Peter Guthrie Tait FRSE (28 April 1831 – 4 July 1901) was a Scottish mathematical physicist and early pioneer in thermodynamics.

He is best known for the mathematical physics textbook Treatise on Natural Philosophy, which he co-wrote with Lord Kelvin, and his early investigations into knot theory.

[1] He was educated at Dalkeith Grammar School then Edinburgh Academy, where he began his lifelong friendship with James Clerk Maxwell.

He studied mathematics and physics at the University of Edinburgh, and then went to Peterhouse, Cambridge, graduating as senior wrangler and first Smith's prizeman in 1852.

[citation needed] In 1860, Tait succeeded his old master, James D. Forbes, as professor of natural philosophy at the University of Edinburgh.

His earliest work dealt mainly with mathematical subjects, and especially with quaternions, of which he was the leading exponent after their originator, William Rowan Hamilton.

Two years later, researches on "Charcoal Vacua" with James Dewar led him to see the true dynamical explanation of the Crookes radiometer in the large mean free path of the molecule of the highly rarefied air.

This was for the benefit of thermometers employed by the Challenger expedition for observing deep-sea temperatures, and were extended to include the compressibility of water, glass, and mercury.

Many other inquiries conducted by him might be mentioned, and some idea may be gained of his scientific activity from the fact that a selection only from his papers, published by the Cambridge University Press, fills three large volumes.

"Thomson and Tait", as it is familiarly called (" T and T' " was the authors' own formula), was planned soon after Lord Kelvin became acquainted with Tait, on the latter's appointment to his professorship in Edinburgh, and it was intended to be an all-comprehensive treatise on physical science, the foundations being laid in kinematics and dynamics, and the structure completed with the properties of matter, heat, light, electricity and magnetism.

But the literary partnership ceased in about eighteen years, when only the first portion of the plan had been completed, because each of the members felt he could work to better advantage separately than jointly.

Tait's articles include those he wrote for the ninth edition of the Encyclopædia Britannica on light, mechanics, quaternions, radiation, and thermodynamics, and the biographical notices of Hamilton and James Clerk Maxwell.