396 MATHEMATICS AS OF 1700 when we enter upon physics,we compare those proportions with the phe- nomena of Nature. ."Here physics refers to experimentation and obser- vation.Newton's mathematics would be regarded as mathematical physics today. 3.Communication Among Mathematicians Up to about 1550,mathematics was created by individuals or small groups headed by one or two prominent leaders.The results were communicated orally and occasionally written up in texts-which,however,were manu scripis.Since copies had also to be made by hand,they were scarce.By the seventeenth century printed books had become somewhat common,though even this improvement did not spread knowledge as widely as might be thought.Because the market for advanced mathematics was small,publishers had to charge high prices.Good printers were scarce.Publication was ofter followed by attacks on the authors from none-too-scrupulous opponents;it was not hard for such critics to find grounds for attack,especially because algebra and the calculus were not at all well grounded logically.Books in any case were not usually the answer for new creations because significant results did not warrant a book-sized publication As a consequence many mathematicians confined themselves to writing letters to friends in which they related their discoveries.Fearing that the letters would reach men who might take advantage of such unofficial docu- ments.the writers often put their results in ciphers or anagrams.which they could then decode when challenged As more men began to participate in mathematical creation,the desire for exchange of information and for the stimulus of meeting people with the same intellectual interests resulted in the formation of scientific societies or academies.In 1601 the Accademia dei Lincei (Academy of the Lynx-like) was founded in Rome by young noblemen;it lasted thirty years.Galiled became a member in 1611.Another Italian society,the Accademia del Cimento (Academy of Experiments)was founded in Florence in 1657 as a formal organization of men who had been meeting in a laboratory founded by two members of the Medici family about ten years earlier.This academy included Vincenzo Viviani(1622-1703)and Torricelli,both pupils ofGalileo among its members.Unfortunately,the society was disbanded in 1667.In Francc,Desargues,Descartes,Gassendi,Fermat,and Pascal, met privately under the leadership of Mersenne from 1630 on.This informal group was chartered by Louis XIV as the Academie Royale des Sciences in 1666,and its members were supported by the king.Paralleling what hap- pened in France,an English group centered about John Wallis began in 1645 to hold meetings in Gresham College,London.These men emphasized mathematics and astronomy.The group was given a formal charter by