Maths notation is needlessly complex [video]
I really need to expand this into a blog post that has been brewing in my head for years, but my overall thesis is that notation is the least difficult part to learn in mathematics, yet because it&#x27;s the first part that is encountered, it is also the most derided one.<p>Sure, notation can be better, and maybe this triangle of power is a cute way to make it better. Notation changes and improves all the time, btw. Well, all the time in the mathematical scale of time, which is two or three millenia. In this scale, things like the Greek letter for the ratio of circumference to diameter are remarkably modern, merely 300 years old. Notation for linear algebra is even newer, all from the 20th century.<p>However, I don&#x27;t think better notation is where we need to focus most of our efforts in order to make our mathematics easier to understand. Logarithms and square roots are very basic things, and if keeping the mainstream notation for them straight is someone&#x27;s biggest problem, then there are far bigger things that are likely to be problematic to this individual. If you start reading, say, the following mathematical discussion of neural networks,<p><a href="http:&#x2F;&#x2F;neuralnetworksanddeeplearning.com&#x2F;chap1.html#eqtn7" rel="nofollow">http:&#x2F;&#x2F;neuralnetworksanddeeplearning.com&#x2F;chap1.html#eqtn7</a><p>you&#x27;re baffled because you don&#x27;t know what those symbols mean, there&#x27;s likely far deeper things that are unfamiliar, such as differentials, rate of change, derivatives, and the multivariable chain rule. A couple of days ago we had someone come to ##math in Freenode asking for help with this, and I tried, but the guy had never had any calculus training whatsoever. Normally going from no calculus to the multivariable chain rule as applied to differentials or as a best linear approximation takes at least three semesters in university, and I don&#x27;t think this path to enlightenment could be shortened much more.<p>I guess I am being very old school and reiterating that the royal road everyone&#x27;s been looking for for the past couple millenia just doesn&#x27;t exist.<p><a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Royal_Road#A_metaphorical_.E2.80.9CRoyal_Road.E2.80.9D_in_famous_quotations" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Royal_Road#A_metaphorical_.E2....</a>