Math Post the Minus First
...I was thinking of this great proof of something you already know yesterday, and I wish I could tell you...
Most people have some idea what money is. Most people can identify what an interest rate is, and most people have an understanding of what it means to go into debt.
Most people have at least a vague notion of DNA -- it's that stuff that makes you a person rather than a chimpanzee, or vice versa. Most people know what an animal is, and most people know about cells.
Most people know about molecules. Most people (with kitchens) have worked with acids and bases, and most people understand that cold things freeze.
Most people have absolutely no idea about groups. Most people have no idea about varieties, and most people have no idea about manifolds, rings, sheaves, or differential equations.
Such are the plagues of the mathematician. When most other scientists talk about their profession, understandings of some of the basics can be assumed of anybody asking "what do you do?" We lose pretty hard on this score; even if I say "prime number," a notion hardly more complicated than "number" itself, I already lose half my listeners. Hrmph.
So, between now and (forever, probably), I'm going to try to write the gentlest possible introduction to advanced mathematics, particularly focusing on my advanced mathematics because I'm horribly egocentric. I'd love to eventually be able to post about the interesting things I hear in talks or classes or read in papers, but before I can even think about doing that I have to give a million back definitions and bend every reader's mind in at least twelve ways to make them care. I'm trying anyhow.
A few ground rules: I'm not requiring background, per se, but I am asking that readers be willing to think, since even the (relatively florid) stuff I want to write will require pondering to understand. I'll start with warmups, but I want to get to genuine stuff soon. I'll try to avoid proofs, much to my chagrin, because I recognize that most readers care much less than I do about what's really happening and really want to just get a vague idea of what's going on; also it cuts down on the writing to only give that vague idea. I'll try to sneak in some stuff about philosophy and methodology (since induction, for instance, really is interesting in its own right) in interludes here and there, but mostly I'll try to leave well enough alone. I'll ask that you be comfortable with symbols and equations, but I'll try to keep the optimal balance -- symbols only when they make things clearer. Lastly, I'll try to build in complexity, starting with the familiar so that reading the archives will get you ready for the exotic, but I want to start almost agonizingly simple and I therefore have to ask that you don't take my tone as too condescending. I'll feel really stupid explaining prime numbers, and many readers, I don't doubt, will feel condescended to, but if I don't start the discipline of talking slow with small words now I'll just start launching into discussions of positive-definite nodegenerate symmetric bilinear forms assuming everybody knows what I'm talking about, which would distinctly be a bad thing.
Well now. Time to commit before it gets too late. First, a brief interlude on symbols and logic; then, the beginnings of number theory.
This will be interesting...
PS: For the record, I'm aiming for Monday-Wednesday-Friday as a posting schedule until I'm remotely up to date. Also for the record, the proof was of why casting out nines works. It's really cute, and I do genuinely wish I could tell you.
Edit: I'm not so clever with the date-time settings sometimes -- this is supposed to be recent, not old. Sorry.
Most people have some idea what money is. Most people can identify what an interest rate is, and most people have an understanding of what it means to go into debt.
Most people have at least a vague notion of DNA -- it's that stuff that makes you a person rather than a chimpanzee, or vice versa. Most people know what an animal is, and most people know about cells.
Most people know about molecules. Most people (with kitchens) have worked with acids and bases, and most people understand that cold things freeze.
Most people have absolutely no idea about groups. Most people have no idea about varieties, and most people have no idea about manifolds, rings, sheaves, or differential equations.
Such are the plagues of the mathematician. When most other scientists talk about their profession, understandings of some of the basics can be assumed of anybody asking "what do you do?" We lose pretty hard on this score; even if I say "prime number," a notion hardly more complicated than "number" itself, I already lose half my listeners. Hrmph.
So, between now and (forever, probably), I'm going to try to write the gentlest possible introduction to advanced mathematics, particularly focusing on my advanced mathematics because I'm horribly egocentric. I'd love to eventually be able to post about the interesting things I hear in talks or classes or read in papers, but before I can even think about doing that I have to give a million back definitions and bend every reader's mind in at least twelve ways to make them care. I'm trying anyhow.
A few ground rules: I'm not requiring background, per se, but I am asking that readers be willing to think, since even the (relatively florid) stuff I want to write will require pondering to understand. I'll start with warmups, but I want to get to genuine stuff soon. I'll try to avoid proofs, much to my chagrin, because I recognize that most readers care much less than I do about what's really happening and really want to just get a vague idea of what's going on; also it cuts down on the writing to only give that vague idea. I'll try to sneak in some stuff about philosophy and methodology (since induction, for instance, really is interesting in its own right) in interludes here and there, but mostly I'll try to leave well enough alone. I'll ask that you be comfortable with symbols and equations, but I'll try to keep the optimal balance -- symbols only when they make things clearer. Lastly, I'll try to build in complexity, starting with the familiar so that reading the archives will get you ready for the exotic, but I want to start almost agonizingly simple and I therefore have to ask that you don't take my tone as too condescending. I'll feel really stupid explaining prime numbers, and many readers, I don't doubt, will feel condescended to, but if I don't start the discipline of talking slow with small words now I'll just start launching into discussions of positive-definite nodegenerate symmetric bilinear forms assuming everybody knows what I'm talking about, which would distinctly be a bad thing.
Well now. Time to commit before it gets too late. First, a brief interlude on symbols and logic; then, the beginnings of number theory.
This will be interesting...
PS: For the record, I'm aiming for Monday-Wednesday-Friday as a posting schedule until I'm remotely up to date. Also for the record, the proof was of why casting out nines works. It's really cute, and I do genuinely wish I could tell you.
Edit: I'm not so clever with the date-time settings sometimes -- this is supposed to be recent, not old. Sorry.
posted by Dennis at 12:13 AM
1 Comments:
While I am not a mathematician (*sigh*), I am interested in math and have often encountered the same frustration when answering the question "so, what is that math book you are reading about?". So I am interested in seeing how your explanations go.
On a related note, this sounds similar to what Penrose tried to do with modern physics in his new book "The Road to Reality". The first half of the book is basically math background. I think he writes on too high of a level for the average "educated layperson", but I enjoyed much of his exposition. I would be curious what others think
Post a Comment
<< Home