A Mathematician’s View of Proof - Sarah Hart

Watch the Q&A session here: • Q&A: A Mathematician's...
The idea of proof is fundamental to mathematics. We could argue that science consists of testable theories, and therefore that it is about what can be disproved, not what can be proved. In law, the test is “beyond reasonable doubt”.
Famous conjectures in mathematics have been tested by computers for trillions of numbers - but we still call them conjectures.
In this lecture we’ll talk about what mathematicians mean by proof, and I’ll show you some of my favourites.
This lecture was recorded by Sarah Hart on 4th June 2024 at Barnard's Inn Hall, London
Sarah is Gresham Professor of Geometry.
She is also Professor Emerita of Mathematics at Birkbeck, University of London.
The transcript of the lecture is available from the Gresham College website:
www.gresham.ac.uk/watch-now/m...
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[@ed.puckett]

Even though I was already familiar with each of these theorems and some (but not all) of the proofs, I still feel enriched by this lecture. Sort of like "filling in the corners" and solidifying earlier understanding. Many times I needed to pause and write something down that the lecture sparked in my mind. The lectures from Gresham College are like this. Thank you Professor Hart and Gresham College!

[@digitalkittycat4274]

What a presentation !!! These kinds of lectures should also be given, now and then, to high school students to inspire them.

[@bazsnell3178]

Sarah Hart. Wonderful overall series. Great present lecture.

[@bobbybannerjee5156]

I wonder if anyone knows how did she manage to prepare the presentation in a way that helped her fill those regions in the circle starting at 7:50

[@nHans]

"Proof by exhaustion" 🤣

[@davidpnewton]

It's a serious way of proving things: exhausting all of the possibilities.

[@tgeofrey]

Thank you

[@drprashantbhatnagar6056]

I think this is only a glimpse of what is available to you for knowing in IKS. Please do make an effort

[@christophergame7977]

The offered proof of Pythagoras' Theorem relies on algebra. It's not a straight geometrical proof.

[@christophergame7977]

There are four phases of matter: solid, gas, plasma, liquid. What fools the ancients were to talk of earth, air, fire, and water! How much cleverer we are today!

[@ecMathGeek]

Just to provide some context: There are more than 4 phases of matter. I think one reason we are generally taught "4 phases of matter" is because those 4 happen to be relatively easy to explain. (Although plasma isn't that easy to explain and doesn't follow the same basic "rules" of the other three.) But it's also possible we have a bias towards those four because they parallel the four classical elements. It should be noted that "fire" is not a plasma. It is a chemical reaction. The state of plasma probably wouldn't have even been known about to ancient greeks.

[@christophergame7977]

@@ecMathGeek As I said, how much cleverer we are today! As a school child, I was taught that there were three phases of matter. I learnt of plasma only later.

[@davidpnewton]

Wrong terminology. A phase is a different thing to a state of matter. There can be many different solid phases of a material for example. They are all one state of matter: solid. However there are indeed more than four states of matter. Examples include a Bose-Einstein condensate and degenerate neutron matter.

[@christophergame7977]

@@davidpnewton Thank you for your valid point that a phase is a different kind of thing from a state of matter. Instead of 'phase'. I ought to have written 'state of matter'. Yes, today we recognise more than four states of matter. How much cleverer we are today! What fools the ancients were!

[@maxsonthonax1020]

That thumbnail is appalling.

[@drprashantbhatnagar6056]

Greeks borrowed their knowledge from Arabs who in turn owe it to Indian Knowledge System which during British colonial era suffered at the hands of their cancel culture. So you are advised to remove your bias and mental block about this fact.