@littmath I don’t think there’s a ceiling. There’s too much maths in the world for one person to know most of it, but if you can handle university level maths then I see no reason to stop at any imaginary ceiling, if it’s an area you want to spend time on
One thing I find obnoxious about “hitting a ceiling in math” discourse is that it’s mostly based on people’s self-reports of having found some topic too hard. But my experience teaching math is that people are often wrong when they make such claims!
Il primo genoma umano fu sequenziato completamente nel 2003. Ci misero 13 anni e spesero 2.7 miliardi di dollari.
Pochi giorni fa sono riusciti a sequenziarlo (molto meglio) in 4 ore, spendendo meno di 1000 dollari.
Questo è il progresso che viviamo oggi nel mio campo.
Solid mathematical ideas almost always outperform contrived engineering tricks.
For years deep learning has been dominated by increasingly complex architectural hacks: CNN blocks, attention layers, channel mixers, residual pathways, normalization stacks.
Every few years a new architecture is announced as if it were a revolution.
One of the most famous examples was Kaiming He and Residual Networks (ResNet). At the time he was paraded around the AI world like a celebrity because residual connections supposedly “solved” deep learning.
But these were largely engineering patches.
Now something much more interesting appeared.
A new architecture called CliffordNet returns to mathematics — specifically Clifford Algebra, developed in the 19th century by William Kingdon Clifford.
Instead of stacking arbitrary modules, the model is built around the geometric product
uv = u·v + u∧v
A single algebraic operation that simultaneously captures inner product structure and geometric interactions.
In other words: the math already contains the interaction mechanism.
No attention blocks.
No mixer layers.
No architectural spaghetti.
The result:
• 77.82% accuracy on CIFAR-100 with only 1.4M parameters
• roughly 8× fewer parameters than ResNet-18
And with strict O(N) complexity.
The paper even suggests that once geometric interactions are modeled correctly, feed-forward networks become largely redundant.
A good reminder for the AI community.
Engineering tricks can dominate for years.
But eventually mathematics shows up and deletes half the architecture.
Paper:
[https://t.co/QIkCCO1tYs)
19th century geometry just walked into computer vision.