Olli Toivanen's mathematics of drowsiness


Based on my vast professional experience as a mathematician, I've tried to write some useful tips for mathematicians and mathematics students:

Mathematics

Academically I have an abitur from 2001, a math major, physics and IT minor M.Sc. from 2006, a math Licentiate from 2008, and a math Ph.D. from the August of 2013.

The M.Sc. thesis is titled “De Giorgin metodi” (The De Giorgi method); the Licentiate is “Varioivan eksponentin kvasisuperminimoijat” (Variable exponent quasisuperminimizers), and the Ph.D. is “Dark Rector: The Story of the Vivian Girls, in What is known as the Realms of the Unreal, of the Glandeco-Angelinnian War Storm, Caused by the Child Slave Rebellion”.

Oh wait no, that was that one dream I once had. “Minimizers and superminimizers of variational integrals with non-standard growth”, that's what it is.

I think mathematics is important to me, you and all of humankind. Mathematics might not be necessary for a happy life, but it is sufficient; and learning to think mathematically, exactly, carefully, is one of the best ways to not be a damn fool, and avoiding damn-foolishness is generally a spot of life improvement. For this increased acuity, the important part is not what you do doing mathematics, but how you do it.

Mathematics is exercise for those mental muscles that let you down when your poor chimp brain fails; and don't feel bad about that; I have a poor chimp brain too; that is what being human is. The things our natural chimpness cannot quite grasp include such matters as probability, logic, complexity and consequences, the very improbable and small, and the very slowly accumulating and the difficult-to-visualize.

Your average mammal isn't born with any particular proficiency with any of these, and they aren't learned automatically and automagically, as shown by the continuing popularity of astrology, pyramid schemes and homeopathy; and mathematics is one exercise which gives work to these unnatural and useful muscles. Mathematics is the study of structure, any structure in its most general and abstract form; and if you don't look for the structure of real life, real life will kick you in the head.

Not to mention mathematics has that whole “cold and austere beauty like that of sculpture” thing going for it.

Also: this is how you over-rigorously calculate two times three.

\begin{align*} & 2*3 \\ = & 2*2' \\ = & 2*2 + 2 \\ = & 2*1' + 2 \\ = & 2*1 + 2 + 2 \\ = & 2 + 2 + 2 \\ = & 2 + 1' + 2 \\ = & (2 + 1)' + 2 \\ = & (2')' + 2 \\ = & 3' + 2 \\ = & 4 + 2 \\ = & 4 + 1' \\ = & (4 + 1)' \\ = & (4')' \\ = & 5' \\ = & 6 \end{align*}

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