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*Edit: there is not suppose to be a constant of integration at the end since this is a definite integral.

Today, Peter
Scholze, Caucher Birkar, Alessio Figalli, and Akshay Venkates won the Fields Medal- the highest honor a mathematician can receive.

8. Finnish mathematician Lars Ahlfors and American mathematician Jesse Douglas were the first recipients in 1936.

To celebrate their victory, we compiled a list of important facts about the award:

1. The Fields Medal is awarded to two,
three, or four mathematicians under the
age of 40.

The Fields Medal |

2. It has been awarded every four years
since 1950 at the International Congress of
Mathematicians.

3. The award “recognizes outstanding mathematical achievement for existing work and for the promise of future achievement.”

4. An individual cannot win a Fields
Medal more than once.

5. Many describe the Fields Medal as the
mathematician's "Nobel Prize."

6. There is a monetary award of about $15,000 Canadian
dollars.

7. The award is named after Canadian mathematician John Charles Fields.

John Charles Fields |

8. Finnish mathematician Lars Ahlfors and American mathematician Jesse Douglas were the first recipients in 1936.

9. Maryam Mirzakhani became the first woman to
win the Fields Medal in 2014

10. Jean-Pierre Serre became the youngest recipient at the age of 27.

11. In 2006, Grigori Perelman, refused his
Fields Medal. He said, "I'm not interested in money or fame; I don't want
to be on display like an animal in a zoo.”

12. So far, 4 mathematicians under the age of 30 have won.

Source:

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*Note: In the video, *k*^{2 }- 1 - 6(*k - *1) reduces to *k*^{2}- 6*k* + 5 NOT *k*^{2} - 6*k* - 5

Friday the 13^{th} is upon us! Across the nation, there are people avoiding black cats, spilled salt, ladders, and broken mirrors. Not everyone, however, is scared of 13 because they have other numbers to fear.

In honor of today, here
are 6 unlucky numbers from around the world.

In China, the number
4 is considered unlucky because it is homophonous
to the word "death." Similar to how the 13^{th} floor is
absent in many buildings in the West, the 4^{th} floor is often left
out in China.

Just like the number
4 in China, the number 9 is a bad omen in Japan because it sounds similar
to the Japanese word for “torture.”

The Roman numeral for 17 is XVII, and an anagram for XVII is "VIXI.” This translates to “I lived," aka “my life is over."

For India, tragedies and
disasters have the pattern of striking on the 26^{th} (the 2008
Mumbai terror attack, the 2001
Gujarat earthquake, the 2004 Indian Ocean tsunami, 2008 Ahmedabad bomb
blasts). For this reason, India doesn't really like the number 26. Can you
blame them?

The number 39 is considered
cursed in Afghanistan due to the fact that 39 translates to ‘morda
gow’ which means ‘dead cow” - which is slang for pimp. Since 39 is linked to prostitution, the number is largely avoided.

**0888 888 888 - Bulgaria**

After three people in Bulgaria with the phone number 0888 888 888 died within ten years, a Bulgarian mobile company suspended the phone number because they believed it was cursed. If you are in Bulgaria, try calling the number. Surely, no one will pick up.

After three people in Bulgaria with the phone number 0888 888 888 died within ten years, a Bulgarian mobile company suspended the phone number because they believed it was cursed. If you are in Bulgaria, try calling the number. Surely, no one will pick up.

If we missed any unlucky numbers in your culture, be sure to comment below. Also, be sure to check out past blog posts about Friday the 13th.

1. 13 Facts about the Number 13

2. Friday The 13th, Math and Music.

1. 13 Facts about the Number 13

2. Friday The 13th, Math and Music.

Sources:

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Check out this Problem of the Week.

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Check out this Advanced Knowledge Problem of the Week.

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Check out this Problem of the Week.

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Solution below.

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Check out this Advanced Knowledge Problem of the Week.

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Solution below.

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Solution below.

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Integration is a vast topic with many diverse techniques meant to help find the integrals of functions. Many delightful and elegant methods are used to tackle difficult integrals. This video series talks about a few of the less common, but still very useful, techniques. These videos cover topics such as the tangent half-angle substitution, integration with a parameter, and how symmetry in integrals can be useful.

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Interested in learning a bit more about complex variables and some theorems about them? Then check out this new video series covering some of the basics of complex analysis! Complex analysis is an immensely useful subject that is found in many branches of mathematics. The residue theorem is especially well known as being an extremely important method for the integration of functions (real or complex!). Some other topics discussed include complex differentiation, Cauchy's Integral Formula, Liouville's theorem, the Möbius transformation, and much more!

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Many mathematicians have been notable not just for their contributions to mathematics, but also for helping teach the next generation of mathematicians. A number of important mathematicians have tutored and helped other important mathematicians progress in their careers. Here are a few such mathematicians.

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Number theory is a very old subject, which is concerned with the set of integers. Number theory started with the concept of integers and simple operations on the integers such as addition, subtraction, etc. Number theory of the greeks is primarily found in the works of Euclid and Plato. Indian mathematicians of antiquity such as Brahmagupta also made significant contributions (one of Brahmagupta's contributions was work on what is now known as Pell's equation). Pierre de Fermat was an important figure in number theory as well, he is responsible for Fermat's theorem as well as Fermat's Last Theorem (a problem which is now solved). Some additional major figures in early number theory were Leonhard Euler, Joseph-Louis Lagrange, and Carl Friedrich Gauss.

Eventually number theory itself started to split into recognizable subbranches, two major ones being algebraic number theory and analytical number theory. Analytical number theory is concerned with the use of real and complex analysis to number theory and can be said to have started with the Dirichlet prime number theorem. Algebraic number theory is concerned with the use of abstract algebra in number theory, and has it origins in reciprocity and cyclotomy.

Despite the significant work done in number theory, there are still plenty of unsolved problems in the field. Many of these problems are easy to understand (although clearly not so easy to solve). Here are a few of them.

Eventually number theory itself started to split into recognizable subbranches, two major ones being algebraic number theory and analytical number theory. Analytical number theory is concerned with the use of real and complex analysis to number theory and can be said to have started with the Dirichlet prime number theorem. Algebraic number theory is concerned with the use of abstract algebra in number theory, and has it origins in reciprocity and cyclotomy.

Despite the significant work done in number theory, there are still plenty of unsolved problems in the field. Many of these problems are easy to understand (although clearly not so easy to solve). Here are a few of them.

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- Tuesday, April 17, 3-4pm, Bernard Teissier: "A geometric introduction to valuation theory via infinite dimensional algebraic geometry, Part 1"
- Tuesday, April 17, 4:30-5:30pm, Bernard Teissier: "A geometric introduction to valuation theory via infinite dimensional algebraic geometry, Part 2"
- Wednesday, April 18, 3-4pm, Bernard Teissier: "A geometric introduction to valuation theory via infinite dimensional algebraic geometry, Part 3"
- Wednesday, April 18, 4:30-5:30pm, Paolo Aluffi: "Segre classes and other intersection-theoretic invariants of singular schemes, Part 1"
- Thursday, April 19, 3-4pm, Paolo Aluffi: "Segre classes and other intersection-theoretic invariants of singular schemes, Part 2"
- Thursday, April 19, 4:30-5:30pm, Paolo Aluffi: "Segre classes and other intersection-theoretic invariants of singular schemes, Part 3"

Links:

A Week of Singularities:

Center of Math Research:

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