Thomas Shaw Brandreth, FRS (24 July 1788 – 27 May 1873) was an English mathematician, inventor and classicist.
Brandreth was the son of a Cheshire physician, Joseph Brandreth. He studied at Eton and received a BA from Trinity College, Cambridge in 1810 as Second Wrangler, second Smith's Prizeman, and chancellor's medalist, attesting to his keen intelligence. He received his MA in 1813, and was subsequently elected to a fellowship at Trinity and called to the bar. He entered legal practice at Liverpool, but was much diverted from advancement by his interest in inventions.
Elected a Fellow of the Royal Society in 1821 for mathematical achievements, he had by that time invented a logometer (an early slide rule), and went on to design and patent a friction wheel and a clock escapement. These achievements led him into friendship with George Stephenson, and he played a role in the survey and engineering of the Liverpool and Manchester Railway, particularly the crossing of Chat Moss. However, he resigned as a director of the line shortly before its completion.
In the early days of railroading, it was by no means clear that the steam locomotive would come to be the principal form of propulsion for trains. Brandreth invented a machine which used a horse galloping on a treadmill as its source of motive power. A prototype, the Cycloped, participated in the Rainhill Trials in 1829, but it had to be withdrawn when the horse broke through the floor of the machine. In any case, the trials proved the superiority of steam motive power in all but exceptional circumstances.