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Hope's father, John Hope, was a professor of botany at Edinburgh University and founder of the new Edinburgh botanic gardens. Thomas, who was born in Edinburgh, studied medicine there and became professor of chemistry at Glasgow in 1787. He returned to Edinburgh in 1795 as joint professor of chemistry with Joseph Black, succeeding Black on his death in 1799. He remained as chemistry professor until 1843.

In 1787 Hope isolated the new element strontium and named it after the town of Strontian in Scotland where it was discovered. At first it was thought to be barium carbonate and was only established as a new metal in 1791. Martin Klaproth made the same discovery independently but a little later.

Hope was also the first to show the expansion of water on freezing and demonstrated that water attains a maximum density a few degrees above its freezing point (actually 3.98°C). He published his results in his paper Experiment on the Contraction of Water by Heat (1805).