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Show HN: I made a puzzle game that gently introduces my favorite math mysteries

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Re: Show HN: I made a puzzle game that gently introduces my favorite math mysteries

#81

Post by blowski »

valenterry wrote: post #38
MCSP wrote: post #15

Earlier quoted context omitted.

Good point! I'll try to think about a better way to phrase this (happy to hear suggestions)

Nah, actually I agree with you. What counts as believe and what as fact is rather abitrary. Is 2+2=4 a fact? Is global warming a fact? What about man-made global warming? Ask 100 people whether something is a fact or a believe. To top that up, it's fact that there have been "proves" that were wrong (or maybe that's just my believe? :^]) even for a long time. Hence, I think we can say that there are 4 options for a th…

Brilliant episode of the BBC’s In Our Time that goes down this rabbit hole. https://www.bbc.co.uk/programmes/b04v59gz

Re: Show HN: I made a puzzle game that gently introduces my favorite math mysteries

#82

Post by SilasX »

MCSP wrote: post #57
SilasX wrote: post #40

Uh, when you draw the map that requires three colors, I couldn't figure out how to submit it to at least be told it's not good enough. Or if it automatically accepts for a 3-min [1], then it was too hard to make sure that the boundary reached the edge of the screen. (I thought I successfully drew five regions around a point.) [1] sorry, 3-chromatic or whatever

Hmm, my guess is you're trying to use the box's borders as lines (they don't count, only the lines you draw count). Let me know if that's not the issue. Also, I'll think about ways to make this more clear!

Ah okay -- the second one had a map with the same shape as the border, which I think made me mentally lump the map's border with the box's borders and invalidate the claim that it's looking at the box's borders as part of the map. I also assumed you wouldn't possibly expect someone to have to explicitly draw all their borders when they can piggyback off the box.

Entirely my mistake because I was kind of ignoring everything you said lol

Re: Show HN: I made a puzzle game that gently introduces my favorite math mysteries

#83

Post by unclad5968 »

karmakurtisaani wrote: post #73
konschubert wrote: post #69

Earlier quoted context omitted.

^ Exhibit A why using "believe" is a bad choice of words. Mathematical poofs are either correct or false. There is no middle ground.

Well.. there is. Middle ground being a very complex, but somehow convincing argument that no one can reasonably check. There was one of these cases in number theory some years ago, can't remember the details. Proofs can be only true or false, but accepting proofs is in the end a social process.

A convincing argument that cannot be checked is not a proof. If you want to extend the definition of proofs you're welcome to do that, but for academic mathematics the meaning of proof doesn't contain a middle ground.

Re: Show HN: I made a puzzle game that gently introduces my favorite math mysteries

#84

Post by nhatcher »

karmakurtisaani wrote: post #73
konschubert wrote: post #69

Earlier quoted context omitted.

^ Exhibit A why using "believe" is a bad choice of words. Mathematical poofs are either correct or false. There is no middle ground.

Well.. there is. Middle ground being a very complex, but somehow convincing argument that no one can reasonably check. There was one of these cases in number theory some years ago, can't remember the details. Proofs can be only true or false, but accepting proofs is in the end a social process.

A couple come to mind

* The proof of the classification of simple groups[0]

* The work on topological four manifolds by M. Freedman [1]

[0]: https://en.m.wikipedia.org/wiki/Classification_of_finite_sim...

[1]: https://news.ycombinator.com/item?id=28471159

Re: Show HN: I made a puzzle game that gently introduces my favorite math mysteries

#85

Post by nirolo »

You might want to get into touch with some museums on science topics to see if they are up to show it. I live in Germany at the moment and know of at least two MINT focused museums that let visitors engage a lot with their (sometimes digital) exhibits and this here checks all the boxes to make a great exhibit.

Very well done, I'll try to see if my children will enjoy that already too.

Re: Show HN: I made a puzzle game that gently introduces my favorite math mysteries

#86

Post by wrsh07 »

nirolo wrote: post #85

You might want to get into touch with some museums on science topics to see if they are up to show it. I live in Germany at the moment and know of at least two MINT focused museums that let visitors engage a lot with their (sometimes digital) exhibits and this here checks all the boxes to make a great exhibit. Very well done, I'll try to see if my children will enjoy that already too.

Absolutely!! Talk to MoMath in NYC too

I'm happy to find a contact there if you want

Re: Show HN: I made a puzzle game that gently introduces my favorite math mysteries

#87

Post by pwmtr »

bgoated01 wrote: post #76

I showed this to my two kids, and we all three enjoyed it. The zero knowledge proof portion didnt really click for me, but we liked the four color map theorem stuff. This led me to download some maps for my kids to attempt coloring on paper, and also got me wondering about how this holds or doesn't on non-euclidian spaces. Turns out the maximum is four colors on a sphere, but 7 colors on a torus! More details here: h…

This video helped me a lot to understand the basics of zero knowledge proof: https://www.youtube.com/watch?v=fOGdb1CTu5c

Re: Show HN: I made a puzzle game that gently introduces my favorite math mysteries

#88

Post by konschubert »

karmakurtisaani wrote: post #73
konschubert wrote: post #69

Earlier quoted context omitted.

^ Exhibit A why using "believe" is a bad choice of words. Mathematical poofs are either correct or false. There is no middle ground.

Well.. there is. Middle ground being a very complex, but somehow convincing argument that no one can reasonably check. There was one of these cases in number theory some years ago, can't remember the details. Proofs can be only true or false, but accepting proofs is in the end a social process.

> Proofs can be only true or false

Yes.

The fact that we don't know the truth doesn't mean there isn't one.

Re: Show HN: I made a puzzle game that gently introduces my favorite math mysteries

#89

Post by ifdefdebug »

MCSP wrote: post #15
baruchel wrote: post #3

Hi, my two cents; you claim "Although mathematicians believe their proof is correct, it is too complex to verify without computer assistance", but I'm not sure "believe" is the correct verb since the proof has been formally verified (see for instance https://github.com/coq-community/fourcolor for a formal verification in Coq). I understand that you want to emphasize the fact that no human can understand the proof wit…

Good point! I'll try to think about a better way to phrase this (happy to hear suggestions)

s/believe/know
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