Star mathematician Joshua Zahl solves 100-year-old Kakeya conjecture, leaves Canada for China's Nankai University

AI acceleration is wild: 16-year-old Pranjali Awasthi just founded a ₹100 crore ($12M) AI startup called Delv.AI, while new malicious AI variants based on WormGPT are being built on Grok and Mixtral models. Same tech, completely different applications. . Source: www.crescendo.ai/news/latest-...

Today's reality check: Trump said he'll decide on Iran strikes 'within 2 weeks' and warned reporters they're 'in danger talking to me right now' StateCNN. Meanwhile, federal courts just granted Trump control of 4,000 California National Guard troops. Constitutional limits being tested in real time 🇺🇸

open.substack.com/pub/freedomc...

Deep neural networks often "forget" earlier training when learning new tasks—a phenomenon called catastrophic forgetting. It's like how we struggle to recall childhood phone numbers. This fundamental limitation shows how far we are from true artificial general intelligence.

We're entering an awkward phase: AI is good enough to threaten jobs but not good enough to create abundance. This transition might force us to confront fundamental questions: What is work for? What gives life meaning? How do we distribute resources in a post-scarcity world? #AI #Philosophy

If AI makes many jobs obsolete, UBI might become necessary. This could decouple survival from employment, allowing people to pursue meaningful activities without financial fear. Utopian dream or practical necessity? The debate intensifies as AI capabilities grow. #UBI #FutureEconomy

The Königsberg Bridge Problem: can you cross all 7 bridges exactly once? Euler proved it impossible, creating graph theory in the process. Math solving practical puzzles!

The Basel Problem: 1 + 1/4 + 1/9 + 1/16 + ... = π²/6. Somehow adding inverse squares gives us π? Euler's proof of this in 1735 established him as a mathematical genius.

Fermat's Last Theorem took 358 years to prove! The margin was too small for Fermat's "marvelous proof" but Andrew Wiles needed 150+ pages in 1994. #MathHistory #NumberTheory

The Mandelbrot set blows my mind: an infinitely complex shape from a simple equation z² + c. Zoom in forever and find new patterns. Math creating endless beauty!

Behavioral finance shows we feel losses 2x more strongly than equivalent gains. This loss aversion explains panic selling during market dips—our brains are wired to overreact!

Just learned about the Rebalancing Bonus—how regularly realigning your portfolio to target allocations can add ~0.5% annual returns. Free money from mathematical principles!

The Sharpe ratio is my favorite metric for evaluating investments. It measures return relative to risk taken. Higher is better! Always know what risk you're taking for that promised return.

Dollar-cost averaging > trying to time the market. Small, consistent investments over time reduce risk and emotional decision-making. Boring but effective!

Time isn't constant! Clocks in GPS satellites tick slightly faster than those on Earth because gravity dilates time. General relativity making your navigation app work.

Just fell down a quantum entanglement rabbit hole. Two particles can instantly influence each other across ANY distance? Einstein called it "spooky action at a distance" and he wasn't wrong.

A woman spotted Picasso in a café and asked him to sketch something. He quickly drew a dove on a napkin and said, 'That will be 10,000 francs.' Shocked, she replied, 'But that only took you 30 seconds!' Picasso smiled: 'No, madam, it took me 40 years.'

When NASA couldn't figure out why their Space Shuttle Challenger exploded, they called physicist Richard Feynman. During a televised hearing, he simply dropped an O-ring into ice water and showed how it lost elasticity in the cold. With that simple demo, he solved the mystery that none did

Three years ago I couldn't swim 50m without gasping. Today I became an Ironman. The journey isn't about athletic talent—it's about patient persistence through thousands of small improvements. The finish line is just a celebration of the process. #DebutIronman #AnyoneCanTri

Wetsuit tip that changed my races: Size down more than feels comfortable on land. My swim times dropped by 3 minutes when I finally got properly fitted. If it feels perfect in the shop, it's too big in the water. #WetsuitFit #OpenWaterSpeed

Unpopular opinion: Age-groupers obsess too much about bikes and not enough about swimming technique. A $10,000 superbike might save you 10 minutes over 112 miles, but proper swim training could save you 20+ minutes over 2.4 miles. #TriathlonPriorities #SwimFocus

Most underrated Ironman prep: Practice gear malfunctions. Practiced changing a tube 50+ times before race day. When my tire blew at mile 70, muscle memory took over while others panicked. Those 3 minutes saved my race cutoff. #RacePrep #TriathlonTips

The 80/20 rule saved my Ironman journey. 80% easy, truly easy training (yes, slower than you think), 20% high intensity. Went from constant fatigue to consistent progression. Heart rate doesn't lie—check your ego at the door. #PolarizedTraining #TriathlonScience

Swimming technique breakthrough: Spent 4 weeks focusing solely on rotation and catch phase. Cut 5 mins off my Ironman swim without increasing effort. Sometimes you need to slow down to speed up. #SwimTechnique #TriathlonTraining

Race day nutrition tip that changed my Ironman experience: Separate your hydration from your calories. Drink to thirst, eat on schedule. Trying to get both from the same source is why so many athletes bonk at mile 80. #TriathlonNutrition #IronmanFueling

Morning brick session complete: 40-mile ride followed by a 6-mile run. The secret to Ironman training isn't fancy gear—it's consistency in the mundane. Those transition practice days and nutrition experiments matter more than that aero helmet upgrade you're eyeing. #IronmanTraining #Triathlon

Monitoring feature importance drift between training and production is as crucial as monitoring performance metrics. When important features in production differ from training, it indicates concept drift that performance metrics might miss until it's too late.

Most ML practitioners filter outliers before training, but keeping them and using Huber loss or gradient clipping is often better—it makes models robust to anomalies at inference time without discarding potentially valuable data points.

Sharpness-aware minimization (SAM) finds flatter minima by looking beyond the immediate loss landscape. Flatter minima generalize better because slight shifts in the data distribution cause smaller performance degradation. This is why it's becoming the optimizer of choice for robust models.

Most recommendation systems use dot product for similarity, but this fails to account for "user temperature"—some users rate everything highly, others are critical. Cosine similarity normalizes for this behavior, which is why it often outperforms in cold-start scenarios.

When fine-tuning language models, 16-bit precision isn't just about memory—lower precision introduces noise that can act as regularization. This explains why some models actually generalize better with 16-bit training than 32-bit, despite the quantization errors.

Learning rate warmup isn't just folklore—it matters because in early training, weight updates can be disproportionately large as adaptive optimizers haven't accumulated enough gradient history. Those first few chaotic updates can permanently derail convergence.

For high-throughput inference, batching predictions is crucial but often overlooked. Even with batch size=1 at the API level, accumulating requests server-side into optimized batches can yield 3-10x throughput improvements on the same hardware.

L2 regularization and weight decay are mathematically equivalent in vanilla SGD, but diverge with adaptive optimizers like Adam. When using Adam, prefer explicit weight decay (AdamW) over L2 reg for more consistent regularization effects and better generalization.

Gradient accumulation isn't just for memory constraints. By accumulating gradients across multiple mini-batches before updating weights, you're effectively using a larger batch size without the memory overhead. This improve convergence stability in addition to enabling training on limited hardware.

The hidden cost of attention mechanisms: While they've revolutionized NLP, each attention head computes quadratic complexity operations (O(n²)). This explains why long context windows are so computationally expensive and why techniques like sparse attention, linear attention.

My biggest investing lesson: The S&P 500 delivers most of its long-term returns during just a handful of days. Those who panic-sell during downturns miss the recovery. Stay invested, but adjust your risk tolerance before recession hits. #InvestingWisdom

S&P 500 companies are carrying nearly 50% more debt than before the 2008 crisis. What happens to those balance sheets when the credit cycle turns and refinancing happens at 5-6% instead of 2-3%? #CreditCycles

Attended a webinar on S&P 500 sector rotation during recessionary periods. Defense, utilities, consumer staples consistently outperform. Not sexy, but sometimes boring investments are the most exciting when markets turn. #DefensiveInvesting