# How do mathematicians analogize / conceive concepts? Many ways. Here’s 7 ways (there’s surely more) of conceiving of “derivative”. 1, 5, 6, 7 ‘click’ with me, the others not much at all. 1) Is a standard growth calculation: (Current – Previous) / Previous. Extremely useful in business for sales. (it’s usually like ((current month – previous month) / previous month) * 100 for monthly, etc. 5) Growth can be thought of as volume increasing/decreasing or it can also be thought of as SPEED, again used a lot in financial things, although usually marketing stuff. “velocity of money” hype. 6) appeals to the pragmatist in me who deals with the perfectionist in me. “It’s an approximation. It’s not perfect. Mark it down and move ahead”. 7) My favorite. There’s probably going to be a zoom limit.

How do mathematicians analogize / conceive concepts? Many ways. Here’s 7 ways (there’s surely more) of conceiving of “derivative”. 1, 5, 6, 7 ‘click’ with me, the others not much at all.

7) My favorite. There’s probably going to be a zoom limit.

6) appeals to the pragmatist in me who deals with the perfectionist in me. “It’s an approximation. It’s not perfect. Mark it down and move ahead”.

1) Is a standard growth calculation: (Current – Previous) / Previous. Extremely useful in business for sales. (it’s usually like ((current month – previous month) / previous month) * 100 for monthly, etc.

5) Growth can be thought of as volume increasing/decreasing or it can also be thought of as SPEED, again used a lot in financial things, although usually marketing stuff. “velocity of money” hype.

Terrance Tao keep recommending it and it is good.
https://arxiv.org/abs/math/9404236
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another way. I like this one oddly enough as it just starts to form a bit of a mental image in my head.
Process and Time. That is big in how I think, why I’m drawn to computing as it’s built on that.

“The result has been that now quite a number of mathematicians have what was dramatically lacking in the beginning: a working understanding of the concepts and the infrastructure that are natural for this subject. There has been and there continues to be a great deal of thriving mathematical activity. By concentrating on building the infrastructure and explaining and publishing definitions and ways of thinking but being slow in stating or in publishing proofs of all the “theorems” I knew how to prove, I left room for many other people to pick up credit. What mathematicians most wanted and needed from me was to learn my ways of thinking, and not in fact to learn my proof of the geometrization conjecture for Haken manifolds.”
“A further issue is that people sometimes need or want an accepted and validated result not in order to learn it, but so that they can quote it and rely on it. Mathematicians were actually very quick to accept my proof, and to start quoting it and using it based on what documentation there was, based on their experience and belief in me, and based on acceptance by opinions of experts with whom I spent a lot of time communicating the proof”