FWIW, I have a slightly different take on mathematics.
To my mind, mathematics is a human concept of abstract representations of one aspect of natural phenomena such as the two cows in a paddock. It seems to me more appropriate to say that the discipline of mathematics has evolved, rather than been ‘invented’ or ‘discovered’. Obviously it's a
discipline used initially for
communication of the notion of numbers either in verbal or written form.
Stone age people such as the aborigines had no written language but they verbally communicated numerical data by pointing to fingers and toes (and other body parts for larger numbers). See
https://en.wikipedia.org/wiki/Australia ... numeration .
An improvement on the use of body parts for counting evolved in the form of the abacus. See
https://en.wikipedia.org/wiki/Abacus . It was an evolved improvement to indicate numbers. It could also be used for a variety of calculations. According to the link above, it has evolved over millennia -
“The exact origin of the abacus is still unknown. Today, abaci are often constructed as a bamboo frame with beads sliding on wires, but originally they were beans or stones moved in grooves in sand or on tablets of wood, stone, or metal.”In written form, the notion of multiples in Roman and Greek numerology was indicated by '1' up to the notion of the sum of '111', and other symbols began to be used (evolved) for larger numbers. I imagine that the work of expressing the notion of '100' as 100 separate repetitive digits resulted in the development of such a set of symbols in small bursts of advancements. For example, the Romans used ‘C’ for 100 and ‘M’ for 1000.
In one of these apparent small advancements, Arabic symbols appeared. There is a suggestion that may never be proved or disproved that the original 9 figures each had an equivalent number of angles corresponding to the number of anything it was meant to represent in every-day life. With centuries of use, these symbols may have become modified in an evolutionary manner into the more roundish symbols we scribble today.
When the Indian contribution of the concept of a zero came into use in about the 9th century AD, all of the necessary ingredients were available for the evolution of decimals, algorythms, calculus, logarithms, calculators, computers etc.
So to my mind, mathematics has
evolved in small advances over millennia. Maybe each minor advance could be called an invention. But rather than ‘invention’, maybe we could say ‘ínsight’, ‘brainwave’, ‘good idea’.