1. numbers (numerals: basic arithmetic operations)

1-4-2-1. Speaking of evolution of mathematics chronologically, necessitates to bring up the first arithmetic operations because they were conceived while or ahead of the time that people invented and developed numerals: addition, subtraction and multiplication.

Addition is one of the undefined concepts (we know that a word can’t be defined with its synonyms). We’re simply adding a notch to a in order to write b (It shows that how intertwined adding and counting are), however it might have taken time that people came to awareness about what they were doing, therefore they called the process addition.

Subtraction on the other hand is taking an amount away from another (can we state that subtraction is an undefined concept too?). Both addition and subtraction were conceived when people found the change in quantity of things around. For example they wanted to know how many sacks of rice are left when they cooked or sold out two sacks.

To count eeeeee they needed to add five to itself six times. That’s why they came up with multiplication to simplify addition.

So we see that the concepts of basic arithmetic operations were conceived by people who used the tally marks, and they were one of the reasons for evolution of numerals, apart from writing or reading them.

P.S. I found out that the tally marks font can't be shown on some systems which don't support it, so in the second paragraph if, instead of one notch and two notches, you had a and b, they'd mean one and two respectively; and in the forth paragraph if you had six e's, it'd mean six fives.