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# Category Archives: Quotes/People

## 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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## 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

Posted in Books, Number Theory, Quotes/People
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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

Posted in Combinatorics, Fun Stuff, Quotes/People
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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 ö 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

Posted in General, Problems, Quotes/People
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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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## 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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## 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

Posted in Learning, Quotes/People
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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

Posted in Learning, Quotes/People
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## Byss and Abyss

Saw this quote attributed to Winston Churchill. A search on google books revealed that it came from chapter III of his autobiography, My Early Life: 1874-1904. I had a feeling once about Mathematics, that I saw it all — Depth … Continue reading

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## SEND SOME MORE MONEY

It’s been 9 years since I blogged on SEND MORE MONEY. I got back into this because I found out that the author of SEND MORE MONEY is Henry Dudeney and the puzzle apparently appeared in Strand Magazine vol. 68 … Continue reading

Posted in Fun Stuff, Problems, Quotes/People
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## Fermat

was born on 17th August 1601. Incidentally [tex] 1601 = 1^2 + 40^2[/tex] is a prime.

Posted in Number Theory, Quotes/People
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## 3.14.15 and Einstein

14 March 2015, was supposed to be the Pi day of the century — for obvious reasons. 14 March is also Einstein’s birthday, and 2015 interestingly marked 100 years of the theory of relativity. I liked this article written by … Continue reading

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## Under Promise and Over Deliver

Mr Lee Kuan Yew, the man responsible for making modern Singapore what it is today, passed away on 23 March 2015, aged 91. Incidentally it was also Emmy Noether’s birthday. I have wanted to start off my class by showing … Continue reading

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