When did Latin cease to be an important language for international scholarly communication?

It come about at different times in different subjects, for example Latin names of conditions and anatomical objects are still used in medical science. It generally happened in the 18th and 19th century.

The answer of Alex gives some nice examples on when it happened.

The reasons are manifold and somewhat complex:

• In the Middle Ages the only subject considered worthy for scholarly interest were theology and philosopy and ancient history (this is a stereotypical oversimplification, there were books on medicine, herbs, art, etc... too), so the main occupation of scholars was to read works of ancient auctors writing in Latin. (or rarely Greek, Hebrew or Arabic) After the 17. century new disciplines and fields emerged, many of them based on experiments or newly invented everyday activities (like economics or engineering). It would have been cumbersome to invent, introduce and learn latin worlds for all these new concepts.

• In the Middle Ages 'everyday' languages were divided into many dialects and often lacked fixed spelling, leaving no other choice to a humanist living in Florence and writing letter to his peer in Paris (and perhaps even in Naples) than to use Latin, which both of them knew from their ecclesastical education. Later as modern nations emerged and started to take pride in their culture and ancestry, and printed books become common, the national languages were unified, their grammar fixed and their wordbase enriched. (Sometimes words were purposefully invented to make the language fit for science, as it was the case in Hungary)

• As the nations grew powerful, each of them created it's own Accademies, Royal Societies and similar national scientific institutions, which often encouraged works in native language. Meanwhile the numbers of scientist and scholars waxed rapidly, allowing meaningfull cooperation in the same country. (Earlier there were often just three scholars in the whole Europe researching some marginal topic, so international cooperation was unavoidable)

• The Reformation made it possible to work in native tongue in theology and religious teaching, and after that the use of modern languages slowly permeated all the other areas of written word like law, governance or high literature.

• The possibility to reproduce images and mathematical formulas (which also became an unified language) in litography and later in print decreased the need for lenghty written decriptions (did you ever tried to read a 15. century aritmetic book? or reconstruct the Temple of Salamon from the desription in the Bible? The figures and illustrations in modern scientific publications are a great gift.)

• In the most critical decades of the 18th and 19th century it was expected from an educated European man to understand French, so there was a replacement international language ready.

• When the international cooperation needed for 'big science' became important in the 20th century, Anglo-saxon countries had already grabbed the lead in many modern sciences and technologies, so their language became the standard.

• Latin was considered 'cool' in Renaissance and Classicism, while it was definitely 'uncool' in Romanticism.

• Some of the Latin (and Greek) words survived assumed new meaning: proton, electron, momentum, integral, nucleus, equilibrium, quantum...

To expand the answer of b.Lorenz with few examples: it was a slow process, and the speed in various areas was very different. Some examples. Proceedings of St. Petersburg Academy (mid 18th century) had the following rule: papers in all sciences are published in French, except mathematics, mathematics was published in Latin.

The last important mathematical book that I know which was written in Latin is Fundamenta Nova by Jacobi (1829). But no one wrote on physics or chemistry in Latin in 19th century.

In medicine the importance of Latin lasted much longer. In the middle of 20th century Latin was a mandatory subject in the curriculum of Soviet medical institutes, recipes for pharmacies were written in Latin and a surgeon normally spoke Latin with his/her assistants during the surgery. (Of course in many cases this was a mixture of Latin and Russian, but it was prescribed that they speak Latin. One reason I was given for this is that the patient does not understand their talk:-)

But most journal papers were not published in Latin since the middle of 19th century, in all sciences.

Latin disappeared from the mandatory curricula in high schools and universities in the beginning of 20th century (in many European countries like Russia and England).