Phyllida Barlow: The sculptor on splodges, what she learnt from her mother – and not teaching the YBAs

I've been called 'the mistress of the splodge' [in recognition of her preference for sculpting rounded works], which I rather like. But even when critics are rude they have revealed things about my work that's accurate. [The Sunday Times art critic] Waldemar Januszczak once described a piece [for a show at the Serpentine Gallery, in 2010] as like snot thrown on the wall. But I think the disgustingness of a spillage or a splodge has its own beauty, and fascinates me.

I have a dread of authority and sculpture can be horrendously authoritarian; the upright tower or monument that declares itself very didactically, occupying space that could otherwise be occupied by a human. So my work is about creating amorphous, fat, anti-monumental structures [using low-grade materials].

The western world is as monument crazy as the dictatorships I often think there's a strange paradox there in that, though they may take a different visual form, both are coming from a highly individualistic place, supposedly celebrating their own endeavours and positions with incredible displays, which is where I think the circle meets.

Growing up in post-war britain gave me a great insight into making things I wouldn't want to sentimentalise the period, but when you're thrown on your own devices, things can happen: I remember my mother demonstrating how to make dolls' house furniture out of matchboxes and conkers – using what's around to make what you wanted. That had a big impact on me.

I don't miss anything about teaching [Barlow was a professor of art for more than 40 years, most recently at the Slade School of Art, London, until 2009]. I enjoyed seeing work produced by students, but the higher up the ladder I went, into administration, the more out of depth I was.

I never taught Martin Creed, Rachel Whiteread or Douglas Gordon [all Turner-Prize winning artists who studied at the Slade]. So when Martin said recently that I was the best teacher who never taught him, it was a relief as I felt my role [as teacher to the YBAs] in the press had got out of control: it was embarrassing meeting these people who were probably thinking, why is she using my name?

I'm finally fulfilling my ambition I've always been busy as an artist, generating things, but right now I've never been busier with shows for museums and the private sector [including recent installation Dock14 at Tate Britain], and it feels exhilarating. I wasn't ready 10 to 15 years ago to do that, but when you get older you finally don't mind if you make a fool of yourself.

Being an artist is a great age leveller All the questions I have – who the work is for, where is it going, whether we always need an audience etc – seem like universal questions, whether someone is my age or 19, and I find that very moving.

You can't rely on other people or institution If you want to do something, it's up to you to get on and do it. Yet today there seems to be an expectation [among students] that magic can be worked because, say, you go to [Central] Saint Martins. I'm not putting down Saint Martins, but 90 per cent of ambition needs to come from ourselves.

I am an addict when it comes to eating cake. But I don't drink much or take drugs. Mostly it's pretty ordinary homemade cakes, from recipes remembered from my mother.

Barlow, 70, is a sculptor. Her latest exhibition, Fifty Years of Drawings, runs from Friday until 26 July at Hauser & Wirth, hauserwirth.com