proofs from “The Book”

#12

Post by ggm »

yantrams wrote: post #11
ggm wrote: post #9

Earlier quoted context omitted.

I think Davis and Hersh say this. Ruben Hersh "what is mathematics really" felt like it was opening the door to the sausage factory.

Brilliant book that. The way he explains how a polished rigorous proof hides the process(compared with frontend and kitchen views of a restaurant) by which a mathematician has arrived at it changed my perception of how mathematics is done. I notice the same phenomena in programming too. The final piece of code that works doesn't reflect all the failed attempts at solving a problem. This is why I tend to not delete/cl…

Do you mean "proof and refutations" ?

Re: In Search of Proofs from “The Book”

#13

Post by extr »

tacomonstrous wrote: post #7

As a working mathematician, I'm uncomfortable with this apotheosis of 'the proof'. While there's always room for aesthetics, this might support the rather misleading premise that mathematics is about digging up chiseled beauties, when it is really about hours, days and months of flailing around, trying to understand one thing, or even what it means to understand that thing. And it's rarely pretty.

You sound like a jaded professional, but keep in mind most people are not working mathematicans and never will be, so anything they hear from the pros they're going to take at face value. When it comes to the general layperson, I think popularizing the idea that math is all "months of flailing around, trying to understand one thing" is more unhelpful than portraying it as the pursuit of beauty and simplicity, even if it's more true on a practical level. If you bring up the word beauty in reference to math, most people are a little surprised you even would link the two concepts, let alone get the impression that pursuing clever little proofs is all there is to it. Better to start by giving people get the idea they might enjoy it, and let them find out it's not all about elegant proofs in undergrad or whatever.

Re: In Search of Proofs from “The Book”

#14

Post by cocoa19 »

ggm wrote: post #9
tacomonstrous wrote: post #7

As a working mathematician, I'm uncomfortable with this apotheosis of 'the proof'. While there's always room for aesthetics, this might support the rather misleading premise that mathematics is about digging up chiseled beauties, when it is really about hours, days and months of flailing around, trying to understand one thing, or even what it means to understand that thing. And it's rarely pretty.

I think Davis and Hersh say this. Ruben Hersh "what is mathematics really" felt like it was opening the door to the sausage factory.

To those like me, not familiar with the term "sausage factory":

"An unpleasant process, especially one that is hidden from public view, that is used to produce a widely consumed product" - Urban Dictionary

Re: In Search of Proofs from “The Book”

#15

Post by yantrams »

ggm wrote: post #12
yantrams wrote: post #11

Earlier quoted context omitted.

Brilliant book that. The way he explains how a polished rigorous proof hides the process(compared with frontend and kitchen views of a restaurant) by which a mathematician has arrived at it changed my perception of how mathematics is done. I notice the same phenomena in programming too. The final piece of code that works doesn't reflect all the failed attempts at solving a problem. This is why I tend to not delete/cl…

Do you mean "proof and refutations" ?

Ah yes, thanks for correcting me :)

Re: In Search of Proofs from “The Book”

#16

Post by [deleted] »

extr wrote: post #13
tacomonstrous wrote: post #7

As a working mathematician, I'm uncomfortable with this apotheosis of 'the proof'. While there's always room for aesthetics, this might support the rather misleading premise that mathematics is about digging up chiseled beauties, when it is really about hours, days and months of flailing around, trying to understand one thing, or even what it means to understand that thing. And it's rarely pretty.

You sound like a jaded professional, but keep in mind most people are not working mathematicans and never will be, so anything they hear from the pros they're going to take at face value. When it comes to the general layperson, I think popularizing the idea that math is all "months of flailing around, trying to understand one thing" is more unhelpful than portraying it as the pursuit of beauty and simplicity, even if…

[deleted]

Re: In Search of Proofs from “The Book”

#17

Post by wolfkill »

As a mathematician and a believer in God, I get uncomfortable when people start attributing math to God. I see math as being very much a construct of the human psyche and as astounding as it is, there are enormous gaps between mathematical models and physical observations. So in my mind math is to reality as human is to Divine.

Re: In Search of Proofs from “The Book”

#18

Post by joe_the_user »

ggm wrote: post #9
tacomonstrous wrote: post #7

As a working mathematician, I'm uncomfortable with this apotheosis of 'the proof'. While there's always room for aesthetics, this might support the rather misleading premise that mathematics is about digging up chiseled beauties, when it is really about hours, days and months of flailing around, trying to understand one thing, or even what it means to understand that thing. And it's rarely pretty.

I think Davis and Hersh say this. Ruben Hersh "what is mathematics really" felt like it was opening the door to the sausage factory.

Well,

It is interesting that a lot of great mathematicians have believed in truth beyond the sausage factory. Not that the reality isn't a sausage factory but belief in an ideal (truth, beauty) seems to often be what keeps them going.

Kurt Godel proved that the machinery of mathematics couldn't create a complete truth system accessible through proofs (which are ultimately a mechanical process) but he definitely was on the side of ideal-truth when he said "Either mathematics is too big for the human mind, or the human mind is more than a machine."

Edit: And Grigori Perelman was certainly famous for rejecting what he saw as the sausage factory of mathematics.

Re: In Search of Proofs from “The Book”

#19

Post by empath75 »

wolfkill wrote: post #17

As a mathematician and a believer in God, I get uncomfortable when people start attributing math to God. I see math as being very much a construct of the human psyche and as astounding as it is, there are enormous gaps between mathematical models and physical observations. So in my mind math is to reality as human is to Divine.

The roots of mathematics in the west are fairly inextricably tied up with the development of religion via Pythagoras and especially Plato. Plato (or at least Platonists) taught, for example that God literally was One -- as in the number 1. And that all of reality is the result of successive emanations from 1 -- to the dyad (2), then the rest of the numbers, on through geometry and so on. Those beliefs influenced the philosophical development of all the major monotheistic religions.

Re: In Search of Proofs from “The Book”

#20

Post by pfortuny »

tacomonstrous wrote: post #7

As a working mathematician, I'm uncomfortable with this apotheosis of 'the proof'. While there's always room for aesthetics, this might support the rather misleading premise that mathematics is about digging up chiseled beauties, when it is really about hours, days and months of flailing around, trying to understand one thing, or even what it means to understand that thing. And it's rarely pretty.

I am also a professional. Sometimes your job deals with the pretty marigold and sometimes with the nasty slug.

Reality has its thing.

And sometimes you need a jeweler’s tool and other times just your fists.

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