He was a brilliant mathematician and made significant contributions to cryptography, combinatorics and computing theory.
Alonzo Church, who had the misfortune of being far less fashionable than Turing (he was an American, a churchgoing Evangelical and a family man) came up with the solution to Godel's "decision problem" before Turing did and that's why it's called Church's theorem rather than Turing's theorem.
Einstein was a mighty good mathematician, IMHO.
To have had the imagination and intellectual power to visualize relativity as the solution to the observed invariant speed of light, and then to take hold of that vision and express it mathematically, shows an almost superhuman ability to express in mathematics a vision of something fragile, complex and subtle.
Few mathematicians have Einstein's ability to use their skills to express in symbols underlying physical realities of the universe that won't be experienced directly by ordinary humans for hundreds of years, if ever.
I certainly think Einstein was on a par with Newton.
Whether or not Turing deserves to be in the same realm, I don't know. I've never been able to get my mind around cryptography and the mathematics that attends it. To me, cryptography is necessary but not very interesting. Cryptography is only necessary because of the sinful nature of human beings.
Great breakthroughs often seem simple..but only after someone else has discovered them.
Turing’s description of the “Turing Machine” is such a breakthrough...as is the concept of zero, as is Newtons creation of the Calculus (also a hat tip to Leibniz). These all seem very simple now only because someone else created them and we merely have to learn about them.
The conception of the Turing machine is the true beginning of the science of computing.... and it does indeed seem simple.
Oh geeez...don’t mention Shockley...inventing the transistor doesn’t come close to absolving him from is purported belief in black inferiority...
He got crucified for that.