The 12 Most Controversial Facts In Mathematics

Here’s something I came across the other day and found super interesting, even though it broke my brain. While “controversial” in mathematics usually refers to unsolved problems or conjectures, here are 12 notable and often-debated mathematical concepts: (all links will open in a new window)

  1. 1. The Riemann Hypothesis:This famous conjecture proposes a specific relationship between the distribution of prime numbers and the behavior of a complex function. It remains unsolved despite extensive research. 
  2. 2. The Goldbach Conjecture:This states that every even integer greater than 2 can be expressed as the sum of two prime numbers. It’s been verified for large numbers, but a general proof remains elusive. 
  3. 3. The P vs NP Problem:This problem asks whether every problem whose solution can be quickly verified can also be solved quickly. A positive answer would have significant implications for computer science and cryptography. 
  4. 4. The Four Color Theorem:This theorem states that any map can be colored with only four colors so that no two adjacent regions have the same color. It was famously proven with the aid of computer analysis. 
  5. 5. Fermat’s Last Theorem:This theorem states that no three positive integers a, b, and c can satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2. It was proven centuries after its formulation by Andrew Wiles
  6. 6. The Monty Hall Problem:This probability puzzle involves a contestant choosing a door with a prize behind it, and the host then revealing a door with no prize. Should the contestant switch their choice, or stay with their initial selection? The counterintuitive answer is that switching increases the odds of winning. 
  7. 7. The Twin Prime Conjecture:This conjecture suggests that there are infinitely many pairs of prime numbers that differ by 2. While there’s no proof, extensive research suggests it’s true. 
  8. 8. The Poincaré Conjecture:This conjecture, proven by Grigoriy Perelman, states that any simply-connected, closed 3-manifold is homeomorphic to the 3-sphere. It was one of the Millennium Prize Problems. 
  9. 9. The Collatz Conjecture:This conjecture, also known as the “100 problem”, posits that starting with any positive integer and repeatedly applying the rule (n is even, n = n/2; n is odd, n = 3n+1), you will eventually reach the number 1. 
  10. 10. The Birch and Swinnerton-Dyer Conjecture:This conjecture is a deep result in number theory concerning the number of rational points on algebraic curves. It remains unsolved. 
  11. 11. The Hodge Conjecture:This conjecture relates the algebraic structure of a complex projective variety to its topological structure. It’s a major unsolved problem in algebraic geometry. 
  12. 12. The Navier-Stokes Equations and Yang-Mills Existence and Mass Gap:These two problems are fundamental in mathematical physics and fluid dynamics. They concern the existence and properties of solutions to certain differential equations. 

While some of these problems are unsolved, others are well-established results with ongoing discussions about their implications or

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Things I Found While Eff’ing Around – Volume 1

I got this idea after reading a couple of my favourite blogs. It’s really just a list of a handful of websites that I’ve visited on my travel through the internets that I thought you might like. So, without further ado, I present to you…

Things I Found While Eff’ing Around
(all links will open in a new window)

In 2010 alone, more than 3,400 button battery swallowing cases were reported in the U.S., resulting in 19 serious injuries and in some cases, deaths. Get the facts here.

The science of storytelling.

I had to use the Wayback Machine for this one but it’s totally worth it. It’s all fun and games until CPS shows up.

Test your social intelligence.

Mind. Blown.

The Honest Toddler

Amazing and stunning works of art that aren’t photographs.

This link is now behind a paywall but the Wayback Machine indexed it beforehand: I’ve always been fascinated by linguistics. In fact, a game I like playing (it makes an especially fun ice-breaker!) starts with compiling a list of 20-30 words that have different pronunciations (depending on what part of the country you’re from). The list is then provided and everyone takes turns saying each word out loud. OK, so when I type it all out like this, it sounds really nerdy and lame. Oh, well. 22 Maps that Show How Americans Speak English Totally Differently From Each Other.

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How does she do it?

I’ll be bringing back some of my previous posts from an earlier iteration of this site. Here’s one that was originally published on December 3, 2013.

The majority of my mom friends only have one or two children. So whenever we get together and/or have a chance to talk, it’s inevitable that they remark about how much more I have to handle and deal with. 

And it’s true. Having 5 children certainly does make for more chaos! I just brush these comments off though because little do they know that I have a handful of secrets to manage the stress. Most moms with less than 2 or 3 children will not understand these methods, and that’s OK. Moms of 4 (or more) will totally get this. There are numerous issues I encounter while trying to get through my day. These issues include:

  • Idle hands spend time doing terrible toddler things (e.g., picking their nose, putting their hands in their diaper, dumping cat food into the cats’ water bowl).
  • When toddlers step out of line, the punishment must be swift and harsh.
  • When toddlers do good work, the reward must also be swift (and sometimes harsh.)

The following are 4 of my secrets for getting through the day without beginning to drink at 8:45 a.m.

Secret #1: Your 2-year-old is more capable than you think.
Put their incessant energy to good use by making them perform the household chores that you hate. For example, let your toddler wash their own bottles. In addition, have them finish up the leftover dishes from the previous night’s dinner:

Also, cleanliness is next to godliness, so have them wash their hands repeatedly. This is a double bonus, because they will have relatively clean hands (for a couple of minutes) and they find this exercise enjoyable:

Secret #2: 2-year-olds are excellent at doing laundry.
Here you can see Coraline cleaning out the lint filter. Another double bonus, because the lint problem gets taken care of and thoroughly punishes the toddler who has just spent 20 minutes washing her hands:

Secret #3: Your 1-year-old is more capable than you think.

For example, Halsey does an excellent job of (re)formatting his father’s Kindle:


Also, they say a 1-year-old’s mouth is cleaner than a dog’s, so let him disinfect those germ-ridden game controllers:

When your 1-year-old does his chores appropriately, a suitable reward is letting him play with plastic bags:

However, when your 1-year-old tries to run from helping fold laundry…

Suitable punishments include making him smash his own fingers in the kitchen hand towel drawer:

Locking him in a dark bathroom:

Making him watch TV from outside of the family room gate:

One item of importance is making sure your 2-year-old doesn’t get lazy. You’ve got to make her sharpen her incredible gymnastic skills:

Also, you can’t let your toddler get too comfortable. A good way to keep them in line is making them nap without their favourite blanket. Note the look of glee on my 2-year-old’s face. She clearly enjoys my creative methods for compliance:

Secret #4: Your cat can actually be helpful.

Here is Lieutenant Clawhugs reporting for duty:

He helps by using his entire furry body to dust off the kitchen table:

Cats are also excellent inspectors:

In fact, cats are very thorough inspectors:

Once your cat is done inspecting your toddler’s work, he’ll likely want to take a break by laying on a cleankitchen towel. (This is because cats are notoriously lazy.):

At least he makes up for his laziness by voicing his complaints. (Cats hate the paparazzi.)



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I need these in my life.

Y’all, I’m about to go on an epic vacation but one thing I suffer from when I travel is horribly swollen feet. That’s why I’m super excited about these highly rated compression socks. I really hope these work as well as described.I’ll be writing a review upon my return.

Cute Compression Socks

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I wrote a book!

Check it out here: Raising Irish Twins— A Semi-Survival Guide.

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