nail art journal image
OK
I look at the abstract math being published in journals by professors and graduate students and wonder how it does anyone any good, or ever will. I am an engineer and have a pretty good understanding of math, especially what is practical and useful. I don't ever see any use for this stuff they are publishing.
Answer
When Gauss first noticed the intrinsicness of curvature for surfaces in three dimensional space, he had no idea that his ideas would lead Poincare and Weyl to revolutionize the way people thought about geometry. When Poincare and Weyl developed the abstract tools of topology and differential geometry, they had no idea that Einstein would (with the help of Hilbert and other mathematicians) use their ideas to revolutionize the foundations of classical mechanics. And when Einstein developed his general theory of relativity he had no idea that one day NASA scientists would notice that the curvature of space-time induced by the Earth's gravity as predicted by his theory accounted precisely for the problems faced by early versions of what we now know as GPS systems.
So my first point is that many mathematicians (as well as scientists and engineers of all disciplines) have no idea if their work will one day have "practical applications", and that should be OK with you. To demand that every scientist have a specific gadget in mind that will one day fit in our living room is to require one person to have the vision to see beyond the next two or three revolutions in human knowledge. The mathematical community has a pretty effective agreement with the rest of the scientific community: let the mathematicians decide what is important, and the scientists who make the great breakthroughs of tomorrow will probably have the right conceptual tools for understanding and quantifying them just waiting there to be used. Of course, given how much mathematics has infiltrated the cutting edge of physics, biology, engineering, economics, and most other sciences, it is not unreasonable to expect many of the breakthroughs of tomorrow to be motivated by mathematical developments.
My second point is that your understanding of mathematics is probably nowhere near good enough to justify the statement that you "don't ever see any use for this stuff". And I say that without even a trace of arrogance: it is impossible for your understanding of mathematics to be that good. Are you an expert in partial differential equations? If not, then you are ill-equipped to understand the state of the art in fluid modeling, thermodynamics, or optics. Are you an expert in algebraic geometry? If not, then there is little chance that you will understand the latest in cryptography or theoretical physics. Are you an expert in algebraic topology? If not, then the most recent developments involving the protein folding problem, network theory, economics, and quantum field theory will elude you. I could go on and on, but you get the idea: people really are doing something with this stuff. That doesn't mean it will be possible to justify every mathscinet article you pull up according to the standards of practicality, but then again if we knew exactly what is useful and what is not then we wouldn't call it "research".
My final point is that it is simply the nature of human curiosity that not every idea people come up with is going to have a particular, identifiable "use". Mathematicians are not gods that can immediately hone in on the right way to think about a problem - sometimes mathematical research starts somewhere interesting but then meanders off into a place that in hindsight wasn't as relevant as it seemed. When mathematicians start to zero in on a useful pattern or an interesting formalism but can't nail down exactly what is going on, often it is useful to sort through some obscure counterexamples that hint at how to proceed. Mathematical research is an organic, creative process that only works when nothing is off-limits, as long as it can be proven.
When Gauss first noticed the intrinsicness of curvature for surfaces in three dimensional space, he had no idea that his ideas would lead Poincare and Weyl to revolutionize the way people thought about geometry. When Poincare and Weyl developed the abstract tools of topology and differential geometry, they had no idea that Einstein would (with the help of Hilbert and other mathematicians) use their ideas to revolutionize the foundations of classical mechanics. And when Einstein developed his general theory of relativity he had no idea that one day NASA scientists would notice that the curvature of space-time induced by the Earth's gravity as predicted by his theory accounted precisely for the problems faced by early versions of what we now know as GPS systems.
So my first point is that many mathematicians (as well as scientists and engineers of all disciplines) have no idea if their work will one day have "practical applications", and that should be OK with you. To demand that every scientist have a specific gadget in mind that will one day fit in our living room is to require one person to have the vision to see beyond the next two or three revolutions in human knowledge. The mathematical community has a pretty effective agreement with the rest of the scientific community: let the mathematicians decide what is important, and the scientists who make the great breakthroughs of tomorrow will probably have the right conceptual tools for understanding and quantifying them just waiting there to be used. Of course, given how much mathematics has infiltrated the cutting edge of physics, biology, engineering, economics, and most other sciences, it is not unreasonable to expect many of the breakthroughs of tomorrow to be motivated by mathematical developments.
My second point is that your understanding of mathematics is probably nowhere near good enough to justify the statement that you "don't ever see any use for this stuff". And I say that without even a trace of arrogance: it is impossible for your understanding of mathematics to be that good. Are you an expert in partial differential equations? If not, then you are ill-equipped to understand the state of the art in fluid modeling, thermodynamics, or optics. Are you an expert in algebraic geometry? If not, then there is little chance that you will understand the latest in cryptography or theoretical physics. Are you an expert in algebraic topology? If not, then the most recent developments involving the protein folding problem, network theory, economics, and quantum field theory will elude you. I could go on and on, but you get the idea: people really are doing something with this stuff. That doesn't mean it will be possible to justify every mathscinet article you pull up according to the standards of practicality, but then again if we knew exactly what is useful and what is not then we wouldn't call it "research".
My final point is that it is simply the nature of human curiosity that not every idea people come up with is going to have a particular, identifiable "use". Mathematicians are not gods that can immediately hone in on the right way to think about a problem - sometimes mathematical research starts somewhere interesting but then meanders off into a place that in hindsight wasn't as relevant as it seemed. When mathematicians start to zero in on a useful pattern or an interesting formalism but can't nail down exactly what is going on, often it is useful to sort through some obscure counterexamples that hint at how to proceed. Mathematical research is an organic, creative process that only works when nothing is off-limits, as long as it can be proven.
what should i use and write in my noteboook?
cici
okey i got tons of notebooks! i love notebooks! xD
this is what i got so far:
journal
diary
art journal
graditude journal
random journal
summer journal
smash book
junk journal
notes and ideas book
lyrics book
clebrity book
thoughts book
and a stories book
Okey i know that really narrows it down to like nothing LOL but i jut got this black compisation book, and i decorated it with nail polish, but inside its all blank! i want a unique idea please help i'll rate you 5 stars! xD
Answer
Dang! You've been doing some major writing. True it does narrow it down to almost nothing. Lol. But let me brainstorm for a sec....................... Hm, you coud:
1. Jot down your dreams down when you wake up.
2. Find a bunch of pictures of yourself growing up and create a journal about different parts of your life or you growing up. You can write about what you remember, too.
3. Make a collage book, where you throw in a bunch of pictures and drawings to create a random page. It can be themed, random, or expressive (examples: sad, angry, happy, cheery, sorrowful).
4. Have you ever tried writing poems? You like to write lyrics and similar things to that so you might like to write a book of poems? I'm guessing?
5. Fashion journal. I think this one is pretty self-explanatory. :D If not, you can just do whatever you want with outfits and stuff. Draw them, write about what you think of fashion these days... The pages are yours to fill.
Plus, you could always use journals for the same purpose. Writing down random thoughts, notes, everything and anything that you feel like jotting down is always an amazing idea. I think it's awesome that you write in journals so much! It's actually really good for you for several reasons. One of them being that you release any emotions, fears or worries your holding onto. Releasing stress. Which helps in almost everything.
If you get time could you answer mine please? Thank you so much if you do! Here's the link:
http://answers.yahoo.com/question/index;_ylt=ApPldPkRT0rLapLFkeLxfwnsy6IX;_ylv=3?qid=20120717182154AAzHave
Bye! :)
Dang! You've been doing some major writing. True it does narrow it down to almost nothing. Lol. But let me brainstorm for a sec....................... Hm, you coud:
1. Jot down your dreams down when you wake up.
2. Find a bunch of pictures of yourself growing up and create a journal about different parts of your life or you growing up. You can write about what you remember, too.
3. Make a collage book, where you throw in a bunch of pictures and drawings to create a random page. It can be themed, random, or expressive (examples: sad, angry, happy, cheery, sorrowful).
4. Have you ever tried writing poems? You like to write lyrics and similar things to that so you might like to write a book of poems? I'm guessing?
5. Fashion journal. I think this one is pretty self-explanatory. :D If not, you can just do whatever you want with outfits and stuff. Draw them, write about what you think of fashion these days... The pages are yours to fill.
Plus, you could always use journals for the same purpose. Writing down random thoughts, notes, everything and anything that you feel like jotting down is always an amazing idea. I think it's awesome that you write in journals so much! It's actually really good for you for several reasons. One of them being that you release any emotions, fears or worries your holding onto. Releasing stress. Which helps in almost everything.
If you get time could you answer mine please? Thank you so much if you do! Here's the link:
http://answers.yahoo.com/question/index;_ylt=ApPldPkRT0rLapLFkeLxfwnsy6IX;_ylv=3?qid=20120717182154AAzHave
Bye! :)
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