The UK May Not Hike Rates Until Well Into 2015 (Wells Fargo)

The consensus among economists is that the UK will commence tightening its monetary policy in Q1 2015. Wells Fargo believes there's reason to think it could come a bit later.

"The Bank of England has pledged to keep its Bank Rate at 0.50 percent, where it has been maintained since March 2009, until spare capacity in the British economy has been more fully absorbed," they write. "Unfortunately, spare capacity is an unobservable variable, and it can vary over time due to fluctuations in actual GDP growth and changes in potential GDP growth, which is also unobservable. Wage growth is an observable variable that should be inversely correlated with spare capacity in the labor market (i.e., as spare capacity in the labor market falls, wage growth should rise), and we think that it will be very important to watch wage growth in coming months—the MPC has essentially told us to do so—to determine the timing of the first rate hike by the BoE since 2007. The consensus forecast among economists (as measured by Bloomberg) looks for the MPC to commence its tightening cycle in Q1-2015, and the yield curve implies that investors believe the first rate hike will happen by then as well. Our forecast looks for the first rate hike to occur in the
second quarter of next year. In any event, the MPC likely will not raise rates this year, unless wages accelerate significantly over the next few months."

Nine Out Of 16 Equity Valuations Above Average (Josh Brown)

Josh Brown points us to this table from Bank of America showing a snapshot of the S&P500's valuation on sixteen metrics. US large cap stocks are currently at or above their historic valuation on nine of them.

Stick With Energy Stocks (BlackRock)

BlackRock's Russ Koesterich believes that on valuations alone, energy stocks still look good, regardless of what's happening geopolitically.

"Despite outperforming year-to-date, energy sector valuations still have room to grow, as measured by looking at the S&P Global 1200 Energy index," he writes. "Multiples are still at a discount to their 10-year average and fund positioning is low, as I point out in my new Market Perspectives paper. In addition, I continue to see good free cash flow and several recent investment projects are beginning to bear fruit. In particular, I see good opportunities in certain integrated companies and exploration and production companies where there is resource growth. You can read more about my outlook for oil prices, and what this means for investors, in the full Market Perspectivespiece, “Oil’s Precarious Balance, and you can listen to a client call on the subject here.

About That Secular Stagnation Book (VoxEU.org)

On Friday Paul Krugman said a new book compiled by Vox.eu on secular stagnation is a must-read. He happens to be a contributor, but he has a point. 

"Our authors are far from a homogeneous group – they come from different continents and different schools of thought," VoxEU says. "Their contributions were uncoordinated and they do not entirely agree, but a fairly strong consensus has emerged on three points. 

• "First, a workable definition of secular stagnation is that negative real interest rates are needed to equate saving and investment with full employment.
• "Second, the key worry is that secular stagnation makes it much harder to achieve full employment with low inflation and a zero lower bound on policy interest rates.
• "Third, while it is too early to tell whether secular stagnation is going to materialise in the US and Europe, economists and policymakers should start thinking hard about what should be done if it does. Doing so is a no-regret option.

Bond Yields Won't See A Massive Sell-Off Yet Because Corporations Have Plenty Of Cash And Credits Have Been Performing (The Financialist)

As the Federal Reserve winds down its quantitative easing program, people have started to worry about the bond market.

Credit Suisse's Senior Advisor, Robert Parker "expects a slow burn over the next 18 months in which bond yields do rise but still remain well below their historical averages." Despite the fact that he isn't expecting "further upside" for corporate bonds, he also doesn't expect a massive selloff because most credits have been performing, and corporations "are also sitting on plenty of cash and are less leveraged than in recent years".

He also points out interesting investment opportunities in equities. He believes that North Asian markets (including Japan, South Korea, China, and Taiwan) are attractive. And he expects Southeast Asian markets to underperform.

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If scrolling through your Facebook feed yields nothing more than videos of your friends, neighbors, and family dumping buckets of water on their own heads, that makes sense.

Facebook says 1.2 million videos of the Ice Bucket Challenge have been posted on its site, according to Time. All in all, the craze has raised $5.5 million in donations for the ALS association since it began a little over two weeks ago on July 29.

Last year during this same period, the group raised just $32,000. August is typically a "slow month in the nonprofit world," the Washington Post wrote.

Facebook calculated that more than 15 million people have interacted about the challenge in some way this summer, either from uploading a video, liking a post, or commenting on one. Facebook also shared an infographic mapping out who challenges who to dump water on their heads.

Each line represents at least 10 connections between challengers and their targets, Time says. Facebook suggests that Boston seems to be a hub because of the widespread popularity of former Boston College baseball player Pete Frates, who was diagnosed with the disease in 2012.

Since then, other high-profile challengees have gotten involved, probably a huge boost to the movement's momentum.

SEE ALSO: Mark Zuckerberg, Satya Nadella, and Dick Costolo dump ice cold water on their heads

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Mo'Ne Davis is one of just 18 girls to play in the Little League World Series and she reaffirmed her position as the star of this year's tournament, pitching a complete game 2-hitter as the Tanney Dragons from Philadelphia won their opening game.

After the game, Davis took her status from star to legend when she was interviewed by ESPN. When former Major Leaguer Barry Larkin asked if there was a Major League pitcher she emulates, she had an amazing answer.

"I throw my curveball like Clayton Kershaw's and my fastball like Mo'Ne Davis," said Davis.

Perfect.

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Despite eyewitnesses seeing a column of Russian military vehicles crossing into Ukraine on Thursday that was reportedly attacked on Friday by the Ukrainian military, The White House released a statement saying it was "not currently in a position to confirm" this series of events.

"We are working to gather more information regarding reports that Ukraine’s security forces disabled vehicles in a Russian military convoy inside Ukraine. We are not currently in a position to confirm these reports," National Security Council Spokesman Caitlyn Hayden said. "Even as we work to gather information, we reiterate our concern about repeated Russian and Russian-supported incursions into Ukraine. Russia has no right to send vehicles, persons, or cargo of any kind into Ukraine, under any pretext, without the Government of Ukraine’s permission."

While the Russian government has dismissed claims its convoy was attacked as "fantasy," Hayden went on to describe Russia's actions as a threat to Ukraine's stability. 

"The escalation in Russian activity designed to destabilize Ukraine in recent weeks is extremely dangerous and provocative," she said. "It includes supplying separatist fighters with tanks, armored vehicles, artillery, and multiple rocket launchers (MRLs). Russia has also been firing artillery and rockets from Russian territory into Ukraine on a regular basis, and has been moving multiple-rocket launchers (MRLs) and surface-to-air missile systems (SAMs) across the border to fire on Ukrainian positions -- including its newest air defense systems, the SA-22, into eastern Ukraine."

Hayden concluded by urging Russian President Vladimir Putin to stop supporting the efforts of pro-Russian rebels in Ukraine. 

"Yesterday, President Putin pledged to 'do everything in (Russia’s) power' to end the conflict in Ukraine. He can start by ending Russian firing into Ukraine; stopping its supply of weapons, support and cash to separatists; and closing the border to militants, including by facilitating an effective border monitoring mission under the auspices of the OSCE," said Hayden.

Russia has said the convoy was filled with humanitarian aid supplies. Hayden implied it was not a "legitimate" humanitarian effort, since Moscow is not coordinating with the Red Cross. Further, the supposed humanitarian convoy was joined by armored personnel carriers, anti-aircraft weapons, and helicopters, The Guardian's Shaun Walker reported.

"The continued Russian military intervention into Ukraine is entirely at odds with legitimate efforts to provide humanitarian assistance and negotiate a peaceful resolution to the overall crisis," Hayden said.

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Texas Gov. Rick Perry (R) isn't backing down after being indicted by a grand jury.

Not long after news of the indictment broke Friday evening, Perry's office released a statement maintaining his innocence and declaring he "will ultimately prevail."

"The veto in question was made in accordance with the veto authority afforded to every governor under the Texas Constitution," said Mary Anne Wiley, Perry's general counsel. "We will continue to aggressively defend the governor's lawful and constitutional action, and believe we will ultimately prevail."

Perry, who is looking at making another run for president in 2016, was indicted on felony counts of abuse of official capacity and coercion of a public servant, according to the Associated Press, for carrying out a threat to veto funds set to go to state prosecutors investigating public corruption.

"The indictment is the first of its kind since 1917, when James 'Pa' Ferguson was indicted on charges stemming from his veto of state funding to the University of Texas in effort to unseat faculty and staff members he objected to. Ferguson was eventually impeached, then resigned before being convicted," the AP reported.

Update (9:31 p.m.):In an even more aggressively-worded statement, another Perry counsel, David Botsford, weighed in late Friday evening.

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Recep Tayyip Erdogan, Turkey's prime minister, certainly knows how to win elections. Since he helped to found the Justice and Development (AK) party 13 years ago, he has scored eight victories in a row. On August 10th he made it nine, winning Turkey's first direct election to the presidency, with a crushing 52% of the vote. Given what have been broadly fair polls, with mostly high turnouts, nobody can seriously challenge Mr Erdogan's democratic credentials.

His achievements in over 11 years as prime minister are equally impressive. Since AK came to power in November 2002, economic growth has averaged some 5%. Inflation has been tamed. The army has been brought under greater civilian control. Mr Erdogan has made more progress than any previous political leader in giving Turkey's Kurds greater rights. In 2005 he achieved something that had eluded all his predecessors: the start of membership talks with the European Union.

Yet there are reasons to worry about Mr Erdogan's ascendancy to Ankara's Cankaya palace. With the army, the secular establishment and the political opposition all cowed, he has grown more autocratic. When Turks took to the streets in last summer's Gezi Park protests, his reaction was to send in riot police with tear gas. After a corruption scandal erupted last year, engulfing even his own family, he took firmer control of the judiciary. He has responded to criticism with assaults on free media and on individual journalists (including virulent public attacks on The Economist's long-serving Turkey correspondent), and with attempts to censor the internet.

What makes this more troubling are Mr Erdogan's plans to give the presidency, hitherto a ceremonial job, far more power. He wants to turn it into an executive position, as in France. To do this he must change the constitution, which usually needs a two-thirds majority in parliament. AK is unlikely to achieve that on its own, but it could secure enough votes by doing a deal with the Kurdish party. That would put Mr Erdogan in sight of his goal of an enhanced presidency, backed by a pliable prime minister, in which he could stay up to and beyond 2023, the centenary of Ataturk's republic.

Such an outcome is unappealing to those who believe in political pluralism. Powerful presidencies can work, but they need to be constrained by strong institutions of a sort Turkey still lacks. Mr Erdogan's own autocratic tendencies compound this problem. But why should he pay any heed? There are two answers: a vulnerable economy and his own legacy.

The biggest reason for Mr Erdogan's poll victories is his delivery of rapidly rising living standards. But the economy is slowing. A gaping current-account deficit makes the country highly dependent on capital inflows; when global interest rates rise, Turkey could suffer. And it is caught in a "middle-income trap", losing competitiveness in the basic goods it produces, but unable to move up to higher-tech ones. To keep growing, Turkey needs both liberalising reforms and foreign capital. Mr Erdogan has shown scant interest in reform. And although foreign investors stomach autocratic regimes around the world, they don't much care for social instability of the sort that Mr Erdogan's type of polarising politics usually portends.

The hope that Turkey will one day join the EU has also kept investors interested. This is where Mr Erdogan ought to think of his legacy. Building giant infrastructure projects is all very well, but if he is to underpin Turkey's modernisation he needs to pull it back onto its European course. EU membership is a remote prospect just now, but moving away from Europe's liberal democratic norms will make it an impossibility.

Gul, not Putin

The first test of Mr Erdogan's intentions will be the choice of prime minister. This week Turkey's outgoing president, Abdullah Gul, threw his hat into the ring (see "Turkey's presidential elections: The next sultan?"). Not only is Mr Gul widely respected, both at home and abroad, but he has also briefly held the job before. Moreover, as a co-founder of the AK party, he has enough political clout of his own to stand up to Mr Erdogan. Mr Erdogan should accept that a strong prime minister would be better for Turkey. If he insists on having a puppet instead, people may start to compare him not to Ataturk but to his Russian counterpart, Vladimir Putin.

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Landing your first "real," post-college job as a 20-something can be exiting and scary. 

You finally get the chance to prove yourself, but there's more room than ever to mess up.

Lauren Berger, founder and CEO of InternQueen.com, knows the latter well. Despite feeling prepared with 15 internships under her belt, Berger says she struggled through her first job, getting behind on email and forgetting important tasks.

But she learned from her mistakes, and went on to start her own company.

In her new book, "Welcome To The Real World," Berger chronicles this experience along with everything she learned about making the most of a job and turning what you love into a career. 

Here are 15 ways 20-somethings can stand out:  

Be confident. 

First and foremost, have confidence in yourself. "Your confidence can make or break you," Berger says. It's impossible to accomplish anything worthwhile if you're not willing to put yourself out there. Berger credits her strong sense of confidence to years of trying, failing, and trying again. By putting herself on the line time after time, she was able to watch potential failures turn into successes. 

Get used to being uncomfortable.

Once you decide what you want to do, go for it — even if it's uncomfortable to put yourself out there at first. If you can train yourself be okay with feeling uncomfortable, you'll open yourself up new opportunities everywhere. "When I feel myself tensing up or getting scared or insecure about any situation I try to push myself to do it anyway, because I know forcing yourself outside your comfort zone forces you to mature and grow," Berger says. 

Accept rejection — and move on. 

When you're still learning the ropes, rejection will become a common occurrence. Get used to it. Your ideas, pitches, and attempts to impress your boss will all be rejected at one time or another, Berger says. However, it's important to accept these moments, realize that no one gets it right every time, and learn from the experiences. Berger suggests focusing on your successes instead, which will motivate you to push forward.

Never settle. 

If you hate your job, or your boss, or you're simply bored at work, do something about it. "If there is a problem, spend your time figuring out how to fix it," Berger says. "Don't settle for an okay job — go after your dream job." It's impossible to get the most out of anything, especially your career, if you wait for opportunities to fall into your lap. "They won't," she says. You need to push yourself and make things happen on your own time. 

Don't take things personally.

Don't take criticism at work personally — no matter how difficult that seems. "People make decisions for all kinds of reasons and usually it's chalked up to business as usual and it has nothing to do with you," Berger says. If your boss points out weaknesses during a performance review, take her comments as goals to work toward, not jabs at your personality. It's her job to evaluate how you perform as an employee, not how much she likes you. "Remember the difference."

Create a system that works.

If you enter a job that already has systems in place, for anything from sorting the mail to arranging meetings with clients, find a way to improve them. Sticking to the previous system might mean sticking to a flawed approach, so don't be afraid to tweak things and find what works for you. "You'll be much more effective if you organize things in a way that's easiest for you," Berger advises. Additionally, taking initiative will likely impress your boss. 

Pay attention to email etiquette.

Email has become an inextricable part of every industry, so whenever you send an email it should reflect your highest level of professionalism, Berger says. It's important to be aware of the tone you're giving off, as you don't want to sound ungrateful or annoyed.

Berger suggests keeping emails concise but still friendly, double checking that the recipients are correct, and always including a signature.

Don't say "I don't know." 

Berger points out a hard truth of the working world: No one will hold your hand if you proclaim "I can't" or "I don't know how." Instead, it's important to learn how to figure things out yourself. "If you don't figure out solutions, your boss will be disappointed with your lack of initiative," she says. When a tough situation arises, be resourceful; don't give up and hand the problem back to your boss.

Stay organized.

Keep your desk neat, update your calendar regularly, and stay on top of your inbox at all times. If you're diligent about being organized, nothing will slip through the cracks and you'll prove that you can handle more responsibilities. "There is no worse mistake than when an important task is delegated and then is forgotten about or pushed too far down on the list of priorities," Berger says.

Make deadlines — and stick to them. 

Deadlines mean everything in the working world, and missing one not only affects you, but your boss, the client, and anyone else involved on the project, as well. Always give yourself extra time when determining a deadline, and hold yourself to that date.

If a deadline isn't assigned, set one for yourself, and don't be shy about asking your boss for a timeline, Berger suggests. It's always better to check in with your boss than to automatically assume you're on the same page.

Find a mentor. 

A great mentor can help you navigate your new workplace, solve problems at the office, and advance in your career. Look for someone who you're comfortable talking to and asking for support. Seek out someone who's been there, and can offer valuable insight and assistance when you face tough situations in your job and career overall. 

Stay connected. 

Once you've made a professional contact, you need to maintain the relationship or you'll lose it. Berger follows  a "three times per year" rule for staying in touch with industry contacts, and checks in with them in the fall, spring, and summer. "When you reach out to employers, you just want to drop them a short paragraph telling them how you are doing," she says. "Don't ask for anything unless you need to." You want to form genuine relationships; not use people to get ahead. 

Dress appropriately. 

The classic adage, "dress for the job you want," still holds true. "Every day, when you get dressed for work, you are representing the person you want to be in the workplace," Berger says. To get your colleagues to take you seriously, always aim to look professional and polished. Even if your office embraces a laid-back dress code, it's still important to mind how you look. That means no leggings, flip-flops, or ripped jeans. Ever. 

Don't act entitled. 

Now that you've landed the job, it's time to prove yourself. Never expect things to be handed to you or think that an assignment is beneath you. Instead, learn to be humble and work your way up. "When you are an entry-level employee, no task should be too small," Berger advises. "You should volunteer and eagerly do the work no one else wants to do in hope that people will recognize your genuine spirit."

Set goals.

Your first job probably isn't going to be your "forever job," but it's easy to get swept up in the work and end up staying put for longer than you want, Berger warns. To combat this complacency, continually make and update your goals and priorities so that you're always pushing yourself forward. Your goals can be anything from getting promoted to developing a better understanding of the industry. 

SEE ALSO: 5 Money Mistakes 20-Somethings Make

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Jim Rogers first made his name when he cofounded the Quantum Fund with George Soros. 

In 2007, he packed up and moved to Singapore where he is essentially shorting the West.

Behind Rogers' quick wit and endless charm are brilliant investing insights he gained during his lengthy and legendary career.

We put together 14 of the best insights that every investor will find helpful.

"Most successful investors, in fact, do nothing most of the time."

Once you've invested in something, done your research, made money, and decide to sell, you need to be careful, Jim Rogers says:

Now that is a very dangerous time. It is dangerous because you think you are really hot. It is the time when you think you know that this investing thing is an easy game. It is the time that you should open the curtains, look out the window, go to the beach, do anything but think about investing. Because now is when you're most vulnerable. You think: I have to find something else. I have to do it again. This is wonderful. This is so easy. Just as I thought after tripling my money with my puts. ... It is the great mistake people make."

Source: Street Smarts

"If you want to make a lot of money, resist diversification."

Brokers will tell you to diversify, but Rogers writes that this is mostly to protect themselves.

"If you buy ten different stocks, chances are some will be good," he writes. "You are not going to go broke, but you are not going to make a lot of money, either. ... The way to get rich is to find what is good, focus on it, and concentrate your resources there. But make very sure you are right. Because it is also a fast way to go broke."

Source: Street Smarts

"It is remarkable how many people mistake a bull market for brains."

"There is nothing quite like a bull market to make people think they are smart," Rogers writes, adding: "All big bull markets, secular bull markets, end in a bubble. Everyone chases the conventional wisdom, following what they read in the press, and that presents the smart investor with opportunities."

Source: Street Smarts 

Tinder has been used the world over to hook people up. It's even produced marriages.

But this may be the first record deal to come as a result of the swipe-right matchmaking app.

Ryn Weaver, a 21-year-old rising pop starlet based in Los Angeles, talked with The FADER's Aimee Cliff on Friday, the day her debut EP "Promises" was released.

Weaver told Cliff the story of how she met producer Benny Blanco — who has worked with artists like Katy Perry, Maroon 5, and Wiz Khalifa — and after losing touch with him, met him again through Tinder. She said:

It was four years ago, I moved to New York City and it was actually on Halloween that I met Benny through my ex-boyfriend. We went out that night, and we ended up talking about music and all sorts of stuff. Then, [months later] randomly—are we ready for the real real?—my friend had a Tinder account, and we were out in LA, and she was like, “Who is this guy? We have mutual friends!” And I was like, “Oh my god, swipe yes! I know him!” And so we ended up asking [Benny] what he was doing here in LA. He was like, “I come here half the year to make music.” And then we all were going back and forth…and he was like, “Come to my birthday party tomorrow.” So we go to this party, it was so silly. My friend was going for him, and I was like, “Um, let me talk to you for a second, I’ve been really trying with the music thing.” And he was like, “Well, good luck.” [laughs] So then I sent him my Soundcloud, along with a couple of his friends, and he ended up calling me like two days later like, “We really want to work with you.” Tinder got me a record deal.

Read the whole interview with Weaver.

SEE ALSO: The CEO Of eHarmony Thinks Dating Apps Like Tinder Are Superficial And Will Never Work

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This week, the International Mathematical Union announced that Iranian-born mathematician Maryam Mirzakhani was one of the four winners of the Fields Medal, the most prestigious award in mathematics.

This is a particularly historic moment, since Mirzakhani is the first woman to win a Fields Medal.

Here's what she did to be recognized as one of the greatest young mathematicians in the world.

Mirzakhani's research is based on compact Riemann surfaces. These are geometric structures constructed by cleverly stretching, bending, and gluing together parts of the complex number plane: the geometric representation of the complex numbers, made up of sums of real and imaginary numbers. The imaginary numbers are represented as multiples of the square root of -1, written as i.

To see how this works, check out the image of the complex plane. There are dots drawn in at each of the points where both the real and imaginary parts of the complex number are integers, giving us a grid.

Imagine taking the plane, and rolling it up like a rug along the vertical imaginary axis, so that each point in the grid with a given real part is touching all the points with the same real part, but different integer imaginary parts. 1+i gets "glued" to 1+2i, 1+3i, 1+4i, and so on.

After we've rolled up our plane in this way, we end up with a cylindrical tube. Now, we can repeat this process, rolling up our tube along the horizontal axis just as we did above, gluing together points that have the same imaginary part. At the end of this process, we get a torus, or something that looks like a donut: one of our Riemann surfaces.

A torus winds up being a fairly simple type of Riemann surface, and there are many ways to stretch around and glue together the complex plane or parts of the plane that lead to much more complicated structures.

A classic result from topology shows that there are only a few options for the overall global structure of surfaces: a sphere, a bunch of donuts glued together, or a bunch of things that look like Mobius strips glued together. These structures can be twisted and stretched in many different kinds of ways.

That last group of surfaces, made up of Mobius strips, is extremely peculiar: they don't have well defined "inside" or "outside" areas the way spheres and toruses do, they can't be represented in three-dimensional space without getting jumbled up with themselves, and it's possible to walk all the way around such a surface and come back to your starting point with your left and right sides reversed. 

When we take the complex plane or part of the complex plane and stretch and glue it together to make a Riemann surface, we get something that looks like one of those first three types of surfaces: a sphere, a torus, or a bunch of toruses glued together, like the double torus.

Their exact geometric structures — their shapes — are determined by what parts of the complex plane are getting glued together. The surfaces can be twisted all over the place, stretched in different directions.

In the most interesting cases, when we're working with a surface that has a broad structure of two or more donuts glued together, these geometries take on a non-Euclidean hyperbolic nature, in which strange things happen.

In the usual, flat plane, if you have a line and a point not on that line, there is exactly one line going through the point that is parallel to the original line. In a hyperbolic space, there are infinitely many parallel lines. Triangles on a hyperbolic plane have angles that add up to less than 180°.

On a hyperbolic surface, we don't have straight lines, given the curvature of the surface. Instead, geometers consider "geodesics" when working in a non-Euclidian space. Geodesics are the natural analogue of lines: just as a line segment in a plane is the shortest path between two points, a geodesic on a Riemann surface is the curve with the shortest hyperbolic length between two points on the surface.

Mirzakhani's doctoral research focused on a counting problem involving a special type of geodesic on Riemann surfaces. Because of the compact closed nature of surfaces, geodesics can sometimes loop around the surface and come back to their starting point, and these are called closed geodesics. Closed geodesics that don't intersect themselves while tracing their path around the surface are called simple closed geodesics.

Mathematicians like counting things, and so Mirzakhani's doctoral thesis answered the question "how many simple closed geodesics shorter than some given length can there be on a particular Riemann surface?"

Mirzakhani found a formula, based on the given length, that says roughly how many curves of this type can be on a particular surface. What's truly amazing about her research is how she went about finding that formula.

As mentioned above, the interesting hyperbolic Riemann surfaces all have a broad global structure that looks like some number of toruses or donuts glued together. It's possible to take two surfaces made out of the same number of donuts and deform by pulling or stretching on one surface to get the other surface, and so these surfaces are in some way related to each other. The number of donuts a surface is made out of is called the genus of the surface.

Another thing mathematicians like doing is taking a collection of mathematical structures that are related to each other, like Riemann surfaces of the same genus, and turning that collection into a mathematical structure on its own.

If we take all the Riemann surfaces of a particular genus, view those as points, and then define the "distance" between two surfaces to be, very roughly and loosely speaking, based on how much we have to do to stretch one surface to turn it into the other, we get a geometry of sorts on the entire collection of surfaces, called a moduli space.

Moduli spaces have extremely complicated and strange geometries, and mathematicians are still far from a full understanding of them. Mirzakhani, however, was able to use that strange geometry to answer her counting question. She showed that certain types of volume measurements in moduli spaces are related to the number of simple closed geodesics on a particular space.

What's remarkable about Mirzakhani's work is that she's answering a question about a particular surface by looking at the moduli space of all surfaces. As the International Mathematical Union puts it in their press release on Mirzakhani's award, while the number of these special curves "is a statement about a single, though arbitrary, hyperbolic structure on a surface, Mirzakhani proved it by considering all such structures simultaneously" by looking at the geometry of moduli spaces.

Mirzakhani's later and current work goes into the structure of moduli space itself. She has solved similar kinds of counting problems involving geodesics, not on a particular surface, but within the complicated geometry of moduli space itself. Her work also involves various links between geodesics in moduli space and certain problems in the field of dynamical systems, in which mathematicians study how a system evolves in either an orderly or chaotic fashion. 

Few mathematicians have been able to directly attack problems within the strange realm of moduli space with the same skill as Mirzakhani, and her Fields Medal testifies to her abilities in this largely unexplored area.

For more detail, check out the International Mathematical Union's press release here.

NOW WATCH: The Math Formula That Explains All Those Strange Coincidences

SEE ALSO: The 12 Mathematicians Who Unlocked The Modern World

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If you're a big Amazon shopper, you've likely spent some time poking through the reviews before you make a big purchase. Generally, the advice and warnings people leave are helpful. 

But sometimes it's just hilarious. 

We found this Quora thread of the most ridiculous Amazon reviews, and picked out our favorite gems. 

(Warning: Some are a little NSFW.)

This titanium watch costs nearly $80,000 — but it's clearly worth it.

Source. 

Just your average tin of radioactive Uranium ore ...

Source. 

This three wolves T-shirt has some special powers ...

Source. 

When Bungie released the beta version of its next-generation sci-fi adventure “Destiny” in July, players only got to explore a few limited areas of the Earth and the moon.

But in the latest trailer to debut, Bungie shows off what “Destiny” missions will look like on Mars in all its rust-colored glory.

Here’s what the description for the trailer says:

What little we know of Mars may as well be a myth. We built a massive metropolis in the red dust. No one knows what remains of our lost age, now buried beneath the dunes.

Though Mars is the only planet revealed in this trailer, Bungie says all planets and moons featured in "Destiny" can be found in our own solar system. Gamers will be able to visit them all starting September 9.

Check out the full trailer below.

"Destiny" will release on PlayStation 4, PlayStation 3, Xbox One, and Xbox 360 on September 9.

SEE ALSO: I Played The Most Anticipated Game Of The Year For Five Straight Hours And It Blew Me Away

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The first rule of Apple University is you don't talk about Apple University.

The second rule of Apple University is you don't talk about Apple University.

Unless, of course, you're the New York Times, which recently got a glimpse inside the tech giant's internal training program with the help of unnamed sources. The program is similar to Google's forward-thinking curriculum, though more secretive and full of fine arts metaphors. 

"(Apple's internal training program) is highly secretive and rarely written about," the Times reports. "Apple employees are discouraged from talking about the company in general, and the classes are no exception."

But having navigated that web of secrets, here's what we can tell you about Apple University: 

It's elite.

The training goes on year-round at company headquarters in Cupertino. There are full-time instructors from Yale, Harvard, Stanford, and other top schools. Joel Podolny, once the dean of the Yale School of Management, designed the course at Steve Jobs' request. 

It teaches you how Apple makes business decisions. 

In one course you analyze Apple case studies, like the decision to make iTunes and the iPod compatible with Windows.

"This was a topic of fierce debate among executives," the Times reports. "Mr. Jobs hated the idea of sharing the iPod with Windows, but he eventually acquiesced to his lieutenants. It turned out that opening the iPod to Windows users led to explosive growth of the music player and the iTunes Store, an ecosystem that would later contribute to the success of the iPhone."

It teaches you how Apple communicates.

In one class about how Apple crafts its message, an instructor showed a slide of Pablo Picasso's "The Bull," a series of 11 drawings by the Spanish artist. The first plate is full of hooves, horns, and other details; the last is an abstraction, though still a bull. 

That's the Apple method. 

"You go through more iterations until you can simply deliver your message in a very concise way, and that is true to the Apple brand and everything we do," a person who took the course told the Times.

It shows you what makes Apple, Apple.

In a course called "What Makes Apple, Apple," students are shown the remote for Google TV and the remote for Apple TV.

The Google remote has 78 buttons. The Apple remote has three. 

The difference in product comes from a difference in how teams are run, says course instructor Randy Nelson. As the Times reports: 

How did Apple's designers decide on three buttons? They started out with an idea, Mr. Nelson explained, and debated until they had just what was needed — a button to play and pause a video, a button to select something to watch, and another to go to the main menu.

The Google TV remote serves as a counterexample; it had so many buttons, Mr. Nelson said, because the individual engineers and designers who worked on the project all got what they wanted. But, Apple's designers concluded, only three were needed.

It reminds us of an organizational maxim called Conway's Law: "Any organization that designs a system ... will produce a design whose structure is a copy of the organization's communication structure."

At Apple, it's slick. 

And secretive.

SEE ALSO: Here's What Google Teaches Employees In Its 'Search Inside Yourself' Course

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Although some Democrats are calling for Texas. Gov Rick Perry's (R) resignation after he was indicted by a grand jury on Friday, a number of left-leaning observers immediately panned the allegations as unimpressive.

Perry, an expected presidential candidate in 2016, is accused of"abuse of official capacity" and "coercion of [a] public servant" by publicly threatening to zero out a state prosecutor's funding and then actually doing it. Several pundits, including Vox's Matt Yglesias and New York magazine's Jonathan Chait, wrote on Twitter they couldn't see what the big deal was.

"Hard for me to imagine these Rick Perry charges sticking," Yglesias wrote, adding, "Does anyone think this Perry indictment makes sense?"

"My *very* preliminary reaction to the Rick Perry news: I don't understand what law he broke," Chait opined.

ThinkProgress, the liberal-oriented news site, reported that Perry's own attorneys "may have a point" when they argued his veto of the prosecutor funding "was made in accordance with the veto authority afforded to every governor under the Texas Constitution."

"The Texas Constitution gives the governor discretion to decide when to sign and when to veto a bill, as well as discretion to veto individual line-items in an appropriation bill. Though the state legislature probably could limit this veto power in extreme cases — if a state governor literally sold his veto to wealthy interest groups, for example, the legislature could almost certainly make that a crime — a law that cuts too deep into the governor’s veto power raises serious separation of powers concerns," ThinkProgress wrote. "Such laws would rework the balance of power between the executive and the legislature established by the state constitution, and they would almost certainly be unconstitutional."

The Lawyers, Guns & Money blog appeared to agree.

"I’m as contemptuous of Perry as anyone, but this seems really thin," the site said in a post reacting to the indictment. "To the extent that the statute reaches Perry’s behavior, itself kind of a stretch, it’s hard to see how the statute is consistent with the separation of powers established by the state constitution."

But not all Perry critics were skeptical of the indictment against the governor. Indeed, some of the leading voices in Texas Democratic politics called for his resignation, according to KXAN News.

"We call on Governor Perry to immediately step down from office," Gilberto Hinojosa, president of the Texas Democratic Party, said. "Texans deserve real leadership and this is unbecoming of our governor."

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There have been plenty of instances of sports fans getting onto the field and being chased by security, but a man rushing the field during an English Premier League soccer match managed to actually get into the action.

During the second half of a Saturday game between West Ham and Tottenham as players were getting set for a free kick, the man headed out to do the kick himself. Surprisingly, he made it over the line of blocking players and was on target for a goal, although the keeper caught the ball.

As Fansided notes, he did this all mid-stride and continued on his way, with a security guard chasing in tow. He even raised his hands triumphantly as if he had made it.

Tottenham's Christian Eriksen didn't fare any better, and missed the free kick. Tottenham won the game 1-0.

Here's the full video:

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A couple in Union, Kentucky has been arrested by the FBI for allegedly selling prohibited military-grade electronics to China. 

Louis and Rosemary Brothers, who own Valley Forge Composite Technologies, came under investigation after the State Department received information they had used the company to provide International Traffic in Arms Regulations items to China, according to the Associated Press.

“The FBI is dedicated to detect, deter and defeat the threat posed by state sponsored groups, individuals and organizations attempting to illicitly acquire technology,” the agency said in a statement released after the arrests.

The couple was booked and then released on bond, and the company website appeared to be taken down, according to WLWT 5 Cincinnati. It was unclear what the specific items in question were.

Valley Forge Composite Technologies is a publicly traded company whose trading was suspended in April by the Security and Exchange Commission due to a lack of current and accurate information about the company, the SEC stated in a release. 

SEE ALSO: Here's A Breakdown Of The Military-Style Gear Used On The Streets Of Ferguson, Missouri

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The man who sent out the world's first tweet is using the platform to provide on-the-ground updates from the protests in Ferguson, Missouri.

Jack Dorsey, cofounder of Twitter and current founder and CEO of payment startup Square, traveled on Friday to St. Louis, Missouri, which happens to be his hometown. Since then, he's been tweeting from the protests — stemming from the fatal police shooting of 18-year-old Michael Brown — and posting a ton of Vine videos.

Born and raised in St. Louis, the billionaire entrepreneur traveled from his current residence in San Francisco to join the protests. "Feels good to be home. I'll be standing with everyone in Ferguson all weekend," he tweeted Friday.

You can check out his full timeline at @jack, but here are some of his posts:

People's cameras outnumber and outbroadcast the cameras. https://t.co/wW7Z9jvQFr

— Jack (@jack) August 16, 2014

https://t.co/rKCXb1BXc2

— Jack (@jack) August 16, 2014

Man gives out free sandwiches in #Ferguson#DONTSHOOTpic.twitter.com/A1FdDaqnhg

— Liz Peinado (@LizPeinadoSTL) August 16, 2014

Marching #fergusonhttps://t.co/qaxOI3CXEt

— Jack (@jack) August 16, 2014

Cpt. Johnson #fergusonpic.twitter.com/uVKkkK7aXE

— Jack (@jack) August 16, 2014

Cpt. Johnson walking with us. #handsupdontshoothttps://t.co/vJxaedfgvr

— Jack (@jack) August 17, 2014

Marched with Alderman @AntonioFrench. Amazing calm. Thank you Alderman! #fergusonpic.twitter.com/U7HJbliIG3

— Jack (@jack) August 17, 2014

SEE ALSO: The Fabulous Life Of Twitter Cofounder Jack Dorsey

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A common source of anxiety stems from wondering what jobs robots will take over from humans.

Some people are worried that the rise of robots will have profound economic effects, causing some extreme winners and extreme losers, depending on whether you own the robot or get replaced by the robot.

And some people are just concerned that robots will take their job specifically.

Pew recently reviewed a 2013 paper that showed which careers have the highest "Routine Task Intensity." If there's one thing that robots are good at, it's routine tasks, the same activity over and over again. Jobs that entail routine tasks are the best candidates.

Here's the list of careers with the highest Routine Task Intensity (RTI).

Looking at the above list, it should be kind of intuitive that these jobs are susceptible to automation.

Here are the jobs with very low RTI:

(Via Boston.com)

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The financial crisis was so traumatizing, people haven't been able to stop worrying that it could happen again very soon.

Questions like "when's the next crash?" or "when will be the next bailouts?" have been talked about basically non-stop since 2009.

According to Goldman, another real bust (by which they mean a big stock market drop, a housing market drop, and a recession) is pretty unlikely.

Historical analysis of past big busts done by top economist Jan Hatzius and Sven Jari Stehn shows that while there is growing risk of a stock market drop (because of the big rally) we're missing one of the key preconditions needed for a true bust: high credit growth.

They write:

[C]redit growth is the most important predictor of house price busts, especially when we focus on busts that involve a recession. House price busts have also tended to follow periods of high inflation, high equity volatility and large current account deficits, although all of these effects become less pronounced when we focus on recessionary busts. .

...

[T]he current picture looks reasonably reassuring from a macroeconomic perspective. The runup in equity prices since 2009 has modestly raised the estimated risk of an equity bust from low to near-average levels. However, the risk of a recessionary equity bust or any kind of housing bust remains low. The key reason is the weakness of credit growth in recent years.

To have a real painful crackup you need to have a major credit buildup. There have been some signs of credit accelerating lately, but overall we've barely gotten anywhere.

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