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iagoleal.com | ||
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www.jeremykun.com
So far on this blog we've given some introductory notes on a few kinds of algebraic structures in mathematics (most notably groups and rings, but also monoids). Fields are the next natural step in the progression. If the reader is comfortable with rings, then a field is extremely simple to describe: they're just commutative rings with 0 and 1, where every nonzero element has a multiplicative inverse. We'll give a list of all of the properties that go into this "simple" definition in a moment, but an even more simple way to describe a field is as a place where "arithmetic makes sense. |
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mark.engineer
[AI summary] The user shared an extensive account of their project to compute the first 255 digits of π using an Intel 4040 CPU, which is over 50 years old. They described their hardware setup, firmware modifications, and optimization techniques to achieve the computation within a significantly reduced time compared to earlier estimates. The project involved custom firmware, precise timing control, and a spigot algorithm to calculate π's digits efficiently on vintage hardware. The final run completed the task in approximately 69 hours, showcasing the potential of optimizing algorithms for older processors. |
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terrytao.wordpress.com
One of the most notorious problems in elementary mathematics that remains unsolved is the Collatz conjecture, concerning the function $latex {f_0: {\bf N} \rightarrow {\bf N}}&fg=000000$ define... |
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scilogs.spektrum.de
The eerily prescient thoughts of Alan Turing, the visionary who laid the foundations of computer science, remain remarkably relevant to today's discussions concerning AI. Read more |
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