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This is real, and incredibly dangerous. The Russians ran their first major tryout of cyber warfare to try to shut down Estonia TEN YEARS AGO. It took the Estonians several days to recover, and is why this tiny nation now has awesome cyber defenses https://t.co/4C4hplSUo5 https://t.co/hj53UWiAQF
— Keith Devlin (@profkeithdevlin) July 15, 2018
This problem dedicated to the Memory of our friend Alexander Bogomolny. @CutTheKnotMath @nntaleb @SvetlanaBogom13 #math pic.twitter.com/pFepfWfNDb
— Sam Walters ☕️ (@SamuelGWalters) July 14, 2018
Juego de Diagramas de Voronoi #MathGames https://t.co/gfroTj920b
— Juan Miguel Ribera (@juanripu) July 15, 2018
Estoy seguro que @ClaraGrima , @juliomulero y muchos otros pasarán un rato entretenido jugando pic.twitter.com/mID70LrbrG
Richard #Feynman's Integral Trick. (Neat bit of integration. If an integral is hard but depends on a parameter t, try differentiating it with respect to t to see if it could help solve it.) https://t.co/v93YbVKQYy
— Sam Walters ☕️ (@SamuelGWalters) July 17, 2018
Should zero be included in the set of natural numbers?
— Joshua Bowman (@Thalesdisciple) July 11, 2018
Antimatter is amazing: it means negative numbers are real. Yes, you can have -3 particles: it's called having 3 antiparticles! Just as 3 - 3 = 0, three antiparticles can annihilate three particles of the same kind. But the discovery of antimatter is a funny story (cont.) pic.twitter.com/XWGQFLUDTe
— John Carlos Baez (@johncarlosbaez) July 15, 2018
Amazing how much fun can be had with random points on a sphere! A team of mathematicians on Twitter just discovered a cool connection between Catalan numbers and the distance between random points on the sphere in 4d - using the quaternions!https://t.co/g40n7DWAK1
— John Carlos Baez (@johncarlosbaez) July 11, 2018
We've discovered a surprising fact about the probability distribution of distances between random points on spheres! A mysterious mathematician known only as "Lucia" finished the job. It's fun having collaborators you don't even know.https://t.co/3TrODkZTLO
— John Carlos Baez (@johncarlosbaez) July 12, 2018
#Mathematics is about interesting #algebra processes too. Here's an old one that I very much enjoy: obtaining #Euler's product formula for the #Riemann zeta function involving prime numbers - using only very basic algebra. (Note the rhythm!) pic.twitter.com/z4pLF5rdyc
— Sam Walters ☕️ (@SamuelGWalters) July 12, 2018
The equations of general relativity have solutions that describe weird things that probably don't exist but *might*. Einstein didn't believe in the Big Bang and black holes at first. They exist. His theory also allows black holes that move at light speed. Do those exist? pic.twitter.com/5hz2Yt2kvJ
— John Carlos Baez (@johncarlosbaez) July 16, 2018
A five day workshop focused on women in academic leadership will take place @umanitoba in October. https://t.co/g7V3MIaS1O
— James Colliander (@colliand) July 11, 2018
Today we learn about the Spectral Theorem (in a nutshell). If you take a Hermitian matrix, and you diagonalize it, you can break it down into it's "eigen-components," thereby obtaining a representation that is readily generalizable to infinite dimensional Hilbert space. #math pic.twitter.com/hwQ0HCjFpZ
— Sam Walters ☕️ (@SamuelGWalters) July 11, 2018
Though matrices don’t generally commute, here’s a simple case where they can be switched around a third matrix. (It’s not hard.) #math #algebra pic.twitter.com/UWlhJPUiEx
— Sam Walters ☕️ (@SamuelGWalters) July 14, 2018
Every time I see a person in a coffee shop with a notebook and lots of colored markers I just assume they're a low dimensional topologist.
— Anna Haensch (@extremefriday) July 12, 2018
Enriched profunctors sound scary, but here's a nice one. Two islands C and D with one-way toll roads between some cities - and one-way plane trips from some cities in C to some in D. What's the cheapest trip from E to c? I explain the theory here: https://t.co/a3IYJ0sgrO pic.twitter.com/YtYwsoF9je
— John Carlos Baez (@johncarlosbaez) July 14, 2018
Our 3-D model of immune cells attacking tumor cells after testing immunogenicity is fully #opensource. It comes free in every #PhysiCell download! Please feel free to extend it. (Citations to the @PLOSCompBiol paper appreciated! ;-) )#opensource and #openscience at #SMB2018 pic.twitter.com/if48vlJlla
— Paul Macklin (@MathCancer) July 12, 2018
Entrevistra a LA mestra de mestreshttps://t.co/TIfRdni9de
— Daniel Ruiz Aguilera (@druizaguilera) July 15, 2018
The notion of a tensor is a generalization of a vector. Tensors are very essential in #Einstein's General Relativity and in #Quantum theory. Tensor products and tensors are very much related -- by means of tensor products one can build all tensors. #math #physics pic.twitter.com/62kGwkPdRA
— Sam Walters ☕️ (@SamuelGWalters) July 17, 2018
In 1977, Kip Thorne and Anna Żytkow figured out what happens when a neutron star - a ball of neutronium 25 kilometers across - hits a normal star. It's called a "Thorne-Żytkow object" or TŻO. Now astronomers may have found one in the Small Magellanic Cloud! Read on.... pic.twitter.com/dr7WK0y6OQ
— John Carlos Baez (@johncarlosbaez) July 17, 2018
This is the free modular lattice on 3 generators, where "modular" means A∨(B∧C)=(A∨B)∧(A∨C) when A<B or A<C. The free modular lattice on 4 generators is infinite! This one is connected to representations of the D4 quiver, but big mysteries remain: https://t.co/2PVLAWNpc4 pic.twitter.com/lRCQuyhLDp
— John Carlos Baez (@johncarlosbaez) July 14, 2018