In their article  Billy Grierson et al, took up a task of illustrating TRIZ 40 Principles with examples from chemistry. It could be interesting and useful, if only they remembered that "40 Principles" is short for "40 Principles of Technical Contradiction Elimination". As such, illustration of these principles should consist of examples of technical contradictions, in chemistry, and of demonstration, how the 40 Principles help to eliminate the contradictions. Since this crucial aspect of what the 40 Principles are about has been completely ignored by Billy Grierson et al, the task they took up was meaningless, useless and extremely easy: just to show that there is, in chemistry, something segmented, extracted, combined, nested, etc. Would anybody expect that thare is not?
Following the authors' approach, here is illustration of how the 40 Principles of TRIZ may be applied directly to mathematical problems:
1 Segmentation: Separation into smaller parts. Example: 2=1+1
2 Extraction: Take out or separate something. Example: 2-1=1
3 Local Quality: Different parts of an object carry out different functions. Example: 2+1=3
4 Asymmetry: Introduce, or increase the degree of, asymmetry. Example: 30=29+1
5 Combination (Consolidation). Example: 33=(29+1)+(2+1)
6 Universality: Use an object to perform several functions. Example: 11*(2+1)=11*2+11*1
7 Nesting: Putting one thing inside another. Example: 11*(2+1)=(11*2+11*1)
8 Counterweight: Compensate for the weight of an object. Example: 10001-9999=2
And so on.
Unlike Billy Grierson et al, I don't think that this list would help introduce TRIZ to mathematicians in terms they understand. The illustrations in  are equally worthless.
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