Sporadic Groups - Prof Richard Borcherds - The Archimedeans

Prof. Richard Borcherds received a Fields medal in 1998. He is most famous for proving Monstrous Moonshine, a conjecture of John Conway and Simon Norton relating the Monster group to modular forms. Professor Borcherds' work has also played an important role in Quantum Field Theory and other areas of physics.
The longest published proof in mathematics, covering maybe around 20000 pages, is the classification of finite simple groups. It shows that every finite simple group is either contained in one of 18 infinite families, or is one of 26 exceptions called the sporadic groups, ranging in size from the Mathieu group M11 with 7920 elements to the Fischer-Griess monster group with 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000 elements. This talk will describe some of these sporadic groups.
No prerequisites are required, but it would be helpful to know what a group is.
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[@m.alperenyasar3118]

I am not a mathematician nor a physicist but Prof. Richard Borcherds was so clear even I understood this topic. I'm really glad that I have found this video ^^

[@j.mauricerojas3650]

What a beautifully clear talk! So nice to see a Fields medalist take the time to give such an accessible talk! Thank you!

[@bman420_]

Great questions from the audience

[@henrikljungstrand2036]

The techniques used for proving the classification of finite simple groups might be useful for proving similar results about Hopf algebras, and possibly some classes of loops that are well behaved enough like e.g. Left Bol loops (Moufang loops were surprisingly little more complicated than groups when it comes to simplicity).

[@jimmypk1353]

I hit pay dirt today! Instantly subscribed!

[@nicholaswilliams4507]

Adam (blue shirt) had some great questions! Thanks, Adam, wherever you may be.

[@fjfaase]

For John Conways water based 'computer' (actually more of a logic circuit), google for: This early computer was based on a urinal flush mechanism

[@sasha-2574]

46:34 must be a floating point error or something why those are "almost integers" in some super computer

[@richardboland1935]

OK cool.
So my next dnd adventure is going to feature radiolarians for sure.
😛

[@sasha-2574]

45:18 This is advanced mathematics

[@adrianorizabal6122]

3 little blue boys and a brown guy brought me here

[@user09832]

Strangely enough they look like the greek letter pi

[@hyperduality2838]

Elliptic curves are dual to modular forms.
"Perpendicularity in hyperbolic space is measured in terms of duality" -- Professor Norman Wildberger.
Positive curvature is dual to negative curvature -- Gauss, Riemann geometry.
Gravitation is equivalent or dual to acceleration -- Einstein's happiest thought, the principle of equivalence (duality).
Fractals = self similarity, self equivalence = self duality!
The Klein bottle contains two mobius loops when cut in half -- self intersection = duality.
Energy is duality, duality is energy.
Time duality -- the future is dual to the past.

[@00000ghcbs]

Name checks out

[@hyperduality2838]

@@00000ghcbs Duality within duality = quadrality or meta, hyper- duality.
Mind is dual to mass -- Descartes.
Concepts are dual to percepts -- the mind duality of Immanuel Kant.
Bosons (waves) are dual to Fermions (particles) -- matter or wave/particle quantum duality.
Mind duality is dual to matter duality.
There is a deeper or second level of duality at work.

[@Kalumbatsch]

​@@hyperduality2838 Excuse my adversariality, but I doubt the optimality of this inconsequential banality.

[@hyperduality2838]

@@Kalumbatsch The conservation of duality (energy) will be known as the 5th law of thermodynamics! All energy is dual in physics!
Einstein is telling you that gravitational energy is dual.
Potential energy is dual to kinetic energy.
Apples fall to the ground because they are conserving duality.
Once you understand duality you can create new laws of physics!
Homotopic equivalence = duality!

[@Kalumbatsch]

@@hyperduality2838 But look at the veridical superficiality and potential impracticality of this conceptuality.

[@davidwilkie9551]

Grouped conglomerations of prime-connection coordination in ONE-INFINITY Quantum-fields Mechanism of AM-FM QM-TIME Communication Completeness/Singularity positioning of logarithmic numberness condensation.
I Agree, in absolute principle.

[@rossevans11]

It saddens me that some stupid prank channel can garner millions of subscribers showcasing banal idiocy, but high quality pedagogy, is largely ignored. We really can't claim that we don't have exactly the kind of society we deserve.