What nomenclature do names like fumarate and malate derive from? When reviewing the citric acid cycle, I find names like glutarate and succinate to be helpful in thinking about the structure of the molecules because I was taught about the sequential dicarboxylic acid naming scheme: oxalic (2 carbon), malonic (3C), succinic (4C), glutaric (5C) etc.
But I often struggle with fumarate and malate because I have not learned the numbering or nomenclature system that these names are derived from. Can someone point me in the right direction so that I can learn the background behind these names?
Knowing that will be helpful to my recall of the molecular structure. Then I can stop memorizing and start understanding.
Unfortunately, you will have to memorize the structures and the names because there is no chemical structure hidden in those names.
From Elsevier's Dictionary of Chemoetymology

fumaric acid $\ce{C4H4O4}$, derived from the genus name Fumaria (fumitory), from fumus (Latin:
smoke)

Fumaria plant


malic acid $\ce{C4H6O5}$, derived from malum (Latin: apple)

The same goes for all other common names like oxalic acid, acetic acid etc.