1675 in science

The year 1675 in science and technology involved some significant events.

Astronomy

March 4 – John Flamsteed appointed as "astronomical observator", in effect, the first Astronomer Royal of England.{{cite book|last=Palmer|first=Alan|last2=Palmer |first2=Veronica|year=1992|title=The Chronology of British History|publisher=Century Ltd|location=London|pages=191–192|isbn=0-7126-5616-2}}{{cite web|first=Frances|last=Willmoth|title=Flamsteed, John (1646–1719)|work=Oxford Dictionary of National Biography|publisher=Oxford University Press|year=2004|url=http://www.oxforddnb.com/view/article/9669|accessdate=2011-02-04}} {{ODNBsub}}
August 10 – King Charles II of England places the foundation stone of the Royal Greenwich Observatory near London.
Giovanni Cassini discovers the Cassini Division in the rings of Saturn.

April – The Antarctic Convergence is first crossed by English merchant Anthony de la Roché, who lands on South Georgia.{{cite book|first=Robert|last=Headland|title=The Island of South Georgia|edition=2nd|publisher=Cambridge University Press|year=1992|isbn=0-521-42474-7}}

October 29 – German polymath Gottfried Leibniz makes the first use of the long s (∫) as a symbol of the integral in calculus.
November 11 – Leibniz uses infinitesimal calculus for the first time to find the area under the graph of the function y=f(x).

Antonie van Leeuwenhoek begins to use a microscope for observing human tissues and liquids.

February 25 – Netherlands scientist Christiaan Huygens files drawings of his invention of the balance spring, the key component to the accuracy of portable clocks and pocket watches, in a letter to the Journal des Sçavants.