Author Archives: tpc

Mathematics is a performance art,

but one whose only audience is fellow performers. The above quote according to Hymen Bass in Mathematics and Teaching (2015) is due to Samuel Eilenberg. The next quote, due to Bass himself, is on the approach taken by some mathematics … Continue reading

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Google Books Ngram

Pak’s history of the Catalan numbers mentioned an Ngram chart. But perhaps because I wasn’t reading carefully or possibly due to the fact that I was reading the print copy and did not access url pointing to the said chart, … Continue reading

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Faraday

Compared to mathematics, physics is extremely well-funded. For example, I have attended many talks by Nobel Laureates compared to Fields Medalists. (Locally, I have attended talks by Serre, S.T. Yau and Pierre Louis Lions. I somehow missed talks by Smale … Continue reading

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What are the chances that a bird will poop on my car?

This question was posed as a scenario of mathematics in everyday life. Some googling led to Randall “XKCD” Munroe’s post here. Borrowing similar ideas leads to my own computation below. I park at an open air carpark for work. The … Continue reading

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Queen of Mathematics

Number theory has been called the Queen of Mathematics. Until some fifty years ago, it did not occur to anyone that number theory, especially the study of prime numbers, would have any immediate applications to business. More recently, the Queen … Continue reading

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Triangular numbers modulo powers of 2 and its generalizations

Someone discussed with me an interesting problem that he was working on with his students. They found that the congruence [tex] \frac{1}{2}X(X+1) \equiv a \pmod{n} [/tex] has a solution for every [tex] 0 \le a < n [/tex] if and … Continue reading

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If there is some good inflammable stuff it will catch fire

Do not try to satisfy your vanity by teaching them great many things. Awake their curiosity. It is enough to open the minds, do not overload them. Put there just a spark. If there is some good inflammable stuff it … Continue reading

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Catalan numbers

I really enjoyed reading Federico Ardila’s article in the Mathematical Intelligencer. Apparently there was a vote of 3030 members at an assembly of CUP (Not Cambridge University Press but the Candidatura d’Unitat Popular). The vote had to do with forming … Continue reading

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Truncatable Primes

A colleague asked about sequences of primes a(n) such that a(n+1) is obtained by appending a single digit (in base 10) to the right of a(n). For example: 3, 31, 311 … Some thinking lead to the conjecture that such … Continue reading

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Twin corrections

Today is the 20th anniversary of the passing of Erdős and I would like to make two corrections. I had always thought the accent on Erdős’ name was ö , html code &#246 but it is actually Hungarian, html code … Continue reading

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Bollobas on solving problems

What you should be terrified of is a blank sheet in front of you after having thought about a problem for a little while. If after a session your wastepaper basket is full of notes of failed attempts, you may … Continue reading

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Logical order

The most efficient logical order for a subject is usually different from the best psychological order in which to learn it William Thurston from his book Three dimensional geometry and topology.

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One-seventh ellipse

Fun fact. It is well known that [tex] \frac{1}{7} = 0.\overline{142857} [/tex]. It turns out that if the repeating digits are taken in sequence as (x,y) pairs in the following manner to form six points: (1,4), (4,2), (2,8), (8,5), (5,7), … Continue reading

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Lakatos on Discovery

Discovery does not go up or down, but follows a zig-zag path: prodded by counterexamples, it moves from the naïve conjecture to the premises and the turns back again to delete the naïve conjecture and replace it by the theorem. … Continue reading

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Notes from ICME13

Gila Hanna mentioned the carpet proof of the irrationality of [tex]\sqrt{2}[/tex]. A little digging reveals that it was due to Tennenbaum (1950s) and popularized by Conway (1990s). The original proof appeared in a book but the simple idea is described … Continue reading

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Logic joke

Three logicians walk into a bar. The bartender says:”Do you all want a drink?” First logician says “I don’t know.” Second says “I don’t know.” Third says “Yes!”. Meta: Why is this a joke?

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Hypergeometric functions

Hypergeometric functions are one of the paradises of nineteenth century mathematics that remain unknown to mathematicians of our day. Hypergeometric functions of several variables are an even better paradise: they will soon crop up in just about everything — Gian … Continue reading

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Freeman Dyson

on how mathematics is permanent while physics is ephemeral. it’s the beauty of mathematics, as opposed to physics, that it’s forever. I published my selected papers recently in one volume, and I found out that when you publish your selected … Continue reading

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Halmos on how to study

It’s been said before and often, but it cannot be overemphasized : study actively. Don’t just read it; fight it! Ask your own question, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse … Continue reading

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Discovery

What you have been obliged to discover by yourself leaves a path in your mind which you can use again when the need arises. — G. C. Lichtenberg I am not familiar with Lichtenberg but he was apparently a German … Continue reading

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