I am preparing a talk for our undergraduate Maths Society (perhaps ill-advisedly) with the title ‘A brief history of mathematics: 5,000 years from Egypt to Nottingham Trent’. This will be a stampede through some very selected hightlights, starting with some arm waving about pyramids and ending with something modern. In fact, as well as some recent results that have been reported on this site this year, I intend to end with a recent piece of research published in the department (and a colleague has promised a nice picture of a brain for this^{1}).

Relatedly, a colleague who teaches on our Financial Mathematics degree suggested I include Black–Scholes in my talk, as one of the most recent results included in an undergraduate degree. It’s from 1973. Can we do better? I asked Twitter.

Someone with a private Twitter account said they had taken a second year undergraduate number theory course that covered RSA (1977).

Daniel Rust pointed to the No-cloning theorem (1982) in quantum mechanics.

@peterrowlett http://t.co/HD0Foqc5HB 1982 and understandable by capable undergrads. http://t.co/560wUqRtM9

— Daniel Rust (@Talithin) October 27, 2013

Geoff Robbins suggested the Wiles Fermat proof (1995). I’d be interested to hear if this has been attempted — I commented that although a popular book had been written on the topic, I didn’t think it had given much detail of the proof.

@peterrowlett Somebody *must* have done an undergrad overview of Wiles Fermat proof? (1999 I think)

— Geoff Robbins (@_TheGeoff) October 27, 2013

@peterrowlett Realise solution is far more complicated than FLT is, but if you can write a good pop-sci book on it it’s do-able!

— Geoff Robbins (@_TheGeoff) October 27, 2013

Mitch Keller wanted, quite reasonably, to know what I meant by taught.

@peterrowlett Define “taught”. Validity of Four Color Theorem is officially younger than that, but proof is not taught, obviously. — Mitch Keller (@MitchKeller) October 27, 2013

I suppose that the statement of the Four Colour Theorem (1976) is much older (Guthrie, a student of De Morgan, in or prior to 1852), so if the statement and the fact of its truth is all that is being taught, it is not really covering a 1976 result. Still, this is quite an issue with the statement of my question.

Luke Bacon replied with a lecturer who snuck a recent result of his own into a lecture, though I think that may be cheating!

@peterrowlett geometry lecturer at Imperial covered something which he’d proved about 5 yrs ago (I think) – will see if I can find out what!

— Luke Bacon (@lukebacon) October 27, 2013

So am I only interested in well-known results? What if Wiles gave a course on Wiles’ proof? I still don’t feel like that counts.

Samuel Hansen hammered the final nail in the coffin of my poorly-posed question.

@peterrowlett I don’t know what it would be, but I bet people in an applied math track see some very new algorithms.

— Samuel Hansen (@Samuel_Hansen) October 27, 2013

He’s right, of course, and this makes the question of what is the most recent result taught in undergraduate mathematics very difficult to answer. It is difficult to pose a better question (I’ve tried), but really I am interested to know what is the most recent result that is recognisable to most as being part of undergraduate mathematics.

Beyond being a nice footnote in my talk, I am interested to learn how much influence recent results have had on the modern teaching of mathematics. I remember an applied maths lecturer talking to my undergraduate class about relativity and saying “this stuff is nearly 100 years old, we really ought to be teaching it to you”. Is there merit in that position, or do we accept that modern mathematics is only accessed by the few who advance to mathematics at Masters and PhD level?

- Something to do with complexity and computational graph theory. [↩]

Would classification of finite simple groups count?

This hints at a similar difficulty to the Four Colour Theorem – yes, but how much of it is taught? I expect results from it may be used but isn’t the whole business thousands of pages?