Mathematicians are chronically lost and confused • Hacker News Board

Re: Mathematicians are chronically lost and confused

#181

Post by broolstoryco » Thu, Mar 06, 2014, 11:10 AM UTC

nly wrote: post #20

Secondary math education, for me in the UK, didn't deal with anything outside of elementary algebra, Euclidean geometry, some statistics, and relatively simple calculus. Nobody talked to us about imaginary or complex numbers, or bayes theorem, decision theory, or non-trivial mechanics problems until I was in college (age 16+). Nobody mentioned matrices, broader number theory or discrete transforms until I was in univ…

> group theory right now to help with my understanding of crypto

Im also trying to understand crypto better, from a mathematical perspective. Apart from group theory, what else should I have an understanding of before going further? Do you have any resources that you would recommend?

Re: Mathematicians are chronically lost and confused

#182

Post by edtechdev » Thu, Mar 06, 2014, 11:33 AM UTC

"If you’re going to get anywhere in learning mathematics, you need to learn to be comfortable not understanding something."

That's true of everything. It's fear and anxiety that prevents a lot of people from learning and trying new things. I keep trying to tell students or family members when they are learning to do stuff on the computer, just right click everything, just google anything you can think of, don't worry about it being perfect, don't worry about breaking anything. You have to hold back showing them the "answers" or else they become dependent.

Re: Mathematicians are chronically lost and confused

#183

Post by gchpaco » Thu, Mar 06, 2014, 11:59 AM UTC

vidarh wrote: post #80

nly wrote: post #20

Secondary math education, for me in the UK, didn't deal with anything outside of elementary algebra, Euclidean geometry, some statistics, and relatively simple calculus. Nobody talked to us about imaginary or complex numbers, or bayes theorem, decision theory, or non-trivial mechanics problems until I was in college (age 16+). Nobody mentioned matrices, broader number theory or discrete transforms until I was in univ…

> I loath academic papers. Often I find I spend days or weeks deciphering mathematics in compsci papers only to find the underlying concept is intuitive and plain, but you're forced to learn it bottom up, constructing the authors original genius from the cryptic scrawlings they left in their paper... I systematically ignore maths in CS papers. If the concept isn't described with code or pseudo-code at least, I will l…

Some of the papers I have written actually made the problem simpler with math--XML Schema being notoriously impenetrable, for example, and XACML not being much better.

Re: Mathematicians are chronically lost and confused

#184

Post by twobits » Thu, Mar 06, 2014, 12:03 PM UTC

dwaltrip wrote: post #133

egdelwonk wrote: post #32

What's the best way to relearn math?

Focus as much as possible on the underlying concepts from any math topic and how they connect to other concepts. Try to boil these concepts down to the most simple, clear form that makes sense to you. Test your boiled down conceptual understanding by applying it to related exercises/problems you haven't tried before and seeing what happens. For each sub-topic, most math books give you the tools first and then teach y…

'discern the "how" and the "why" as opposed to the "what". Math is all about "how" and the "why".'

Could you pls expand on the diff between the "how" and the "what"?

Re: Mathematicians are chronically lost and confused

#185

Post by chalst » Thu, Mar 06, 2014, 12:24 PM UTC

j2kun wrote: post #167

chalst wrote: post #26

Earlier quoted context omitted.

Well put; a little quibble: these are the two notions of infinity that most interest set theorists, but there are many other notions of infinity in mathematics, e.g., 1. Representation of geometric entities "at infinity" in, e.g., the point at infinity from the projective sphere that allows straight lines to be treated as circles; 2. Infinitesimals; 3. Game-theoretic constructions of infinite numbers, e.g., in Conway…

A quibble of my own: a lot of the "infinity" constructions in mathematics only use infinity as a name. Projective geometry (1) is a good example of that. The formalization doesn't actually appeal to any sort of infinite quantities.

Projective geometry: even in the simple case I outlined, you have lines being circles of infinite diameter. That infinity is just an additional closure point on the plane for shapes (and you can think of the similar projective line providing the complementary notion of displacement we can use to measure the diameter of infinite circles) doesn't stop the geometry from representing shapes with infinite attributes.

It is the case that all of this can be finitely represented. But this is true of a quite large part of large cardinal set theory as well, which can be represented in constructive type theory - mathematicians make it their business to transform the infinitary into the finitary.

Re: Mathematicians are chronically lost and confused

#186

Post by eli_gottlieb » Thu, Mar 06, 2014, 2:22 PM UTC

makmanalp wrote: post #55

nly wrote: post #20

Secondary math education, for me in the UK, didn't deal with anything outside of elementary algebra, Euclidean geometry, some statistics, and relatively simple calculus. Nobody talked to us about imaginary or complex numbers, or bayes theorem, decision theory, or non-trivial mechanics problems until I was in college (age 16+). Nobody mentioned matrices, broader number theory or discrete transforms until I was in univ…

I've argued the same with a mathematician friend of mine. I hate academic papers because of their seemingly convoluted and backwards way of explaining things. His answer was that papers were not made to convey thoughts to laymen, they were made to communicate facts and proofs with as little ambiguity as possible, optimized for reading by other mathematicians. It's meant to be high bandwidth (hence the terse style and…

In academia, there's some notion that eventually a teaching professor will consolidate many papers into one textbook, which will actually convey the material clearly for those without a graduate-level maths education in the specific subfield.

Occasionally, this even happens.

Re: Mathematicians are chronically lost and confused

#187

Post by cmsd2 » Thu, Mar 06, 2014, 2:26 PM UTC

ska wrote: post #149

pygy_ wrote: post #65

Earlier quoted context omitted.

> The purpose of most academic papers is not to explain (let alone teach!) ideas in an intuitive manner, but rather to express them in formal, correct, unambiguous terms -- that is, to make them as accurate and critique-proof as possible for publication in some journal. Their intended audience is subject matter experts. Their purpose really is to let the authors show off how smart they are, impress their peers, and a…

I assume you mean the "reduction" process. The "redaction" process is an important part of the scientific process! I know you were being sarcastic, but I think you are also being a bit unfair. Publication is necessary these days at perhaps an unfortunate rate, I agree. However at least most research mathematicians publish largely to share ideas. After all, that's the best part of the job. Certainly this is true of th…

Could be mr pygy_ isn't english..

e.g. redaction in german means editing

Re: Mathematicians are chronically lost and confused

#188

Post by j2kun » Thu, Mar 06, 2014, 3:17 PM UTC

nnq wrote: post #180

j2kun wrote: post #172

Earlier quoted context omitted.

This post ignores the central driving force behind why mathematicians do mathematics: mathematics was created by humans for their own pleasure. It's a coincidence that they find such useful applications in the real world, and mathematicians mostly don't care (it's like a bonus if someone finds a nice application of your work, and maybe it provides you more grant money). In this light, why would any mathematician want…

I understand what you say. But my interest is actually into AI, so the same way you find pleasure in creating and understanding interesting proofs, I find pleasure in trying to think about how the human mind works and how to make artificial forms of intelligence that share the properties of human mind but not the damn limitations of the "biological hardware" and of mortality. And I also think that in fields like AI "…

This is the right attitude; more power to you!

Just don't try to justify it by its "benefits" for mathematicians.

Re: Mathematicians are chronically lost and confused

#189

Post by Shamanmuni » Thu, Mar 06, 2014, 4:02 PM UTC

ColinWright wrote: post #160

johnbm wrote: post #138

Earlier quoted context omitted.

Nah, Monty Hall is trivial to demonstrate. Just do it with 100 doors instead of 3. Problem solved, intuition remains.

I never understood this assertion. Most people I explain it to in this way still think it's 50:50 because you only have two doors left.

That's odd, I found the 100 doors example is the most efective way of explaining it.

It's easy, pick a door, then the host discards 98 doors in which the car isn't. Do they still think that the probability of the other door left is the same than the one they picked? I want to play gambling games with them!

Re: Mathematicians are chronically lost and confused

#190

Post by abecedarius » Thu, Mar 06, 2014, 6:05 PM UTC

cs702 wrote: post #22

nly wrote: post #20

Secondary math education, for me in the UK, didn't deal with anything outside of elementary algebra, Euclidean geometry, some statistics, and relatively simple calculus. Nobody talked to us about imaginary or complex numbers, or bayes theorem, decision theory, or non-trivial mechanics problems until I was in college (age 16+). Nobody mentioned matrices, broader number theory or discrete transforms until I was in univ…

Often I find I spend days or weeks deciphering mathematics in compsci papers only to find the underlying concept is intuitive and plain, but you're forced to learn it bottom up, constructing the authors original genius from the cryptic scrawlings they left in their paper... and you realise a couple of block diagrams and a few short paragraphs could have made the process a lot less frustrating. This is SO TRUE. The sa…

formal, correct, unambiguous terms

Unambiguous? I wish! The notation in most fields is way more ambiguous than code; you're expected to resolve the ambiguity by the norms of whatever research community it's for. Code isn't necessarily clear, but at least all the information is there to be decoded.

An example of trying to do better: http://groups.csail.mit.edu/mac/users/gjs/6946/sicm-html/boo...