19th Century Scientific Latin
From G. Waldo Dunnington's 2004 biography of Gauss, Carl Friedrich Gauss: Titan of Science, p. 37-8:
… Of unusual interest is the part which Meyerhoff⁶ took in this book [sc. Gauss's most important mathematical work: the Disquisitiones arithmeticæ]—the correction of the Latin.
⁶Johann Heinrich Jakob Meyerhoff (1770-1812) became in 1794 collaborator, and in 1802 director, of the gymnasium in Holzminden. He was thoroughly grounded and trained in the ancient and modern languages. As a Göttingen student he had won a golden prize medal for a Latin dissertationon the Phoenicians. Yet mathematics was rather foreign to him.
The above is striking enough, if one considers how little Gauss needed to mistrust his own proficiency in this respect. According to Moritz Cantor, Gauss wrote a classical Latin, giving rise to the expression that Cicero, if he could understand the mathematics of it, would have censured nothing in the Gaussian Latinity, except perhaps several customary incorrect modes of expression which Gauss used purposely. But it was Latin just the same and therefore attractive and stimulating to only a narrow circle of readers. Referring to Meyerhoff's work, Gauss wrote:
Of course I understand that it cannot be an especially attractive work for Mr. Meyerhoff, since he does not seem to be sufficiently acquainted with mathematics, in order to look on it just as reading. Thus the word algorithmus was unknown to him. Only on a single point must I take the liberty of disagreeing with him. I well know that si with the subjunctive is not good Latin; but modern mathematicians seem to have made for themselves the rule of constantly using the subjunctive in hypotheses and definitions; I do not remember an example of the opposite, and in Huyghens, who according to my notion writes the most elegant Latin and whom I purposely, therefore, have imitated, I find the subjunctive continually in these cases. I open at random and find Opera, p. 156, Quodsi fuerit; p. 157, Si sit, si fiat, si agitetur; p. 158, si suspendatur; pp. 188 seqq. are examples by the dozen. Therefore, since in this instance the desire to be a genuine Roman would be only purism (which as far as I am concerned would be less allowable, because I am well minded not to be so in any case) and the thing is not at all absurd in itself, I went with the current. I hope Mr. M. will not take offense at me. What was incomprehensible to him in the accedere possunt, p. 5, I have not been able able to guess; I have therefore let it stand. The passage p. 7, which previously ran thus: Si numeri decadice expressi figuræ singulæ sine respectu loci quem occupant addantur, Mr. M. misunderstood, because he probably didn't know that figuræ means numbers; he took numeri for the nominative plural and figuræ for the dative singular and on that account suggested to me that singulus is not wrong; but just for this reason a mathematician will probably not construe it incorrectly, chiefly because it doesn't make sense; nevertheless I have now arranged the words somewhat differently by this time.
Thus, Gauss seems to have worked with a mathematical Latin based on classical Latin. Gauss also wasn't afraid to innovate the Latin. It seemed to be a truly living language to him.
Gauss's Dictionary of Scientific Biography entry says:
He published in Latin not from internationalist sentiments but at the demands of his publishers.
20th Century Scientific Latin
Interlingua, or Latino sine flexione, is a 20th century variant of Latin invented by the Italian mathematician and logician Giuseppe Peano. He intended it to be a language to foster international scientific communication. It is Latin but without inflection (or without "grammar," as Peano called it).
Peano’s mathematical logic and his ideography for mathematics were his response to Leibniz’ dream of a “universal characteristic,” whereas Interlingua was to be the modern substitute for medieval Latin, that is, an international language for scholars, especially scientists. Peano’s proposal for an “interlingua” was latino sine flexione (“Latin without grammar”), which he published in 1903. He believed that there already existed an international scientific vocabulary, principally of Latin origin; and he tried to select the form of each word which would be most readily recognized by those whose native language was either English or a Romance language. He thought that the best grammar was no grammar, and he demonstrated how easily grammatical structure may be eliminated . His research led him to two areas: one was the algebra of grammar, and the other was philology. The latter preoccupation resulted most notably in Vocabulario commune ad latino-italiano-français-english-deutsch (1915), a greatly expanded version of an earlier publication (1909). This second edition contains some 14,000 entries and gives for each the form to be adopted in Interlingua, the classic Latin form, and its version in Italian, French, English, and German (and sometimes in other languages), with indications of synonyms, derivatives, and other items of information.
The basic rules of Latino sine fliexione are, inter alia (ibid.):
Omni vocabulo de Interlingua es latino.
Interlingua non habe grammatica.
Inter synonymos latino, nos elige vocabulos internationale.