I recently sat in a master class where the speaker was commenting on the lack of improvisational skills of current pianists. His perspective was that cadenzas should challenge and showcase the pianism of the interpreter, and that such musicianship has by and large been lost.
I am curious if people in the forum stress this aspect of playing. Also what pianist(s) today perform and improvise their own cadenzas? I haven't come across many. Is there something about music education today which inhibits improvisation?

I have heard Robert Levin play a number of Mozart concerti with the Orchestra of the Age of Enlightenment. He is a gifted improviser with a deep sense of Mozartian style. He improvises the cadenzas, differently in each rehearsal and in performance, while keeping absolutely to the style of the music. He also improvises the decorative elements. He is very much a showman, and the concerts are always exciting.

I've always composed my own cadenzas (as opposed to improvising them).

As an organist, I have no hesitation with improvisation. It is a necessary skill in many church music situations, and there are many resources for organists to study improvisation and hone their skills to a very high level.

At the piano I suppose I'm a bit of an anomaly, as my organ background allows me to improvise in various styles of classical music. I have a feeling that most pianists who do improvise are more likely to do so with pop music or Jazz...

Like whippen boy, I've composed my own cadenzas (for Mozart concertos), but the final versions evolved out of repeated improvisations. I really don't think I'd have the courage to totally improvise one in performance, though I think I could produce something quite ok if only I had the nerve .
I have also improvised a lot as an organist - you need a bit of discipline here so that you actually shape it a bit and don't just go for a meander amongst the keys - see you back in G major in half an hour .
I improvise when I'm getting ideas for something i might be writing, but I suppose the only other "classical" type improvising I might do is the "happy birthday in the style of ... " after a few glasses of wine.
Oh, and the extra bits you put into a song while the singer tries to remember what he/she is doing.

I studied improvisation with several renowned masters of the art. My favorite words of wisdom from one particularly memorable session:

When in doubt, trill!

When I was doing my final exams at uni we had to (amongst other things) improvise a fugue. Well i got going ok, but soon wandered off into remote regions from where I just couldn't seem to return. I kept wandering, every now and then restating the subject so that they'd think I knew what I was doing, whilst frantically trying to get back to the right key. Finally found it, and I don't think mine was the only sigh of relief!

Currawong, I notice you are from 'down under'.

I suppose that means all of your fugues start off in retrograde and inversion?

Please forgive me I'm suffering from the effects of strong cold/flu medicine. Yep... it's that time of year...at least in the northern hemisphere!

Ah yes, inversion holds no fears for us down here.
Retrograde - well that's another matter

How exactly does one accomplish such a feat of improvisation?

I love to improvise, but my limited knowledge of music theory, or improvising in general, reduces my improvisations to simple triads. While many variations and such on these triads may sound good the first time, by the thousandth time, it begins to become the same old thing, if you catch my drift!

So do you have any advice to take my improvisations further than simple triads? I'm not necessarily interested in jazz improvisation. Classical improvisation is the elusive goal for which I seek.

Thank you for the help!

I'll be interested to hear whippen boy's answer. The route by which I came to improvisation was:
1 - playing from lead sheets then playing by ear. Really trying to find the exact right chord for what I was hearing. Some of this was pop music, but I was also inclined to play classical tunes by ear.
2 - playing a lot of music! Trying to play some of the common sorts of progressions in different keys, by ear.
3 - studying theory and harmony.
All this was long ago, when I was a teenager. All three were helpful, but [3] only confirmed what I found I already knew through [1] and [2]. When I studied keyboard harmony and improvisation as part of my music degree later on, we did quite a lot of playing by ear, and practising playing progressions in different keys.
Another thing I do with my students sometimes is to give them a title and get them to make up a little piece. Or start with words and improvise a short song. Just keep doing it, whilst expanding your harmonic vocabulary by the music you play. Theory is good, but make sure it's about sound and not just paper learning. If you read about dominant 7ths, play them.

Anyway, for what it's worth.

Here's my experience in a nutshell (a huge nutshell - sorry)! I can't point to any one thing; rather it is the sum of several things:

I played by ear at age six, then abandoned that when I started reading music at age seven.

As a teenager I studied Theory & Composition at two prestigious conservatories, and also at a third college. I started composing at a young age.

Like currawong, I read as much music as I could get my hands on. I have fragments of thousands of compositions floating around my mind, and locked into the muscle memory of my fingers - that helps immensely when improvising!

I accompanied many a voice lesson, which sometimes required transposition and/or playing from a lead-sheet. I 'pretended' to play Jazz for many years! I hope to study it one day...

When I became an organist at a very big church I was required to improvise interludes in the style of the anthem or offertory and to modulate as needed (it was a tradition of that church, as established by some very talented predecessors). Sometimes the styles are divergent to the point of absurdity, but that only allows me to stretch my capabilities.

If necessary I can improvise over a quarter of an hour for Communion music, and a Prelude and/or Postlude (for example if I've misplaced my score)!

As my organ career got underway I studied improvisation with well-known organ improvisateurs in the US and in France, where organ improvisation has been maintained at a very high standard for centuries.

The American Guild of Organists publishes a monthly magazine called "The American Organist" - from time to time they will have a recurring column with advice on improvisation. As currawong said, you have to acually try out & practice the things you read.

I don't claim to be an expert - I just acquired certain skills.

It is great to read that some pianists strive to keep this aspect of their playing alive...I am sometimes surprised upon listening to a pianist(s) with prodigious technique literally freeze when called upon to improvise. I've been playing some music by Rzewski which explicitly calls for this. From my perspective, working out themes to guide you through a cadenze give you a more intimate sense of 'ownership' of the piece.

This week I was listeninig to Dubravka Tomsic play Beethovern Concerto #1 and admired her cadenza -- it was brilliant playing AND sounded very "Beethovenesque" - It must be a challenge to create an artistic cadenza that sounds like the composer could have written it.

I'm composing my own cadenza for Mozart's 21 Concerto. I'm almost done with it but I have a question - are you supposed to summarize several different themes from the movement, or are you supposed to just take one or two main ones and elaborate on them? Is it completely up to me? So far I've taken several themes and had great fun playing around with them, but I'm concerned I'm quoting too much material...

Also, im certain sections, is it okay to use similar harmonic framework and progressions that Mozart does, just with my own material instead of his (obviously still in the style)?

Are their any guides to cadenza's in the style of Mozart? My teacher writes his own and I have a lesson with him tomorrow, but I was wondering if there was anything I could read in the meantime.