Plato already distinguished between different professions and also different intellectual capacities in his Republic. His master discipline was the statesman who placed all professions in the right place in the city - read republic - so that they can best flourish. This is his conception of the philosopher-king, he who marries well both thought and action. This was in counterpoint to the politics of his day which tended to benign tyranny at best. Although it's common today to praise Athenian democracy, Plato himself didn't think much of it - until faced with worse. In today's democracies, this role is not played by persons, but by institutions.
This of course, is not the kind of multi-disciplinary work that you mention. And I think it's important to distinguish this from inter-disciplinary work which builds bridges between fields, rather than simply being fluent in two, very different fields.
Of course Plato also thought it important to focus on the educational policy of a republic to build a republic and part of his The Republic is devoted to this subject. Music was an important branch of this - so one might say here, the arts. As well as mathematics, and so science. Given his views on the professions, and supposing that technology, ie techne, is the focus of the professions then this captures all three of the divisions you have pointed out. One key aspect that is often forgotten in Platos discussion of education is physical activity. It's not enough to train the mind, one ought to train the body. So the real division is not merely three ways - but four.
It's a good question to ask what kind of physical activity Leonardo got upto. And it's possibly a reflection on our own cultural/educational matrix that we don't think of asking - as though physical education is somehow missing the point of education. It's worth reflecting on this next time the medical profession points out the epidemic of obesity that is afflicting affluent countries.
In early medieval Europe, around the 6th C, liberal education drew on Plato to establish the trivium, the three fields of rhetoric, logic and grammar; this as preparatory for the quadrivium, which was composed of arithmetic, geometry, music and astronomy. These were distinguished from the practical - read technological skills - of medicine and architecture.
As one can see, the disciplinary differences were established early. Notably, CP Snow, on his essays on the two cultures of the arts and sciences wasn't about the disciplinary differences as such. After all, even in the sciences there are distinctions. For example, between mathematics and physics. His point was that these two large fields were no longer on speaking terms. Worse, that they failed to comprehend each other. One might think that in an earlier era, this role was played by philosophy or theology - the then unifying disciplines. This role, after the break with Christianity in the West can no longer played by it - at least in the same fashion. Nevertheless, for the episteme of a people, a nation or a civilisation to flourish, this conversation has to somehow be begun, and then sustained. Hence, perhaps - though given I've never worked in a university - and so am not in a position to say, the renewed emphasis on multidisciplinarity/inter-disciplinarity today.
The 'increasing' or 'explosive' increase of knowledge has been noted by many thinkers, with Simone Weil, for example, criticising the 'useless piling up of knowledge' as though that constitutes progress. Da Vinci, was alive when the renaissance of science was just beginning and one can judge that his famous drawing of The Vitruvian Man, of man encircled by a geometric figure, was his 'prophecy' of a science in harmony with that of man. Whereas on the cusp of the 20th C, Francis Bacon replied with a painting of man enslaved and eviscerated within a matrix of cubic satanic lines: the development of technological 'progress' rather than freeing man, has made of him a slave.
Simone Weil, considered that the critique of religion begun by Marx and his contemporaries (and which does not neccessarily mean it's overthrowing) had to be accompanied or replaced by a critique of technology and science. In the secular west, she considered this as the replacement of religion as the new opium of the people.
This cannot be done without surveying the whole and is another motivational reason for inter-disciplinary as well as multi-disciplinary studies.
