In the order of knowledge, Latin and Greek have always played the role of a tree to the trunk, and many classicists would continue to argue that they do so.
Training the mind to read Latin and Greek has the benefit that training the mind to read in any foreign language has (which is considerable), but it has more.
For one thing, since Greek and Latin are exoskeleton languages, the reader becomes exceedingly aware of the structure of Language.
For another, Greek and Latin humanities remain the foundation for all European humanities, perhaps especially French and Italian, but also English, German and the rest.
For another, to know Greek and Latin is to stop window shopping at the Great Ideas Emporium and to walk inside and converse. No other languages can boast a continual 2500 year dialogue in every matter that has ever mattered to human beings. Was it Nock who said that to read Latin and Greek is to gain a mature mind.
But in spite of the frequently disproved claims of Thorndike from the late 1800?s, perhaps the greatest benefit of Latin and Greek for those who seek utility is the habits of mind that the proper study forms in the student. Look at the great scientists from Roger Bacon through the early 20th century. Which of them was not classically educated.
Math is a glorious element of classical education. There is a reason the Greeks developed it so far and so fast. However, if calculus is the new Latin and Greek, then civilization no longer exists.
For civilization, tenuous as it is, is the property of a community that strives and to some degree is successful to embody the true, the good, and the beautiful in the thoughts, habits, and artifacts of its members. We always fail, but the Greeks showed us how valuable the failed attempt was. Without Homer, Plato, and Vergil, all the calculus in the world won’t feed a single soul.
If you want great scientists, great statesmen, great mathematicians, great theologians, great philosophers, great poets, and great humanists, make sure that a significant number of your children study enough Latin and Greek to hate it. The more branches of learning, the stronger the trunk needed to hold them together.