Wolfgang Palm invented wavetable synthesis in the late '70's which he used in the PPG Wave synthesizer that was hugely popular in the '80's with artists like Thomas Dolby and Frankie Goes to Hollywood. He later went to work at Waldorf who ended up continuing to develop wavetable synthesizers. There's a great company history on his website.
A few years ago, he started developing iOS apps starting with the PPG Wavegenerator, a next generation wavetable synthesizer that true to Moore's Law, blows away the original PPG Wave at tiny fraction of the cost. That was followed by the Wavemapper, a new take on the Wave GUI and interface, and Phonem which focused on speech synthesis. His latest is Infinite, and he says it's the synthesizer he's always dreamed of making. It uses a powerful combination of additive sine waves and noise as a sound source. He has analyzed a lot of sounds and Infinite comes with a huge selection of what he calls 'Sine Resources.' Each Sine Resource is a complex evolving sound with every single harmonic (some resources have hundreds of harmonics!) able to be edited in an intuitive user interface that recalls the old Fairlight CMI touch screen but much, much easier to use. The app uses an XY controller screen to morph between five sine resources and three noise resources and then sends that to the Molder which is essentially a very versatile filter. Additionally, there is a matrix system for routing modulation sources for further manipulation of sounds and you can import sounds from Wavegenerator, Wavemapper and Phonem.
As this is Mr. Palm's fourth iOS app, the GUI is elegant and intuitive, super easy to use (and figure out) and uses the 2D touch screen interface to it's fullest. At just under $20, this app blows away a lot of full blown soft synths and even hardware synths that cost ten to one hundred times more money. Infinite is a great example of why the iPad and iOS are where some of the most cutting edge software synthesis is taking place.