Wednesday, May 30, 2012

The House Conundrum

A mathematician, a biologist, and a physicist are watching as two people enter a house. Some time later, three people can be seen leaving the house.

The scientists make three different observations.

The physicist: "Our measurements were flawed."

The biologist: "They must have reproduced."

The mathematician: "If one person now enters the house, it will be empty."

Note: That is a well-known math joke. Here's another famous one:

Wanted - Schrodinger's Cat, dead and alive.

Saturday, May 9, 2009

Advanced Math

Once, a really great computer science student found himself struggling through calculus classes. It surprised him greatly, as he could easily write a program to do the homework for him, but he could not complete it himself. Thus, his poor test scores reflected his true weakness in the area he considered "advanced math."

He went to his calculus professor and explained the situation.

"You see, sir, with computers, the idea is to figure out how to write a program to perform a process on some data and produce some kind of desired output. With calculus, it's different. You are given a lot of different processes to solve the problems, but the trouble is figuring out which ones to use on a given problem, rather than writing a program to perform those processes. Thus, I'm excellent at programming, but terrible at this advanced math."

The professor replied, "First of all, this isn't advanced math..."

Friday, May 8, 2009

A More Difficult Test

Once right before a final, the professor declared that he would be leaving the room for the duration of the test, and returning in two hours, the amount of time the students were allowed for the final. He stipulated that they were not allowed to leave the room until the professor had returned, regardless of when they each completed the final.

The students were incredulous. But, just as he had stated, the professor handed out the tests and left the room, shutting the door behind him. The students waited a few moments, to be sure the professor would not barge in, and immediately began collaborating and cheating on the final. They shared notes and answers, got out their books, and began really laying into the test.

After two hours or so, the last student finally turned his paper face down. The professor came in shortly afterward, and declared that everyone had failed the test. He left, and the students all sat in their chairs, stumped.

Little did the students know that the professor had built a private study room for himself right behind the classroom, and had put a one-way mirror in between the two rooms. He had left the room and simply walked into his private study, sitting there and gleefully watching his little experiment unfold. The professor had decided before giving the test that any student who did not cheat and take advantage of the professor's "absence" would be given a 100% on the test, regardless of what his or her actual test score might have been. However, all those that he saw cheating would be given a zero.

As he had predicted, and very unfortunately for them, the students took full advantage of his absence. Every single one of them failed the final.

Tuesday, May 5, 2009

A Math Prodigy

One time a math professor noticed, as he was teaching his first class session for the semester, that a single student was absent on the first day. He wrote some problems on the board, and declared class dismissed.

After that, the student who had been gone showed up every single day. It was as if that first day had never happened. In fact, he was the only student with only one absence; most of the other students skipped on a regular basis.

Towards the end of the semester, the professor realized that the student who had been missing on the first day of class now had the best grade of all his students. This did not surprise him, however; the student did his work diligently and never missed an opportunity to learn.

On the last day of class, that very student strolled into the professor's office.

"Professor, I was wondering when you were going to take up our homework problems."

"Excuse me? I haven't given out homework for the past few weeks."

"I meant the problems you gave us the first day of class. I copied them from another student's notes."

"Oh really? You didn't manage to solve any, did you?" asked the professor. At this point, he was intrigued. The problems he had written down on the first day of class were not homework, but were the eight unsolved problems in mathematics at the time.

"Yes," replied the student, "I managed to solve the first six, but those last two were monsters!"

Sunday, May 3, 2009

Proof That Time Travel Is Impossible

Here is an interesting proof that time travel is impossible. You can decide for yourself whether it is true or not.

pf. I hereby vow that if, at any point in the future, I am able to time travel, I will travel back to this point in time and prevent myself from writing and publishing this blog. Since this blog exists and is published, time travel (at least for myself) must be impossible. QED.

Saturday, May 2, 2009

The Professor Who Could Prove Anything

There was once a math professor who could prove anything, if it was indeed true. For as we all know, trying to prove something which is really false is quite ludicrous, as well as being impossible. This man was a great mathematician, and also quite a comedian in the brief intervals between his proofs. He was known to his students as Dr. Proof. His true last name was actually a mystery, and he had never told anyone what it was, for fear that they might prove him to be wrong by providing a counterexample.

Several students on his campus noticed one day that Dr. Proof did not own a vehicle. They became quite curious to know how he arrived on campus each morning, and left each night for his home. They all knew he owned a house, because he had once proved it.

"I know how he does it! He walks to campus. This explains why he is so healthy," guessed Joe.

"That can't be it. It's too simple an explanation," reasoned Mark.

"But remember Occam's razor!" suggested Louis. "Perhaps Joe is correct."

"We would have seen him walking back home, though," insisted Steven. "I've never even seen him leave the mathematics building."

"This must be true," said Mark, "that he never leaves. Remember that day he proved that Steven never lies?"

"Right, I remember it." said Joe. "That was one of the best proofs ever. I can't remember how he went about proving it, but I thoroughly enjoyed it."

Kirk, who had been quietly listening to the conversation and reasoning on his own, suddenly piped up. "I have it! I know how he does it."

"What? How?" inquired the rest of the boys.

"Just think about it. How does Dr. Proof do anything? He proves it! When he's at home, he simply walks up to his blackboard and writes a proof that he's here on campus, and bang! he's here. When he wants to leave, he waits until no one is around to watch, and writes a proof that he is at home, and there he is."

The other boys were greatly impressed with Kirk and his explanation. They realized that this was the only valid way the professor could have been getting around, and never bothered to verify the claim by spying on Dr. Proof. They respected him too much to be caught spying on him.

Dr. Proof was once even able to prove that he could prove anything, and thereafter, rather than proving anything new, he simply stated that by this earlier proof that he can prove anything, that actually proving it was unnecessary.

When Dr. Proof was getting on in years, he decided he no longer had any use for his life, and wrote a proof that he had never been born. This prevented the students from mourning his absence the next day, since they had, in fact, never met him. It was easier all around, he thought. There was a strange sadness that surrounded the campus, but no one could determine the source of it. It was as if someone never existed that really should have.

The Legend of Pythagoras

Some mathematically-inclined friends were having a boat trip. There was all sorts of food, drink, and numerical merriment aboard the S.S. Pythagoras. That is, until one of them brought up a proof he had recently been working on.

"Friends, there DOES exist a number that is not rational. I have come up with a most ingenious proof of this!" said Julius.

"WHAT?" exclaimed the rest of the group.

"Indeed! You see, if you draw a triangle, such that one of its angles is ninety-degrees, and such that the two incident sides to the right angle are each of length one, then the hypotenuse's length is irrational. It would be equivalent to the square root of the number two, but that number cannot be written as one integer divided by another. One or both numbers would have to be..."

But it was at this point that the group of friends, led by the famous Pythagoras of Samos, declared poor Julius a heretic and threw him overboard. The night air was immediately rent with his screams and pleas for help, and the laughter and singing and celebrations of the rest of the group as they sailed away. For a great mathematical secret died that night with Julius as he drowned, and was not discovered again until a great number of years later. He had, in fact, been correct--the square root of two, as well as many other numbers, are irrational, and cannot be written as one integer divided by another.