Des McHale, a truly extraordinary Mayo man

A master of mathematics who has firm views on artificial intelligence

by Dr. Richard Martin

I met a man from 12 Marian Row.

Des McHale. Emeritus Professor of Mathematics in UCC.

He is now 79 years of age.

He studied mathematics in Galway as an undergraduate and completed his PhD in Keele University in 1972.

He became a member of the faculty in UCC soon after and remained there for the duration of his academic career.

Along with his research in pure mathematics, specifically in Group Theory and Ring Theory, he is also the definitive authority on George Boole (a mathematician in UCC from the 19th century who is widely regarded as a founding father of computer science) and the film The Quiet Man.

He has also published numerous books on humour and wit including the famous Kerryman jokes.

In total he has published 80 books. By any metric he is an extraordinary man.

And it just so happens he’s one of us. A lad from Marian Row.

RM: Now, can I say to you, the first time I ever heard your name was actually when I was in second year in St. Gerald's.

DMcH: Right.

RM: I did very badly in my summer test in maths.

DMcH: Right.

RM: And I met Christy Tynan.

DMcH: Yeah.

RM: I showed him my maths exam. And he said, hold on a second. This is all over the place. You need to be structured the way you write it.

And then he told me about a guy that was in his class called Des McHale, who did very badly in first year.

DMcH: I did.

RM: His parents kept him in during the summer, and he worked on maths. And then he got better at it, and because he got better at it, he liked it. This is where it started. Is that true?

DMcH: That's true. I was lucky. I arrived there the day that the new headmaster, Brother George Sheridan, started.

And he's the guy that made me turn into a mathematician, because he just... He seemed to know how to do mathematics and do it clearly, and he pushed me. If I got a question out, he'd say, now go on, do it again, do it a different way. Sometimes he made me do a question three, four, five different ways.

We have something in common, by the way, that you may not realise.

We both won the Peel Prize for Geometry at UCG.

RM: Wow.

DMcH: Well, I was in 1964, and you were about 2014…

RM: That's amazing.

DMcH: That is amazing. That's prestigious, like, you know.

I remember the prize money was £13.

And there was fierce competition for that.

RM: I got a cheque for €1,000. I actually solved the geometry question using calculus.

DMcH: Would you believe it? I did something like that.

I solved one of the geometry questions by inversion, like Brother George had taught me.

RM: Tell us more about St. Gerald's College. Because I have a great love for St. Gerald's.

DMcH: I went into St. Gerald's when I was 10. And by the time I graduated in 1962, I was only 15, and I was too young to go to college.

I went back to St. Gerald’s, but I didn't go back for a year, I went back for two years. So, I had a leisurely two years to do anything.

RM: And were you the first ever to do honours maths?

DMcH: I think we were.

RM: Was it you, Paddy Gilligan and Christy Tynan?

DMcH: We started off with about 12 people in the class. And we had an extra hour every day, after school.

And then it gradually whittled down. Only three of us actually did the exam. Paddy, Christy and myself.

When I was in UCC, I gave my Leaving Cert papers to the incoming Leaving Class, and they found they couldn't do most of it.

RM: When was this?

DMcH: This was about the year 2000. They could not do it.

RM: Do you think the curriculum should be harder?

DMcH: Oh, absolutely, yeah. It's too easy.

It's too easy. And it's busy. There's no bite.

There's no depth. And of course, what do they call this new practical maths? To me, it's crazy. They don't teach them the fundamentals.

RM: What did your parents do?

DMcH: My mother was a hairdresser, and my father was a psychiatric nurse.

And I would have been the first person, not to go to college, but to go to secondary school of a thousand generations of McHale. I was just lucky.

RM: Tell us about your career as a mathematician.

DMcH: Ok, I'm a mathematician. It was interesting because there's strong algebra in Galway.

And I just found algebra very doable. And this actually relates to Boole's notion of mathematics.

That mathematics consists of symbols and the rules that those symbols obey and nothing else.

No interpretation, no nothing. And I like that approach.

That you're given what you are allowed to work with. And then you're given the rule, like chess.

RM: What do you think of Artificial Intelligence?

DMcH: I always felt AI was just two words. I'd be doing theorems in Ring Theory, and there was one theorem that I could not prove, and I'd just spend ages and ages…...

And nobody else could prove it out as far as I could see. I offered a prize for someone to prove it in some journal, and nobody would respond to it. So, I happened to be looking up the web on Mathematical Humour, and this guy had a page on Mathematical Humour, and I thought, geez, that's it.

I bet I know it all. But I didn't. It was all newish sort of stuff.

I wrote to him, and then I noticed on his CV, he said he does machine proofs with artificial intelligence.

RM: Yeah, what was his name?

DMcH: Michael Kinyon, at the University of Denver, Colorado.

I just told him about this problem.

He said, all right, I'll have my prover machine have a go at it. Damn it, didn't he solve it.

In a couple of hundred steps, but he solved it.

RM: And you went through it step by step.

DMcH: Yeah.

RM: And you were happy with it.

DMcH: Well, yeah.

RM: How do you feel about AI then?

DMcH: Well, I'm scared of it now.

I mean, if it can do things that I couldn't do, that I mean, I spent years and years working on.

RM: How long were you trying to do that theorem?

DMcH: Oh, I suppose 10 years at least.

RM: You spent 10 years.

DMcH: Yeah, but I mean, on and off. Yeah, but you'd be thinking about it.

And this is the AI. And it solved lots of similar theorems as well.

RM: And when did it do that?

DMcH: About a year ago.

RM: What do you feel then about the future of AI going forward? Are you worried about the human race?

DMcH: No, no. Funnily enough, we had, you know, Geoffrey Hinton, the guy who won the Nobel Prize for physics. He was at our house last April. He's the great-great-grandson of George Boole.

And he was in Cork. He said he wanted to see me. He wanted to see Boole's grave.

And this was before he got the Nobel Prize. And he's so worried about AI that he resigned from Google. And he's trying to warn people that it will take over.

I don't know. The one thing I could argue with him about was humour. And I felt that machines will never duplicate humour and really good jokes.

He said, yes, they will. They’re nearly there, he said. I said I would believe it when I see it.

Because I don't think that machines have the subtlety. They don't have the human experience.

There's just something lacking in their...

RM: Do you know what I think? What machines lack? Emotion.

DMcH: That's true. That's true, yeah.

RM: Do you know what I do sometimes after I submit a piece into Tom Kelly? For the craic, I copy and paste it into Chat GPT.

Just to see what comes back, right? And what I always feel is that it's a very powerful tool, but it lacks emotion.

DMcH: Right, yeah.

RM: So. I don't think...

DMcH: It lacks experience as well.

RM: That's it. Let's say Yeats' poetry, right?

Something like “When you're old and grey and full of sleep, and nodding by the fire” ……I don't think a machine could write that.

DMcH: No, I don't think it could.

The how and the why. And I mean, most people just take the how. But the why is a lot more... I don't think machines know the why.

They know the how. They know how to do it. Well, maybe when machines start designing machines, that's when we get worried.

Because they'll probably do new things that we couldn't think of doing.

But now, look at this. Suppose you had a Rembrandt painting.

A Rembrandt painting consists of little specks of paint on a canvas. Now, suppose you could physically duplicate that completely. Get the coordinates of each point on the canvas.

And in the exact spot, have a little speck of yellow paint or blue paint. And now you show it to somebody and say, could you distinguish between this and the Rembrandt? Some people say, yes, there's just something about the way Rembrandt did it. The brush stroke, the shades, the colours.

There's something over 325 different colours of red. Scarlet, vermilion, turquoise, you know.

So, I mean, how would a machine choose which colour. It says paint this dot red, which red do you pick? If you didn't know what Rembrandt had done. And I think the same with music.

RM: Tell us about George Boole.

DMcH: Boole's main achievement, I'd say. First of all, he turned logic, which is the basis of all mathematics and all human thought, into mathematical symbols.

And what I say is that if you take a syllogism like,

*All girls are beautiful,

* Mary is a girl,

* Therefore, Mary is beautiful.

Now, that's prose. And that's dependent on the English language, and that's dependent on understanding the English language.

Boole turned that into

* All A are B.

* C is A.

* Therefore, C is B.

And that means that all girls are beautiful. And that's purely symbolic.

There's no language there. It's purely symbolic. It could be understood by anybody, in any language, in any culture.

So that was a huge achievement.

And that's what led to computers, because machines could duplicate that, because they just can manipulate the symbols.

RM: So, you don't see that as kind of trivial maths?

DMcH: No. Gosh, no.

At this juncture three Leaving Cert students knocked on the front door. I let them in and introduced them all. His face lit up. We sat on chairs in a huddle around him in my living room.

All three will be studying maths at third level next year. I wanted them to meet him. I felt it would be a powerful experience for them. It was.

One of the things he told them was……

DMcH: The one thing that everyone says, I used to be a genius. I figured I wasn't a genius.

The notion of the fellow who never opened a book in his life and sat there and took everything is a total myth, you know.

I've had at least half a dozen world-class students who are now professors in various universities of the world. And the one thing they had in common is that they worked, and they worked, and they worked…….

After the chat, banter, guidance and advice, we walked up to the Mall as a group and took a photo. A bright summer’s day. We parted ways a short while later.

Language, like mathematics, has its limits.

It’s possible for any man or any machine to find the combination of words to describe what it meant for me to finally meet Des McHale.

I certainly can’t.