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The two cultures of mathematics and biology
I’m a (50%) professor of mathematics and (50%) professor of molecular & cell biology at UC Berkeley. There have been plenty of days when I have spent the working hours with biologists and…
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Computational Knowledge and the Future of Pure Mathematics
Proposing technology for pure mathematics: curating concepts, constructs, theorems, & literature; precise symbolic language; automated computations...
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Gray Code
What are Gray codes, and why are they so useful?
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How medieval astronomers made trig tables
Clever tricks used by medieval astronomers to tabulate sines at every degree, before calculators and before calculus.
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Cylinders in Spheres
What is the largest volume cylinder it is possible to carve from a solid sphere? Also, so you know about the napkin ring problem?
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On the Computational Complexity of MapReduce
I recently wrapped up a fun paper with my coauthors Ben Fish, Adam Lelkes, Lev Reyzin, and Gyorgy Turan in which we analyzed the computational complexity of a model of the popular MapReduce framework. Check out the preprint on the arXiv. Update: this paper is now published in the proceedings of DISC2015. As usual I’ll…
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Why 'gallons per mile' is better than 'miles per gallon'
Why we should really be quoting fuel consumption figures as 'gallons per mile' and not 'miles per gallon'.
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Correlation is usually not causation. But why not?
Correlations are oft interpreted as evidence for causation; this is oft falsified; do causal graphs explain why this is so common, because the number of possible indirect paths greatly exceeds the direct paths necessary for useful manipulation?
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How a mathematician constructed a decision tree to solve a medical problem
Here’s an excerpt from Love and Math, a book by Edward Frenkel. The author writes about mathematics and his career. One of the stories is about …
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A Gentle Introduction to Backpropagation
A gentle introduction to backpropagation, a method of programming neural networks
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Terry Tao on how to compute non-converging infinite sums (2010)
The Riemann zeta function $latex {\zeta(s)}&fg=000000$ is defined in the region $latex {\hbox{Re}(s)>1}&fg=000000$ by the absolutely convergent series $latex \displaystyle \zeta(s) = \su…
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A Gentle Introduction to Data Compression
Joe Bertolami's portfolio and blog covering artificial intelligence, game development, computer graphics, data compression, and more.
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How to compile with continuations
In terms of unreasonable effectiveness, the transformation to continuation-passing style (CPS) ranks with the Y combinator .
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The Generalist – On Alexander Grothendieck
I never met Alexander Grothendieck. I was never in the same room with him. I never even saw him from a distance. But whenever I think about math — which is to say, pretty much every day ̵…
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Making of “Introduction to A*”
(Warning: these notes are rough – the main page is here and these are some notes I wrote for a few colleagues and then I kept adding to it until it became a longer page)
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Planjure: A* and Dijkstra's in Om
I wrote Planjure to learn ClojureScript and Om. It’s a fun little program. You paint islands on a canvas and run path-planning algorithms to find the optimal path for your ship to traverse from start to finish. Sailing across blue ocean is faster than hiking through green islands. The three algorithms implemented are…
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New partition function record: p(10^20) computed
The partition function p ( n ) counts the number of partitions of n , i.e. the number of ways n can be written as a sum of positive integers when disregarding the order of the terms. For example, 4 has the five distinct partitions 4, 3+1, 2+2, 2+1+1, 1+1+1+1, so p (4) = 5. This week, I set a new record by computing…
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Selection bias and bombers (2008)
During WWII, statistician Abraham Wald told the RAF to add armor where it didn't seem planes needed it. But he was right.
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The Derivative of a Number
Are you kidding? Edward Barbeau is now a professor emeritus of mathematics at the University of Toronto. Over the years he has been working to increase the interest in mathematics in general, and e…
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The Firing Squad Problem
In 1957, John Myhill first posed an interesting problem that was closely related to computer programming, but did not require any related background to solve. Dubbed the "firing squad synchronization problem," the puzzle was passed along by word of mouth and first solved by Marvin Minsky and John McCarthy. However…
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