How Google Makes Money

How much do a moose’s antlers weigh? Not a moose, but a moose’s antlers. Finding the answer takes less than 10 seconds thanks to our favorite search engine, Google. Even more impressive than how heavy moose antlers are (about 40 pounds or 18 kg: thanks, Google) is that we can find the answer to this, or almost any other question, for free.


In 2015, Google’s parent company, Alphabet, posted over 75 billion dollars in revenue and is projected to bring in over 80 billion dollars in revenue in 2016. Google brings in approximately 99% of Alphabet’s total revenue; so Google makes a ton of money. Yet a large portion of Google’s products are free to users. How does a company so integrated into our society, producing so much revenue, not charge its users? Easy, ads. Continue reading

What is a Proof?

Thanks to the four color problem, a rift rose between orthodox mathematicians and the budding computer science community over what comprises a proof. Recently when I was refreshing my memory on the four color problem, I became distracted by this disagreement and the question What is a proof?. So, I looked into some info surrounding these topics such as the history of proofs and proof assistants, problems mathematicians raise with proof assistants, and the validity of proof assistants.


Need to fake a proof? Have it generated.

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The Four Color Problem

With an amusing history spanning over 150 years, the four color problem is one of the most famous problems in mathematics and computer science. The four color theorem states that the regions of a map (a plane separated into contiguous regions) can be marked with four colors in such a way that regions sharing a border are different colors.



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P vs NP

If it is easy to verify whether a solution to a problem is correct, is the problem easy to solve? This question is posed as the P vs NP problem and is considered one of the most important unsolved problems in Mathematics. This post will be brief and forgo many technical details surrounding the question for the sake of accessibility.


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Finding Adam

This post will outline the paper Finding Adam in random growing trees by Bubeck, Devroye, and Lugosi. The main question examined in this paper is simply stated and relatively unstudied: given a tree, which has been generated under some attachment model, find the first vertex. “First” here meaning oldest. Think about the spread of a rumor, or disease. In these situations, the resulting distribution is known, but the starting point is not.

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