When archaeologists excavating ancient sites in Mesopotamia found endless small baubles, they often weren't interested. But Denise Schmandt-Besserat was. Tim Harford traces the origins of counting. Oxford Mathematics Public Lecture, online 31 July, 5pm BST: youtube.com/watch?v=BHqxRC…

What’s this got to do with Mathematics? Well, nothing. And everything. This is Godstow Nunnery (or Abbey), closed by Thomas Cromwell in 1539 & one of the places our mathematicians named when we asked them where in Oxford they go to get away from it all. Where's yours?

If someone only has your birth date, gender & brief zip/postcode, surely they can't find you? Think again. Tim Harford discusses data anonymity in this clip from his Oxford Mathematics Public Lecture on the past, present & future of counting. Full lecture: youtube.com/watch?v=BHqxRC…

How sophisticated is the maths in AI? Go on, have a guess. Because guessing is what AI itself would do. Terry Tao introduces his Oxford Mathematics London Lecture, a journey through the potential for AI in science & maths. Watch from 5pm BST, Wed 7 August: youtu.be/_sTDSO74D8Q

Roger Penrose is 93 today (not an interesting number, he says), but where in spacetime does he go to get away? A short walk from Oxford Mathematics are the Trap Grounds, 10 acres of wetland, woodland & grassland where you sit & forget about black holes & twistors etc. Or you don't.

Does AI have a plausibility problem? Or rather, do we have a problem with AI's plausibility? Watch Terry Tao's full Oxford Mathematics Public Lecture (supported by XTX Markets) as he suggests new ways of doing mathematics in an artificial intelligence future. youtube.com/watch?v=_sTDSO…

Mathematicians lend their names to theorems. But behind the name is a life. In Stefan Banach’s case a traumatic one as a Polish man living through World War II. Banach’s contraction mapping theorem features in our latest 1st year student lecture. Watch: youtube.com/watch?v=PEosQo…

Are numbers essential for counting? Probably, in a world where we don’t just want to know if something is good, but exactly how good. But it wasn’t always the case. Watch the full lecture as Tim Harford shows we don't always understand the data we have: youtube.com/watch?v=BHqxRC…

Port Meadow is an ancient area of grazing land on the edge of Oxford that, legend has it, has not been ploughed for 4,000 years. It is home to horses and cows; and Oxford Mathematicians seeking to get away from things, perhaps at sunset, as a paraglider files overhead.

One thing you can guarantee about social media is that if you want 20 million views of your films, don't put up clips from student maths lectures. Unless the lecturer is Philip Maini. He's back with 3 lectures on Mathematical Biology. 40 million? No 1: youtu.be/Kvu1ZiD_nNI

When our mathematicians need a miracle, or just a break, some visit Treacle Well. St Frideswide (d. 727) used the waters to cure all ills. Very handy if you're stuck with a problem. Not just current Oxford Mathematicians. The well stars in Lewis Carroll's 'Alice in Wonderland'.

Might human and artificial intelligence (AI) have more in common than you think? In their creation of language, for example. Terry Tao improvises in his Oxford Mathematics Public Lecture. Watch the full lecture: youtube.com/watch?v=_sTDSO…

Toilet humour has no place in a student maths lecture. Unless you want to get to the bottom of an excitable system. Yes, Philip Maini is our washroom attendant in this clip from the 2nd of 3 of his Mathematical Biology lectures we are showing. Lecture: youtube.com/watch?v=J3rFoi…

Oxford Mathematician and Fellow of St John's College Philip Maini has been awarded the Sylvester Medal by the The Royal Society for his contributions to mathematical biology. Pretty good teacher too. maths.ox.ac.uk/node/68841 Photo: Robert Taylor/St John's

So what do you fancy today? Carrollian holograms? The Möbius function? Software to tackle pollution? Additive v multiplicative structure over integers? We can do all that & more. We've 100s of case studies online: pure, applied & all things combined. maths.ox.ac.uk/research/case-…

Might Artificial Intelligence (AI) make mathematics more accessible to more people? Terry Tao thinks it could. Full lecture: youtube.com/watch?v=_sTDSO…

As university terms heave in to view, how about our 1st year 'Introduction to University Mathematics' course? Eight lectures explaining the mathematical move from high school to higher school. Or, if you're considering maths at university, take a look? youtube.com/playlist?list=…

We miss our undergraduates when they're gone over the cruel summer. The place is just a little subdued. But they'll be back soon, including Luke who, before he left, gave you all a puzzle to ponder. Shine a light Luke, shine the light.

'It's not about me, it's about the team'. You hear it all the time from sports players. Surely it's not true for mathematics? Increasingly it is, notably in mathematical biology. Over to Philip Maini. His 2nd year student lecture on infectious diseases: youtube.com/watch?v=slQ-sR…

As children we put a shell to our ear to hear the sea. We should look more closely at the shell's shape. Nature, all curved edges, non-flat faces and few, if any, sharp corners, has inspired a new class of mathematical shapes: soft cells. maths.ox.ac.uk/node/68734 Alain Goriely