6 ms·

World of Mathematics

322 points by msvan 13y ago

hcarvalhoalves 13y ago
Excellent content and presentation. Happy to see interactive formulas in the book, like proposed by Brett Victor [1]. [1] http://worrydream.com http://worrydream.com
solarmist 13y ago
Wow, this site is slow. I thought it was broken in my browser because there was no content for about 20 seconds.
TrainedMonkey 13y ago
Took almost a minute to load. At first I thought HN effect, but then I realized it preloaded a lot more than just the front page. Edit: I played with it for a bit, and wow. This is so cool. All the cool technology they use meshes seamlessly with content. Added this to my special bookmarks folder along with Statistics Done Wrong and Experimental Design (Norvig).
- rurounijones 13y ago
  They are going to lose a lot of people with load-times like that. Make the landing page quick and static and loads the minimum. After you have the visitors attention with the information on that page THEN the next page can take longer (Give them a warning) The bounce rate on this site must be incredible.
bridger 13y ago
This is great. The animations and interactive content is greatly needed in mathematics. One of my favorite parts of math is puzzling over problems and coming up with solutions myself (even if the solution has been known for thousands of years prior.) I wish this book would set up problems I could puzzle over, rather than just give me the solutions before I knew there was a problem!
auggierose 13y ago
Awesome.
pcmonk 13y ago
This is awesome. Mathematics struggles a lot from bad presentation, but this does an excellent job of taking well-known and interesting problems and explaining them (and their solution). Problem solving is a lot more fun than simply reading mathematical truths. For the areas of math that I know well, the content is exactly what I would expect -- i.e. it's exactly what I would say to my non-math friends if they asked me what I was doing in, for example, my graph theory class.
- rafcavallaro 13y ago
  On the contrary - this fits right in with all the other dreadful presentations of math - it takes so long to load it appears as though the site is off line. It's almost as if the author was at pains to confirm the trope that technical people have no social skills and are hopeless at presenting information to others.
Edmond 13y ago
awesome but you absolutely have to fix the performance.
deleted 13y ago
[deleted]
kimonos 13y ago
Cool! Wish it could load faster..
adriancooney 13y ago
I'd love to contribute to a project like this. Visualizing mathematical formulas and operations has always been a great pastime of mine because it really exercises the mind. The colors in this are absolutely fantastic. It's an incredibly well polished product save the lack of content. I can't wait to see this evolve.
- dave809 13y ago
  Exactly my thought, This kind of math visualization has been on my mind ever since watching the talk "Media for Thinking the Unthinkable"[0] by Bret Victor. I would totally be into contributing to this project [0] http://vimeo.com/67076984 http://vimeo.com/67076984
msvan 13y ago
"Everybody should understand concepts like prime numbers, graph theory or differential equations. They are of fundamental importance in technology and for understanding of the universe we live in, and they are incredible exciting and beautiful. Mathematics is an essential part of our culture, just like Mozart and Shakespeare."[1] This is the key point, I think. Most of my non-technical friends have only vague ideas or know nothing about these topics. Actually working with differential equations might be hard, but most people should at least have an understanding of their use cases and why they are important or beautiful. And this way of presenting math is of course much more compelling than any high school math book I ever saw. [1] http://mathigon.org/about http://mathigon.org/about
- interstitial 13y ago
  "Most of my non-technical friends have only vague ideas or know nothing about these topics." -- and yet, if they are like my friends, they probably have no feelings of regret, or sense of ignorance. They probably feel more qualified to speak about things like Obamacare and evil Profit-mongering Insurance Companies than someone who does know mathematics beyond the sixth grade.
  - yetanotherphd 13y ago
    >They probably feel more qualified to speak about things like Obamacare and evil Profit-mongering Insurance Companies than someone who does know mathematics beyond the sixth grade. I think basic economics is just as important to understanding these topics than mathematics. I hear very naive statement about economics from people who know enough mathematics to easily understand the economics, if they had studied it.
    - alandarev 13y ago
      Exactly that makes me sad too. There are so many newbie friendly tech-oriented sites. Particularly, because the authors of such sites are geeks themselves. Do not get me wrong, that is great that technology, programming, science is so easy to study now. What I wish is similar quality resources being available in other topics, I am bad with: economy, laws, business, psychology... I am placing my bets on these topics being in high demand. Yet it takes a geek interested in technology to be also interested in unrelated subjects. E: grammar.
jrells 13y ago
Most of these concepts are things I try to squeeze in for my Calculus students when we have extra time. If I got to choose the curriculum, this would all be standard. Looks beautiful, wish it would load well.
mililani 13y ago
I'm thinking of switching majors. I'm currently pursuing a masters in occupational therapy, but after a semester, I'm realizing it is just not for me. I did my undergrad in math and chemistry, and I've always regretted not doing at least a masters degree in math. Anyways, anyone else here a math guy? I've been out of math for almost 15 years. I'm kind of scared about going to grad school for math.
- nested 13y ago
  Sounds scary. You know what sounds beautiful though? The idea of you working your ass off and completing it. That part is on you though :)
- analog31 13y ago
  It's funny, but math is both occupational and therapeutic for me at the same time. Maybe you could weave those fields together!
- nocipher 13y ago
  Grad school for math can be a bit scary. If you've been out of math for that long, you'll need to do some review. All of the people I know in my graduate program are experts at at a large swathe of undergraduate topics: calculus, differential equations, linear algebra, combinatorics, probability, etc. And of course, they know even more about the topics they really like. If you have the chops to do it, though, math only gets more interesting from there: Real Analysis, Topology, Modern Algebra, Galois Theory, Knot Theory, Convex Geometry...
- runarberg 13y ago
  I stopped doing math when I was 18, and did an undergrad in psychology. Now I am doing a second undergrad, this time in math. Coming back in after a decade of absence wasn't difficult at all (but then again undergrad is somewhat easier then grad school), and it was definitely worth it.
millerm 13y ago
It's beautiful but unusable at the moment. Hopefully that will get worked out. I'd really like to experience it when it's ready.
deleted 13y ago
[deleted]
tokenadult 13y ago
I have recommended this site to my friends on a specialized Facebook group for discussion of interesting popular topics in mathematics. But I had to pass on the warning about load times. The author should use part of his mathematical acumen to figure out how to improve the page-loading on his site, and could well use some other tips on usability.
- pbhjpbhj 13y ago
  Looks like it needs lazy-loading - it's loading a lot of images that aren't on the splash page. Caching-wise I think having query strings on most of the background images is going to cause problems. Gets good PageSpeed and YSlow results however.
- Steuard 13y ago
  It's a beautifully done site, and I love the concept. I'm a little worried about it feeling fluffy in places: e.g. the monster group is a neat topic, but it's introduced in a fuzzy enough way that I'm not sure what people who don't already know the topic would take away from it (beyond a memory of the cute monster illustration, anyway). It was also odd to find prominent links (that didn't need to be links) to unwritten articles on a site that looks so polished otherwise. But if I may put in a final plea to these and all other web developers: I beg you, stop breaking the browser's "Back" button. I know you included your own lovely, visible back button in your page content, but I'm used to using the one in my browser and I make heavy use of keyboard or gesture shortcuts for it. You shouldn't have to break that to design a beautiful site!
barbs 13y ago
Brilliant. Reminds me of a similar site, though this one's more about demonstrating particular problems, rather than general concepts. http://www.cut-the-knot.org/ http://www.cut-the-knot.org/
ErikRogneby 13y ago
What if the same level of passion and creativity were put in to wikipedia as this?
- VLM 13y ago
  or mathworld.
runarberg 13y ago
Horizontal web layouts are awesome. A petty how difficult they are to achieve, this one does it well. It is beautiful, both the layout and the contents. The only thing, I wished down scroll would take me left, since thats the intuitive continuation direction.
playing_colours 13y ago
I am interested in learning Math, particularly for now Calculus, and combine it with programming execises, like the approach used in "The Haskell road to logic, maths and programming" book. I believe it may add more fun and helps really learn Math, not just get feeling of understanding concepts. I was also eager to try using Julia for exercises. Has anyone tried similar approach?
fractalsea 13y ago
Amazing site. Bookmarked, and I will go through it properly when I get the chance. As someone who has a poor grounding in many areas of maths in general, but deep understanding of specific areas, this resource seems excellent for catching up. I did not experience the slow loading times others did. Maybe the slowness was from the site experiencing a HN hit. Feedback: when I click the Facebook like button, it tries to fit a text box in the area assigned to the button, and simply does not fit.
vayarajesh 13y ago
Awesome
kenshiro_o 13y ago
Great site. I am sending the link to my younger sister who sometimes finds some math concepts too abstracts.
mihaifm 13y ago
any ideas on what frameworks/technologies were used to build this?
richtwiddle 13y ago
This seems very interesting
spot 13y ago
it's unfortunate that he is promoting the fractal image compression hoax. http://world.mathigon.org/Fractals http://world.mathigon.org/Fractals
- thomasfrank09 13y ago
  Correct me if I'm wrong, but isn't fractal image compression a real technique? However, I did read about a hoax in the 90's where there was a claim of a fractal compression technique that could reduce a file down to 1% of its original size, which turned out to just be a program that stored a reference to the file's location instead of an actual compressed file. http://en.wikipedia.org/wiki/Fractal_compression http://en.wikipedia.org/wiki/Fractal_compression http://arstechnica.com/civis/viewtopic.php?f=6&t=885055 http://arstechnica.com/civis/viewtopic.php?f=6&t=885055
  - spot 13y ago
    yes it's real but it's useless and unused. mentioning it without disclaimers is confusing. that wikipedia page was mostly written by one of the people behind the hoax.
    - Fr0styMatt 13y ago
      Do you have references? I'm curious; I've tried Googling but don't get a lot about the hoax part of it. Would be really interested in that story - the last I ever heard fractal compression being mentioned was to do with jpeg2000.
acqq 13y ago
It is shiny but unusable for me :( It would be if it would display the normal html pages instead of this dynamic window-inside thingies for which no normal controls like page down work the way they are expected to work. For some aspects, pity the energy invested. I'd still love to see a normal HTML site and then we can discuss the content, not just the shininess.
pavel_lishin 13y ago
Where can I submit corrections? There's a typo here: http://world.mathigon.org/Polygons_and_Polyhedra http://world.mathigon.org/Polygons_and_Polyhedra > But in the 1970s, the English mathematician Sir Roger Penrose (1931) made an amazing discover.* Should be "discovery", unless it's some weird semi-nounization like "ask" or "spend".
mcgwiz 13y ago
Awesome site! I'm no mathematician, but my gut tells me that advancing mathematics is not the clinical, uninspired, technical process that the "mathematician" stereotype implies. Instead, it seems to be fueled as much by creativity, imagination and mental flexibility as any purely artistic endeavor. Like art, it also requires significant discipline to master its technical underpinnings, is a gamble that pays off in years (if ever), and produces works that have the power to completely alter human understanding. So it's a bummer it has not developed a rebellious and disruptive image, the way pop art careers have. As a result, the field is not benefited by creative, motivated youth with ambitions of changing the world. One can only hope improvements in math education (more conceptual techniques, higher teacher pay, less corporate influence, etc) can make it more accessible and catalyze an eventual change in its perception.
mathgenius 13y ago
I had a look at the group theory page. This is definitely something that should be taught more in basic math so I was glad to see it there. But I must admit i was disappointed at the notation: yes it's colourful, but totally useless for doing calculations. And why use the plus sign for combining transformations? That seems a bit shortsighted.. John Conway's books are still much better than this somewhat chaotic webpage. It's super hard to present mathematical ideas, cool widgets are not enough.
milliams 13y ago
On this topic I heartily recommend the YouTube channel Numberphile (https://www.youtube.com/user/numberphile https://www.youtube.com/user/numberphile and http://www.numberphile.com/ http://www.numberphile.com/). Along with its sister channels Computerphile, Sixty Symbols etc., they're a great source of accessible, intelligent content.

322 points by msvan 13y ago

Excellent content and presentation. Happy to see interactive formulas in the book, like proposed by Brett Victor [1]. [1] http://worrydream.com http://worrydream.com

solarmist 13y ago

Wow, this site is slow. I thought it was broken in my browser because there was no content for about 20 seconds.

TrainedMonkey 13y ago

Took almost a minute to load. At first I thought HN effect, but then I realized it preloaded a lot more than just the front page. Edit: I played with it for a bit, and wow. This is so cool. All the cool technology they use meshes seamlessly with content. Added this to my special bookmarks folder along with Statistics Done Wrong and Experimental Design (Norvig).

rurounijones 13y ago
They are going to lose a lot of people with load-times like that. Make the landing page quick and static and loads the minimum. After you have the visitors attention with the information on that page THEN the next page can take longer (Give them a warning) The bounce rate on this site must be incredible.

bridger 13y ago

This is great. The animations and interactive content is greatly needed in mathematics. One of my favorite parts of math is puzzling over problems and coming up with solutions myself (even if the solution has been known for thousands of years prior.) I wish this book would set up problems I could puzzle over, rather than just give me the solutions before I knew there was a problem!

auggierose 13y ago

Awesome.

pcmonk 13y ago

This is awesome. Mathematics struggles a lot from bad presentation, but this does an excellent job of taking well-known and interesting problems and explaining them (and their solution). Problem solving is a lot more fun than simply reading mathematical truths. For the areas of math that I know well, the content is exactly what I would expect -- i.e. it's exactly what I would say to my non-math friends if they asked me what I was doing in, for example, my graph theory class.

rafcavallaro 13y ago
On the contrary - this fits right in with all the other dreadful presentations of math - it takes so long to load it appears as though the site is off line. It's almost as if the author was at pains to confirm the trope that technical people have no social skills and are hopeless at presenting information to others.

Edmond 13y ago

awesome but you absolutely have to fix the performance.

deleted 13y ago

[deleted]

kimonos 13y ago

Cool! Wish it could load faster..

adriancooney 13y ago

I'd love to contribute to a project like this. Visualizing mathematical formulas and operations has always been a great pastime of mine because it really exercises the mind. The colors in this are absolutely fantastic. It's an incredibly well polished product save the lack of content. I can't wait to see this evolve.

dave809 13y ago
Exactly my thought, This kind of math visualization has been on my mind ever since watching the talk "Media for Thinking the Unthinkable"[0] by Bret Victor. I would totally be into contributing to this project [0] http://vimeo.com/67076984 http://vimeo.com/67076984

msvan 13y ago

"Everybody should understand concepts like prime numbers, graph theory or differential equations. They are of fundamental importance in technology and for understanding of the universe we live in, and they are incredible exciting and beautiful. Mathematics is an essential part of our culture, just like Mozart and Shakespeare."[1] This is the key point, I think. Most of my non-technical friends have only vague ideas or know nothing about these topics. Actually working with differential equations might be hard, but most people should at least have an understanding of their use cases and why they are important or beautiful. And this way of presenting math is of course much more compelling than any high school math book I ever saw. [1] http://mathigon.org/about http://mathigon.org/about

interstitial 13y ago
"Most of my non-technical friends have only vague ideas or know nothing about these topics." -- and yet, if they are like my friends, they probably have no feelings of regret, or sense of ignorance. They probably feel more qualified to speak about things like Obamacare and evil Profit-mongering Insurance Companies than someone who does know mathematics beyond the sixth grade.
- yetanotherphd 13y ago
  >They probably feel more qualified to speak about things like Obamacare and evil Profit-mongering Insurance Companies than someone who does know mathematics beyond the sixth grade. I think basic economics is just as important to understanding these topics than mathematics. I hear very naive statement about economics from people who know enough mathematics to easily understand the economics, if they had studied it.
  - alandarev 13y ago
    Exactly that makes me sad too. There are so many newbie friendly tech-oriented sites. Particularly, because the authors of such sites are geeks themselves. Do not get me wrong, that is great that technology, programming, science is so easy to study now. What I wish is similar quality resources being available in other topics, I am bad with: economy, laws, business, psychology... I am placing my bets on these topics being in high demand. Yet it takes a geek interested in technology to be also interested in unrelated subjects. E: grammar.

jrells 13y ago

Most of these concepts are things I try to squeeze in for my Calculus students when we have extra time. If I got to choose the curriculum, this would all be standard. Looks beautiful, wish it would load well.

mililani 13y ago

I'm thinking of switching majors. I'm currently pursuing a masters in occupational therapy, but after a semester, I'm realizing it is just not for me. I did my undergrad in math and chemistry, and I've always regretted not doing at least a masters degree in math. Anyways, anyone else here a math guy? I've been out of math for almost 15 years. I'm kind of scared about going to grad school for math.

nested 13y ago
Sounds scary. You know what sounds beautiful though? The idea of you working your ass off and completing it. That part is on you though :)
analog31 13y ago
It's funny, but math is both occupational and therapeutic for me at the same time. Maybe you could weave those fields together!
nocipher 13y ago
Grad school for math can be a bit scary. If you've been out of math for that long, you'll need to do some review. All of the people I know in my graduate program are experts at at a large swathe of undergraduate topics: calculus, differential equations, linear algebra, combinatorics, probability, etc. And of course, they know even more about the topics they really like. If you have the chops to do it, though, math only gets more interesting from there: Real Analysis, Topology, Modern Algebra, Galois Theory, Knot Theory, Convex Geometry...
runarberg 13y ago
I stopped doing math when I was 18, and did an undergrad in psychology. Now I am doing a second undergrad, this time in math. Coming back in after a decade of absence wasn't difficult at all (but then again undergrad is somewhat easier then grad school), and it was definitely worth it.

millerm 13y ago

It's beautiful but unusable at the moment. Hopefully that will get worked out. I'd really like to experience it when it's ready.

deleted 13y ago

[deleted]

tokenadult 13y ago

I have recommended this site to my friends on a specialized Facebook group for discussion of interesting popular topics in mathematics. But I had to pass on the warning about load times. The author should use part of his mathematical acumen to figure out how to improve the page-loading on his site, and could well use some other tips on usability.

pbhjpbhj 13y ago
Looks like it needs lazy-loading - it's loading a lot of images that aren't on the splash page. Caching-wise I think having query strings on most of the background images is going to cause problems. Gets good PageSpeed and YSlow results however.
Steuard 13y ago
It's a beautifully done site, and I love the concept. I'm a little worried about it feeling fluffy in places: e.g. the monster group is a neat topic, but it's introduced in a fuzzy enough way that I'm not sure what people who don't already know the topic would take away from it (beyond a memory of the cute monster illustration, anyway). It was also odd to find prominent links (that didn't need to be links) to unwritten articles on a site that looks so polished otherwise. But if I may put in a final plea to these and all other web developers: I beg you, stop breaking the browser's "Back" button. I know you included your own lovely, visible back button in your page content, but I'm used to using the one in my browser and I make heavy use of keyboard or gesture shortcuts for it. You shouldn't have to break that to design a beautiful site!

barbs 13y ago

Brilliant. Reminds me of a similar site, though this one's more about demonstrating particular problems, rather than general concepts. http://www.cut-the-knot.org/ http://www.cut-the-knot.org/

ErikRogneby 13y ago

What if the same level of passion and creativity were put in to wikipedia as this?

VLM 13y ago
or mathworld.

runarberg 13y ago

Horizontal web layouts are awesome. A petty how difficult they are to achieve, this one does it well. It is beautiful, both the layout and the contents. The only thing, I wished down scroll would take me left, since thats the intuitive continuation direction.

playing_colours 13y ago

I am interested in learning Math, particularly for now Calculus, and combine it with programming execises, like the approach used in "The Haskell road to logic, maths and programming" book. I believe it may add more fun and helps really learn Math, not just get feeling of understanding concepts. I was also eager to try using Julia for exercises. Has anyone tried similar approach?

fractalsea 13y ago

Amazing site. Bookmarked, and I will go through it properly when I get the chance. As someone who has a poor grounding in many areas of maths in general, but deep understanding of specific areas, this resource seems excellent for catching up. I did not experience the slow loading times others did. Maybe the slowness was from the site experiencing a HN hit. Feedback: when I click the Facebook like button, it tries to fit a text box in the area assigned to the button, and simply does not fit.

vayarajesh 13y ago

Awesome

kenshiro_o 13y ago

Great site. I am sending the link to my younger sister who sometimes finds some math concepts too abstracts.

mihaifm 13y ago

any ideas on what frameworks/technologies were used to build this?

richtwiddle 13y ago

This seems very interesting

spot 13y ago

it's unfortunate that he is promoting the fractal image compression hoax. http://world.mathigon.org/Fractals http://world.mathigon.org/Fractals

thomasfrank09 13y ago
Correct me if I'm wrong, but isn't fractal image compression a real technique? However, I did read about a hoax in the 90's where there was a claim of a fractal compression technique that could reduce a file down to 1% of its original size, which turned out to just be a program that stored a reference to the file's location instead of an actual compressed file. http://en.wikipedia.org/wiki/Fractal_compression http://en.wikipedia.org/wiki/Fractal_compression http://arstechnica.com/civis/viewtopic.php?f=6&t=885055 http://arstechnica.com/civis/viewtopic.php?f=6&t=885055
- spot 13y ago
  yes it's real but it's useless and unused. mentioning it without disclaimers is confusing. that wikipedia page was mostly written by one of the people behind the hoax.
  - Fr0styMatt 13y ago
    Do you have references? I'm curious; I've tried Googling but don't get a lot about the hoax part of it. Would be really interested in that story - the last I ever heard fractal compression being mentioned was to do with jpeg2000.

acqq 13y ago

It is shiny but unusable for me :( It would be if it would display the normal html pages instead of this dynamic window-inside thingies for which no normal controls like page down work the way they are expected to work. For some aspects, pity the energy invested. I'd still love to see a normal HTML site and then we can discuss the content, not just the shininess.

pavel_lishin 13y ago

Where can I submit corrections? There's a typo here: http://world.mathigon.org/Polygons_and_Polyhedra http://world.mathigon.org/Polygons_and_Polyhedra > But in the 1970s, the English mathematician Sir Roger Penrose (1931) made an amazing discover.* Should be "discovery", unless it's some weird semi-nounization like "ask" or "spend".

mcgwiz 13y ago

Awesome site! I'm no mathematician, but my gut tells me that advancing mathematics is not the clinical, uninspired, technical process that the "mathematician" stereotype implies. Instead, it seems to be fueled as much by creativity, imagination and mental flexibility as any purely artistic endeavor. Like art, it also requires significant discipline to master its technical underpinnings, is a gamble that pays off in years (if ever), and produces works that have the power to completely alter human understanding. So it's a bummer it has not developed a rebellious and disruptive image, the way pop art careers have. As a result, the field is not benefited by creative, motivated youth with ambitions of changing the world. One can only hope improvements in math education (more conceptual techniques, higher teacher pay, less corporate influence, etc) can make it more accessible and catalyze an eventual change in its perception.

mathgenius 13y ago

I had a look at the group theory page. This is definitely something that should be taught more in basic math so I was glad to see it there. But I must admit i was disappointed at the notation: yes it's colourful, but totally useless for doing calculations. And why use the plus sign for combining transformations? That seems a bit shortsighted.. John Conway's books are still much better than this somewhat chaotic webpage. It's super hard to present mathematical ideas, cool widgets are not enough.

milliams 13y ago

On this topic I heartily recommend the YouTube channel Numberphile (https://www.youtube.com/user/numberphile https://www.youtube.com/user/numberphile and http://www.numberphile.com/ http://www.numberphile.com/). Along with its sister channels Computerphile, Sixty Symbols etc., they're a great source of accessible, intelligent content.