That the real meaning of maths “was somehow unclear” was a truth about maths for about four-and-a-half millennia.  Khufu built the great pyramid at Giza using simple maths,   so this aspect —“the use of maths” — had been fully established from the beginning. It was the unavoidable “use of maths”. It gave maths a very positive, practical, public image. Then Plato came along 2,000 years later, and introduced a new vision of maths… as a form of superior language, a performance artform in effect..  Interesting discoveries had recently been made in geometry. Maths was a discipline which was widely admired.  Many of the followers were attracted to maths because it was aristocratic … as well as a charming rule-abiding pursuit which offered an escape from the rough-and-tumble of the messy street milieu.  This meant that the Platonists had no interest at all in where their maths challenges came from,   or where they were destined to assist.  More than two millennia passed, and it still has not dawned on the gurus of maths that their subject is a uniquely important confidence-builder.

Some examples:  ways were found to solve  quadratic and cubic equations,  difference methods were used to draw-up useful maths tables, e.g. sines and cosines. A few types of differential equations were solved. It was a fairly small “crop of results” considering the vast total investment of research hours involved …but as G. H. Hardy said in his book, it was these gems of “pure maths” which were “the most useful bits of maths”!  (This “usefulness”, though, was relative to Hardy’s experience. He didn’t take into account the vast usefulness of maths as a confidence building discipline for people working on hugely ambitious projects.)