<story><title>Math For Programmers </title><url>http://steve-yegge.blogspot.com/2006/03/math-for-programmers.html</url></story><parent_chain><item><author>anonymoushn</author><text>There&apos;s actually a place slightly beyond &quot;able to do it on paper&quot; at which you grok the maths so well that you can apply it in non-obvious situations without any conscious effort.  I&apos;m not sure how to get there in general, but I&apos;ve noticed that I&apos;m more likely to be able to do this for subjects that I learned in proof-heavy classes.</text></item><item><author>nagrom</author><text>I think that in this article Steve discounts the effect of actually doing the math for yourself. It&apos;s comparatively easy to read about something and think that you&apos;ve understood it. It&apos;s another thing entirely to be able to do that math on paper and get the &apos;correct&apos; answer without needing help.</text></item></parent_chain><comment><author>dagw</author><text>I have a Masters in math and the applying things in non-obvious situations is one of the things that I really gained from it.  Several times I&apos;ve been in situations where someone is struggling with a problem, and where I can quickly spot a simple mathematical approach to solve it.  Many times the mathematics itself is quite simple advanced high school or early college stuff, stuff the person struggling with problem has also studied.&lt;p&gt;The difference is that to them linear algebra (for example) is something abstract you use to solve linear algebra problems, while to someone with a more deep and solid understanding of math, linear algebra is a simple and general tool that can be applied in all manners of situations.</text></comment>
<story><title>Math For Programmers </title><url>http://steve-yegge.blogspot.com/2006/03/math-for-programmers.html</url></story><parent_chain><item><author>anonymoushn</author><text>There&apos;s actually a place slightly beyond &quot;able to do it on paper&quot; at which you grok the maths so well that you can apply it in non-obvious situations without any conscious effort.  I&apos;m not sure how to get there in general, but I&apos;ve noticed that I&apos;m more likely to be able to do this for subjects that I learned in proof-heavy classes.</text></item><item><author>nagrom</author><text>I think that in this article Steve discounts the effect of actually doing the math for yourself. It&apos;s comparatively easy to read about something and think that you&apos;ve understood it. It&apos;s another thing entirely to be able to do that math on paper and get the &apos;correct&apos; answer without needing help.</text></item></parent_chain><comment><author>Deestan</author><text>One of the school math topics that I have made us of a lot is function transformation and translation.&lt;p&gt;Being able to see things like &quot;what I really need here is &lt;i&gt;this&lt;/i&gt; part of a sine curve, stretched along the X axis, compressed along the Y axis, and moved up into the positive&quot;, and then write a simple one-liner to do slideshow animation, has proven useful again and again.&lt;p&gt;To be honest, I didn&apos;t really understand the point of it during class, and actually failed that part of the exam.  A few years later when I needed it, it just popped out of my brain attic and made sense.</text></comment>