Recent claims are that DeepSeek-R1 decreases the need for multi-billion dollar compute systems for AI. Is this correct? Here we look at history to find out.

John D. Cook Consulting Blog

29.01.2025

Matrix representations of number systems

Representing complex numbers, dual numbers, and double numbers as real 2 by 2 matrices.

John D. Cook Consulting Blog

28.01.2025

Euler’s formula for dual numbers and double numbers

Analogs of Euler's formula exp(ix) = cos(x) + i sin(x) in other number systems, namely dual numbers and double numbers.

John D. Cook Consulting Blog

24.01.2025

A magical land where rounding equals truncation

The balanced ternary number system has many interesting properties, including the fact that truncation is the same as rounding.

John D. Cook Consulting Blog

24.01.2025

Tricks for radix conversion by hand

Radix conversion is tedious to carry out by hand in general, but in some special cases there are tricks to make it easier.

John D. Cook Consulting Blog

24.01.2025

Double rounding

If you round a number to one precision and then again to another precision, you may get a different result than if you had rounded directly.

John D. Cook Consulting Blog

23.01.2025

Duplicating Hankel plot from A&S

Using Mathematica to reproduce an interesting plot from Abramowitz and Stegun

John D. Cook Consulting Blog

20.01.2025

Quadrilateral area | Brahmagupta and Bretschneider formulas

How to find the area of a quadrilateral from the lengths of its sides. Generalizations of Heron's formula

John D. Cook Consulting Blog

19.01.2025

Chebyshev and Russian transliteration

It's not simple to transliterate Russian names to English. Sometimes there is a unique mapping, or at least a standard mapping, of a particular name, but often there is not. An example that comes up frequently in mathematics is Pafnuty Lvovich Chebyshev (1821–1894). This Russian mathematician's name Пафну́тий Льво́вич Чебышёв has been transliterated at Tchebichef,

John D. Cook Consulting Blog

19.01.2025

Entering Russian characters in Vim with digraphs

How to enter Russian letters in Vim using digraphs. What is the logic to how digraphs correspond to Russian letters

John D. Cook Consulting Blog

19.01.2025

An unexpected triangle | Sonine's formula

Sonine's formula surprisingly evaluates an integral in terms of the area of a triangle formed by the integral parameters

John D. Cook Consulting Blog

17.01.2025

Can AI Models Reason: Is Data All You Need?

Lack of enough training data is widely seen as a limiter for developing more powerful AI models. Is this problem solvable? Here we examine the issues.

John D. Cook Consulting Blog

17.01.2025

Dimensional analysis for gamma function values

Thinking of factorials and gamma function values as having dimensions can make equations easier to remember, find errors, and suggest results.

John D. Cook Consulting Blog

16.01.2025

Why use homomorphic encryption to eliminate third parties?

Encryption technology can eliminate the need to trust third parties, but why is that a good thing? What are the motivations and tradeoffs

John D. Cook Consulting Blog

16.01.2025

Falling power analog of binomial theorem

The Chu-Vandermonde theorem, when written in the right notation, looks very much like the binomial theorem.

John D. Cook Consulting Blog

15.01.2025

Newton series notation and convergence

Newton's interpolation formula is complicated without the right notation. With the right notation it looks very similar to Taylor's formula.

John D. Cook Consulting Blog

12.01.2025

Consulting Podcast

A friend just sent me an audio file of a podcast about my consulting that he created by asking an AI to crawl my web site. The podcast is a remarkably natural-sounding conversation between two synthetic hosts. The only clues that the audio is automatically generated are a couple of mispronounced acronyms. Download

John D. Cook Consulting Blog

12.01.2025

Podcast feed

Announcing a new VERY OCCASIONAL podcast.

John D. Cook Consulting Blog

10.01.2025

RSA security in light of news

Someone factored a 512-bit RSA key for $8 of computing resources. What does that imply about RSA keys of recommended length?

John D. Cook Consulting Blog

08.01.2025

Quick change directory

A shell script to quickly change to commonly used directories.

John D. Cook Consulting Blog

08.01.2025

Can AI models reason like a human?

Many claims and counterclaims are made about the abilities of AI models to reason. Can they think like a human? In this article we explore the issues.

John D. Cook Consulting Blog

07.01.2025

Efficiently factoring RSA modulus from public private keys

If you can factor large numbers, you can break RSA encryption. But if you can break RSA encryption, can you factor large numbers?

John D. Cook Consulting Blog

03.01.2025

Unicode Stegonography

Unicode characters with different values that look the same can be used to hide messages inside other messages. Can also be used maliciously to trick users.

John D. Cook Consulting Blog

02.01.2025

Abelian groups of order 2025

How many distinct Abelian groups are there of order 2025? More generally, how do you find all the Abelian groups of any order?

John D. Cook Consulting Blog

02.01.2025

Carnival of Mathematics 235

Carnival of Mathematics 235. Posts from math bloggers around the internet.

John D. Cook Consulting Blog

02.01.2025

Up to isomorphism

When "up to isomorphism" needs to be said and doesn't need to be said. Isomorphic ways of listing the groups of order 2025.

John D. Cook Consulting Blog

01.01.2025

Details of generating primes for cryptography

RSA public key cryptography requires finding a couple large primes. You essentially do this by testing random numbers until you find primes, but not quite.

John D. Cook Consulting Blog

01.01.2025

Cycle of New Year’s Days

How the day of the week for New Year's Day cycles every 28 years, almost.

John D. Cook Consulting Blog

30.12.2024

What exactly is a second?

A second is now defined in terms of periods of radiation from a cesium atom. Why was this necessary? Why cesium? What the particular number of periods?

John D. Cook Consulting Blog

28.12.2024

Unix Time and a Modest Proposal

Why Unix time is not exactly what it is often described to be, and a proposal for fixing it.

John D. Cook Consulting Blog

25.12.2024

Asymptotic series for the reciprocal of the gamma function

The relation between the asymptotic series for the gamma function and its reciprocal is simpler than we'd expect.

John D. Cook Consulting Blog

25.12.2024

Most popular posts of 2024

Most popular posts on this site in 2024, according to Hacker News.

John D. Cook Consulting Blog

24.12.2024

Starlink satellite configutations

If you see a line of lights in the sky, it's likely a set of Starlink satellites launched at the same time.

home›John D. Cook Consulting Blog›Science

John D. Cook Consulting Blog - Science

Cayley tables and Latin squares

The Buenos Aires constant

1 + 2 + 3 + … = −1/12

Russian Morse Code

Chebyshev polynomials of the third and fourth kind

Multiple angle asymmetry

Sparse binary Pythagorean triples

DeepSeek-R1: Do we need less compute now?

Matrix representations of number systems

Euler’s formula for dual numbers and double numbers

A magical land where rounding equals truncation

Tricks for radix conversion by hand

Double rounding

Duplicating Hankel plot from A&S

Quadrilateral area | Brahmagupta and Bretschneider formulas

Chebyshev and Russian transliteration

Entering Russian characters in Vim with digraphs

An unexpected triangle | Sonine's formula

Can AI Models Reason: Is Data All You Need?

Dimensional analysis for gamma function values

Why use homomorphic encryption to eliminate third parties?

Falling power analog of binomial theorem

Newton series notation and convergence

Consulting Podcast

Podcast feed

RSA security in light of news

Quick change directory

Can AI models reason like a human?

Efficiently factoring RSA modulus from public private keys

Unicode Stegonography

Abelian groups of order 2025

Carnival of Mathematics 235

Up to isomorphism

Details of generating primes for cryptography

Cycle of New Year’s Days

What exactly is a second?

Unix Time and a Modest Proposal

Asymptotic series for the reciprocal of the gamma function

Most popular posts of 2024

Starlink satellite configutations

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