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Avi Wigderson is the only person in history to have won both a Turing Award (computer science) and Abel Prize (math). I interviewed him all about his field. We discussed:
• His intuition on a proof of P vs NP
• Why we use SAT solvers for most NP problems
• Zero knowledge proofs and their impact
• Quantum computation and implications
• Math and computer science's relationship
Where to watch:
• YouTube: https://t.co/zViqAulFCo
• Spotify: https://t.co/iat08Xob17
• Apple Podcasts: https://t.co/jOYDGtGVnt
• Transcript: https://t.co/k4zS7yOhnw
Thank you to this episode's sponsors for supporting my work:
• WorkOS: makes your app Enterprise Ready with easy to use APIs to add SSO, SCIM, RBAC, and more in just a few lines of code, check them out at https://t.co/y8noBzFEem
Timestamps:
00:00 - Intro
01:08 - P vs NP
14:51 - What if you relaxed correctness
25:38 - Why NP complete problems are equivalent
30:33 - Space vs time complexity
43:06 - Why people use SAT solvers
45:53 - Randomness is a resource
55:48 - Randomness depends on computational power
01:21:20 - Zero knowledge proofs and their significance
01:38:30 - Quantum computation and why it matters
01:56:24 - Math vs computer science
02:08:16 - Major breakthroughs and his experience
02:12:31 - Advice for his younger self
02:14:48 - Outro
@PolycomputingAI I have lots to say about the atrocities being committed by Bibi Netanyahu in the name of the Israeli people. It must end. And there must be a two state solution. There must be a way for Palestinians and Israelis to live in peace. The murder of innocents is murder period.
@ShujaaAzmi lol you have no clue what you are talking about. GH was historically ruled by Kashmiri Dogra with a governor appt. This is well documented across so many sources.
Pakistan’s diplomatic efforts between the U.S. and Iran have helped prevent a return to full-blown war.
The EU is ready to contribute to a sustainable and peaceful resolution.
We bring economic leverage, hard-won nuclear expertise, longstanding relationships with Gulf partners, and direct engagement with Iran itself.
My press remarks with @MIshaqDar50 in Islamabad ↓
Local minima are rare in high dimensions because a strict local minimum has to curve upward in every direction, so all Hessian eigenvalues must be positive.
In a D-dimensional toy model where eigenvalue signs are independent, that’s a 2^(-D) event. In GOE-like random matrix models, positive definiteness is even rarer, roughly exp(-cD^2).
So as dimension grows, random critical points are much more likely to be saddles than minima. This is one reason high-dimensional optimization is often a saddle-escape problem, not a bad-local-minimum problem.
Wrote up some of the math here: https://t.co/vkaVqVD64N
@mehroozw congress leaders snubbed a more senior Jinnah for Gandhi, did poverty politics and ensured pakistan was hostile by not giving pakistan its share at independence?