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I believe a lot of people struggle with copywriting - at least online - because of another reason… something incredibly important yet overlooked.When it comes to writing copy online, copywriters and marketers need to take into considering SEO and keyword research.If you want to build your blog audience, you’re going to have to get smarter with your content.One of the biggest challenges that copywriters, bloggers and content marketers face is writing content that’s optimized for search engines, yet will also appeal to people.According to Copyblogger, SEO is the most misunderstood topic online. But, SEO content isn’t complicated, once you understand that people come first, before search algorithms. SEO firms make their money understanding these simple concepts.Thriving in your online business means that you must go beyond simply “writing content.” Your content needs to accomplish two goals: first, appeal to the end-user (customers, clients, prospects, readers, etc.) and second, solve a particular problem.But, how do you create content that meets those goals? How do you create content that ranks well with Google and also persuades people? That’s what SEO copywriting is all about. Don't worry if you can't afford an expensive SEO copywriter. You can do this following simple rules.So first, what is SEO?We all know what happens when you type a search query into a search engine and hit “enter”: You get a list of search results that are relevant to your search term.Those results pages appear as a result of search engine optimization (SEO). In a nutshell, SEO is a method of optimizing (enhancing the effectiveness of) your content for the search engines, in order to help it rank higher than content from other sites that target the same search terms.Alpha Bee Design gives a clear picture of the SEO process:Step by step, then, SEO is when:You research keywords …Then select a particular keyword and …Use that keyword to write content …Which other people then read and share on Twitter, Facebook, their own blogs and other social media platforms.According to Redevolution, Google displays web pages in their search results based on the authority and relevance of the page to enhance the user experience. How does it measure authority and relevance?Google determines the relevance of your page by analyzing its content based on several factors, including where and how often you use certain words in that piece of content.Google measures authority by the number of links pointing to that page and how trustworthy those links are.On the internet, links are like votes, with a slight difference. The winner of the election is determined solely by the number of votes, whereas your web page’s rank doesn’t depend so much on how many incoming links it has (quantity), but rather on the quality of those links. You and your marketing team need to understand this.Quality has become the #1 ranking factor in Google, especially since the Google Panda and Penguin updates.If you want more information on SEO, check out The Beginner’s Guide To SEO and The Advanced Guide To SEO.Understanding CopywritingCopywriting is the art and science of creating content that prompts the reader/end-user to either buy a product, subscribe to a list, take a test drive or take some other action that will benefit you.Copywriting is salesmanship, says Bruce Bendinger. His definition of copywriting will make you smile:Who drives a user to take action? A copywriter does. A copywriter is a skilled professional who writes copy for advertisements, promotions and customer engagement. In the marketing world, they’re often referred to as “creatives.” An SEO copywriter tailors this to online content.A copywriter is someone who understands people, knows what his audience likes and chooses the words that will appeal to them. The headline, words, phrases, sentences and paragraphs used in the content have to persuade and cause readers to take a specific action. An SEO copywriter also understand how Google feels about certain words and phrases, especially long tail phrases.If you’re a blogger, freelance writer or online business entrepreneur, you can become a sought-after copywriter when you develop your creativity and perfect your writing skills.If you want to build a thriving online business and survive in this changing world of SEO, your job is to create useful content that’s interesting, persuasive and well-optimized for search engines -- and you have to do it consistently. That is part of the user experience, getting new fresh content on demand.What is SEO Copywriting?SEO copywriting has evolved, since Google started rolling out their updates.If you want to create highly useful content that ranks well in Google and simultaneously funnels paying clients or customers to your online business, you must think about the components of Google’s Ranking Algorithm.SEO copywriting is all about creating useful, compelling and valuable content that targets specific keywords so that other people will gladly promote it on social media platforms. This increases the authority and relevance of your content and improves its ranking in Google for the selected keywords. So when you highly recommend something, Google sees it relevant and you will achieve greater SEO content results.SEO copywriting helps you target your customers and solve their specific problems with well-crafted content.Step #1: Elements of SEO CopywritingCertain elements of valuable content, such as visual appeal and timeliness, are the hallmarks of copywriting grace.Implementing SEO best practices consistently throughout your content will naturally push your content to the Google top 10 and increase your traffic.However, there are elements that will always enable you to rank highly in Google, as well as increase your conversion rate. Before you implement the elements of SEO copywriting, remember that there are things that should come before on-page optimization.Here are the 6 elements of SEO copywriting that matter:1) Site SpeedA study by Akamai revealed these stats:40% of people will abandon a web page if it takes more than 3 seconds to fully load.47% of end users expect a web page to load in two seconds or less.Site speed has been a ranking factor since 2010 and it's good for users, too. If your load time is more than 2 seconds, which is the standard load time for sites, then you should take steps to improve it.That's because if your content is useful and interesting, but it takes a long time for your page to load fully, your visitors will leave, because their attention span is short. They leave because of a bad user experience.How do you measure your site load time? Follow these basic steps -- I’ll use Psychology Today as an example:Step one: Use Pingdom’s website speed test.Step two: Analyze your site speed. Then, click the “History Tab”You see that Psychology Today is fast. The load time is 1.97 seconds, beating the standard load time by 0.3 seconds.Step three: Check the history. You want to determine the previous load times for your site.In our example, the history shows that Psychology Today had a load time of 2.58 seconds on January 10, 2015. The page size was 1.6 MB at the time. But today, the page size has been reduced to 1.5 MB and the load time improved to 1.97 seconds. This is what SEO firms first and so should you.Go ahead and check your site load time using Pingdom.If you want to improve your site speed, read these step-by-step guides:10 Ways To Improve Your Site Speed - And Improve Conversions By 7%Performance Unleashed: How To Speed Up WordPress Load TimesHow To Make Your Site Insanely Fast11 Low-Hanging Fruits For Increasing Website Speed (with Conversions)Does site speed lead to improved conversion rates? Yes it does.According to Kathryn Aragon, speeding up your site’s load time can improve your conversions by 7%.And, this case study reveals how Smashing Magazine experienced an impressive boost in their conversion rate when they cleared their database of all of the clutter that old plugins had created, then merged all of the databases into one.2) HeadlineYour content may be valuable, but if your headline is mediocre, your click-through rate will be low. Dont wast valuable SEO copy.On the average, five times as many people read the headline as read the body copy. When you have written your headline, you have spent eighty cents out of your dollar. —David OgilvyImpression Marketing noted that a lot of bloggers and SEOs spend 55% of their time on content marketing: creating content, monitoring social signals and consumer reactions, tracking analytics, etc. But, how much time do you spend crafting the perfect headline?In SEO copywriting, your headline should attract people’s attention, then prompt them to click and read further.When you rank in Google’s top 10, if your headline is clickable and attractive, it doesn’t really matter whether you rank #1 or #4, because you will still attract organic visitors to your site. As a rule of thumb, a successful SEO copywriter creates the headline before moving on to the body of your article or blog post.Note: Headlines that convey a specific message or idea work best with search users. According to Conversion XL, headlines with numbers are always winners so, if it makes sense, include a figure in the headline.Several authority content sites use numbers in their headlines. Three out of 5 post headlines use numbers on Lifehack. Sites like Inc, BusinessWeek, Mashable and Upworthy all understand the psychology behind numbers.Headlines that have numbers in them usually get shared more on Facebook and Twitter, as well. For example, the second most popular post on HubSpot is a number-type headline with over 10,000 tweets to date.Generate article ideas: If you’re stuck and don’t know what to write about, you can use the Inbound Now tool to generate blog post/article ideas before you hire that SEO copywriter.There are several resources for writing click-worthy and sharable headlines. To demonstrate, let’s write some fresh headlines in three popular industries: small business, fitness and relationships.Clickable and optimized small business headlines:7 Small Business Trends That Will Affect Your SalesHow To Start a Small Business That Customers Will LoveSmall Business Funding: How To Raise $20,000 In 60 DaysSEO and user-friendly fitness headlines:10 Workout Secrets For Women That WorkBest Way To Lose 10 Pounds After PregnancyPersonal Trainer Kits: Become a Certified Personal TrainerWell-optimized and catchy “relationship” headlines:3 Funny Ways To Get Your Ex-Boyfriend BackHow To Renew Your Love Life with Your SpouseWhat Does It Take To Have a Fabulous Wedding?Analyzing the search engine results: Let’s say that we do a search in Google for “save money.” You can see that most search results are SEO-friendly (and target a keyword), but some of the headlines themselves are not attractive to the user. Adding a long tail to the title might help for those with specific inquiries.New and experienced SEA copywriters highly recommend downloading Yoast SEO as a Wrodpress plugin to help optimize SEO copy. Once you learn SEO copywriting, you can write content that will both rank highly in Google result pages and also attract clicks from prospective customers or clients.Note: If you want your whole title to be visible in search engine results, keep it under 72 characters. This will also increase your click-through rates.3) ContentThe content itself is a vital element of SEO copywriting. The major reason why people conduct searches in Google and other search engines is that they’re looking for useful content. Search engines also feed on fresh SEO content, which is why you must consistently update your site.Marcus Sheridan grew his swimming pool company from less than 10,000 to 80,000 monthly visitors, within 6 months and he grew his organic traffic by blogging 2 - 3 times a week.When Marcus began to target long-tail keywords in his blog posts, everything changed. He said that “within hours of writing an article with specific keyword goals, we were showing up on the first page of Google.”If you want to write the best content that will rank well in Google, you have to target keyword phrases. Avoid stuffing keywords or over-optimization. Ideally, put the keyword in your headline, but make sure that it reads smoothly for your readers.The Google Panda 4.1 update was designed to penalize “thin” or shallow content, by keeping lousy content from ranking highly in Google. A typical blog post or article should be at least 1000 words. But, it’s not all about length, because several detailed articles still struggle to rank and retain their position in Google results pages.Before you write your SEO content, it’s essential to understand your reader. Then, niche down and focus on a particular problem that the reader is struggling with. Dare to solve that problem with your content - that’s another goal of combining SEO and copywriting.Every piece of content you write needs a compelling introduction. The introduction is the portion that comes right after the headline (and sub-headline if you include one in your content). Your introduction should contain at least one of your targeted keyword phrases, especially a long tail keyword.However, it’s crucial to understand that modern SEO copywriting has gone beyond keyword targeting and placement. The best approach now is to write content that addresses keyword intent. You will learn about that later on...4) Meta DescriptionBefore writing your content and again, before publishing it, use meta descriptions to help guide search engines. Meta descriptions help search engines and searchers understand what the topic is and why your targeted keywords and phrases keep appearing in the content. This is where SEO firms earn their money, only because they understand this.Moz noted that the meta description is the HTML attribute that provides a “concise explanation” to the search engines of your page’s content. The tag is enclosed with the <head> section </head> on your web page. This is the code sample:Google uses the meta description on your page as a snippet when people search for keywords that are relevant to your page. This snippet copy is what will determine whether or not you get clicks, no matter how highly you rank in the search results.For SEO purposes, the meta description should be 150 - 160 characters and usually appears like this in Google:Note: If you own a WordPress blog, you can install the All-In-One SEO Pack plugin and use it to set up your title, meta description and relevant keywords. If you’re new to blogging, this guide will help you set up the plugin.The Big Question: How do I write meta descriptions that catch people’s attention, as well as rank well in Google?Step #1: Understand keyword intent. Keyword intent is the main purpose or reason behind keywords (whether seed or long-tail keywords).For example, say you’re a social media consultant and you want to attract clients to your business. Then, your primary keyword might be “social media expert advice.”When prospective clients type that keyword into Google search, what do you think they’re really interested in?What they want is clear - a social media expert with advice on how they can move their online or brick-and-mortar business to the next level.Maybe they want more Twitter followers, greater engagement or tips on how to acquire more leads. Your meta description has to be relevant and appeal to them.Step #2: Once your article or blog post has been written, the next thing is to write your meta description. Swell Path recommends you follow this checklist:To demonstrate, let’s put the tips to work, by writing two meta descriptions that are SEO friendly and relevant to our target audience.a) Begin with a question: Looking for expert social media tips to acquire new leads, convert visitors to customers and improve your brand? First, set a definite goal.Length - 141 characters.b) State the obvious: Many companies have given up on social media marketing, because they don’t know what to do. All you need is expert advice that has produced success.Length - 148 characters.Note: You don’t necessarily need to include your exact keywords in your meta description, especially when it doesn’t flow smoothly. I’ve seen a lot of web pages rank in Google’s top 10 without the main keywords.5) Keyword FrequencyKeyword frequency means how many times your chosen keywords appear on the web page.For example, if your target keyword is “best london hotels,” how many times will this exact keyword phrase appear in your 300, 500 or 1000+ word article? In contrast, keyword density is concerned with the ratio of “best london hotels,” to other words on the same page.Keyword frequency and density are no longer as effective as they used to be, before Google started rolling out frequent updates, but are still important parts of SEO content. Avoid on-page optimization mistakes, like keyword stuffing, excessive keyword insertion and header tag stuffing.However, keyword density still impacts organic ranking to some extent. According to Brian Dean, keyword density/frequency is one of the 200 ranking factors, which means that you should still consider it. But, don’t go overboard.Here’s what Brian Clark had to say about it:The only way to tell if your repetition of keywords is super or spammy is to measure that frequency against the overall length of the content. A keyword density greater than 5.5% could make you guilty of keyword stuffing and your page could be penalized by Google. You don’t need to mindlessly repeat keywords to optimize. In fact, if you do, you’re likely to achieve the opposite result.To check your keyword density, use the SEObook keyword density tool.6) Page LinksLinks are the basic building blocks of your web page. One of the 10 things Google knows to be true is that “there’s always more information out there.”Page links tell Google that you’re connected and sociable and that you’ve got useful content that people can access somewhere else. This content could be your own or it could be from another author or site.Linking out to other authority sites and pages is an indication that you value what other people create. Google will reward you for being in sync with their mission: organizing the world’s information and making it universally accessible. A good marketing team would highly recommend to appropriately link.What copywriters usually do is to find appropriate keywords, research accurate data and then use both to craft irresistible content. That’s why copywriting is one of the fundamental factors of search engine optimization.The rules for linking out to other sites are not set in stone. There are also no hard and fast rules for internal linking. However, as a smart online marketer who wants to achieve tremendous results in the search engines, you should:Link to relevant pages within and outside your site in your introductionLink to more in-depth guides or content on your page or other sitesLink with appropriate anchor text, which flows naturally with the contentAs I said earlier, these rules are not set by Google or other search engines. If you can understand your target audience and you produce the best content that will solve your readers' problems, you don't need to worry about keyword density, page links and social signals, because they will occur naturally.Remember that highly useful content will always attract thousands of social shares, comments, leads, clients and sales. This is your job as the SEO copywriter.SEO Copywriting Tools & Resources: To fully understand and implement SEO copywriting best practices, you need viable tools and resources. Here are some that I recommend:Unsuck-it: This is a free web app that you can use to make your words, sentences and paragraphs flow smoothly. You can replace jargon with fun words in five seconds.RhymeZone: A lot of people love reading poetry and admire poets. Use this handy tool to make your copy appealing to the right audience.Read-Able: This simple tool helps you optimize your content for 7th - 8th grade level. This ensures that a wider audience will enjoy your content and click the headline when it shows up in Google results pages.Live-Keyword-Analysis: Use this free SEO tool to accurately calculate the keyword density ratio for a piece of content.Kill Writer’s Block: Highly recommend this tool to generate creative ideas for your next blog post.Quick Sprout: Find out why you’re not generating enough traffic from Google, even when your long-tail keywords are ranking highly.EMV Headline Analyzer: How much does your headline appeal to your readers' emotions? Highly recommend this free tool to analyze your headline and give you a score.Google’s 200 Ranking Factors: The Complete List - this one is self-explanatory.For a list of other resources and tools that are useful for SEO copywriting, check out Writtent.Copywriting optimization points: Search engine rankings can’t be predicted, no matter how knowledgeable you are, because Google is always updating their ranking algorithm. If you plan on hiring an SEO firm to create CEO copy, realize they are subject to a changing game as well.However, there are actions that you can take to increase the likelihood of your web page showing up in Google for relevant search queries. Let’s explore those factors:Title tags: It's a good idea to know how to write title tags for search engine optimization. Again, Yoast SEO can help here. The title tag is a meta HTML tag, like the meta description we saw earlier. It is like the title of a book. It’s the first thing that appears in Google search results.The title tag should be a concise and accurate description of your web page. Google will display 50 - 60 characters of your title in their search results. As well as thinking about length, write titles that will align with your brand.Moz does highly recommend that the optimal format for your title is: Primary Keyword - Secondary Keyword | Brand NameFor example: Learn CSS online - CSS formatting Tips | WebDesignClubHeading tags: The heading tags are labeled h1 - h6. The heading tags will enlarge your font size and make it stand out. When you write content, it should be well structured for readers.Optimizing your title: This is one of the most important things that you can do to ensure that your title ranks in Google, as well as attracting an audience. This screenshot of the Moz resource on title tags helps you optimize your titles effectively:Step #2: Writing Useful Content For PeopleWords are powerful. Words drive engagement. If you can piece words together to produce a valuable piece of content, your target audience will love you for it -- and they’ll stick around. There is no alternative to writing great content.The number of blogs that produce fresh content daily is ever-growing. Remember that duplicate content, keyword-stuffed content and low-quality content will not help your target audience. This is not a good SEO content strategy and can't be emphasized enough. It also won’t do a thing to improve your organic ranking.A recent study shows that even if your content is useful, it still needs three additional elements, in order to drive organic traffic:Optimized for many keywords with lots of searchesA reasonable number of trusted backlinksAn evergreen idea/topicThat's how Brian Dean increased organic traffic by 110% in 14 days.Search users' intent: Keyword research is still necessary. But, the most important aspect of any keyword used by search users is the intent. Before you can write great content that solves a particular problem, you’ve got to know what each keyword stands for.Greg Meyers advises that you pay attention to keyword classification. In other words, understand whether search users want to buy a product or not.There are two important keyword classifications: informational and commercial keywords.Informational keywords: The major reason why people search with these is that they want useful information without having to pay for it.Informational keywords are usually “how-to” in nature. Here’s an example:The keywords highlighted in red are informational, because the searchers are probably only interested in free articles, videos, blog posts and lessons.As an SEO copywriter, you can write useful content around informational keywords, but don't expect to convert readers into customers, because most of them don’t want to buy. Instead, use informational keywords in your content to nurture an audience, engage them and build your brand.Commercial keywords: Commercial keywords show an ‘intent’ to buy. These keywords usually show “desperation” from the searcher. They want solutions quickly - e.g., “lose 10 pounds in 3 days.”The person searching for commercial keywords is likely going to buy a product, or sign up to an email list that will eventually convert them into customers.The fact that someone typed a commercial keyword into Google means the person is ready to take action. Commercial keywords usually contain certain prefixes and suffixes, like reviews, buy, order, review, comparison, compare, free shipping, best, fast, etc. See this example in the weight loss niche:Note: When you write content around commercial keywords, the ultimate goal is to provide useful information on how to use the product, its benefits and features and how to install it, if that’s required.Should you target keywords? Yes. Google still uses keywords to gauge what a particular web page is about. But, use caution and avoid over-optimization.I follow a 3-step plan, when targeting keywords in my content.I include the primary keyword on the headline. For example if my keyword is: conversion rate optimization. My headline maybe, 7 Ways To Make Conversion Rate Optimization Work For YouI use alternative keywords in the introduction, meta description and title tags. For example, What is the best way to increase your conversion rate with every blog post that you write? You know how important this is, especially when it seems as though your best content isn't generating organic traffic, social shares and sales.I write naturally to please my readers and then deliberately include the primary keyword in the conclusion.Storytelling: As an SEO copywriter, storytelling can set you apart, because human beings love good stories. If you can weave your brand story into your blog post, article or video, you will attract more attention.Kzero research showed that storytelling has been the secret of exponential growth for several digital companies, like Google, Facebook, Netflix and even Zappos.Brand storytelling is not something new. Several brands have used it in the past and still do. According to Kristen Matthews, when you use natural storytelling in your content, you can make the maximum impact on the reader.I’ve shared the story of how a Ferrari made me a million bucks. Recently, I wrote a blog post on How Spending $162,301.42 on Clothes Made Me $692,500. So far, the two posts have been shared more than 2,000 times on Facebook, Twitter and Google+ combined:A great example of a successful brand story is The Lego Movie. According to Marcus Sheridan, who is also a great storyteller, “Lego doesn’t sell ‘blocks’ at all, they sell possibilities.”(Read the full story here: The Best Example of Brand Storytelling Ever: The Lego Movie.)In other words, your story should show others the possibility of achieving the same results. Your story shouldn’t be about you alone, however. Instead, find a way to make it appealing to your target audience.That’s when brand storytelling will help improve your organic ranking, traffic and sales conversions.Humor: One of the reasons why you should write with humor is to keep the reader/audience engaged. You can also infuse humor to simplify an uncomfortable or controversial topic.SEO copywriting is not just about writing useful content that solves a particular problem in a boring manner. Your content also has to excite your readers.They should be excited to click your headline, read the introduction and then move slowly down the body. That’s what it means to write persuasively. If you can do that, it doesn’t matter what you create: people will love it. Whatever you highly recommend, they will buy.Here's an example. A professional blogger and public speaker who usually adds humor to her content is Marie Forleo. Each of her video intros always entertains me.Case study: The case study is one of the 15 types of content that will drive more traffic to your site. Case studies can make for powerful content. I’ve seen them rank in Google’s top 10, because they’re highly useful.A study at Content Marketing Institute shows that B2B buyers prefer case studies and research-based content.And, if you consistently write useful and detailed case studies, your major long tail keywords will start showing up in Google’s top 10 for relevant keywords.Case studies usually explain what your products and services are. A good case study will show the experiments, research studies and interviews that you conducted, as well as the results that you got. An SEO firm can help in analytics but isn't absolutely necessary.You can share any type of case study, even ones that didn’t get the results you hoped for. If you want to create a valuable and optimized case study, this screenshot will guide you:Step #3: Keyword Research for Content CreationMore than 66% of all clicks go to the top 3 search engine results. If you want to tap into this rare opportunity to rank in the top 3 positions, then you should learn keyword research best practices.Long-tail keywords are the best way to go in modern SEO, because top brands are not targeting those terms. And, if you can produce good content while naturally targeting these types of keywords, you will definitely dominate the search engines.SEO isn’t complete without keyword research. That's part of how you determine the mindset and intent of your target audience. Long tails help define that mindset.In niche marketing, picking the right keywords is the most challenging aspect of building a profitable niche site.Once you’ve chosen your topic, it’s time to find relevant keywords in that industry. Let’s find keywords for “waterproof digital cameras.”First step: Go to Google Keyword Planner. Plug the topic into the search box, then click “Get Ideas.”A few of the long-tail keywords that we can optimize our content for are:best waterproof digital camerawaterproof digital camera reviewsdisposable waterproof digital cameraOptimizing content for search robots: Search engine robots or web robots (e.g. crawlers, spiders and so on) are programs that constantly scour the web.When a Google spider crawls your web page, it’s looking for fresh content. Some people even say that spiders/crawlers feed on fresh content and will reward you for freshly updating your site regularly.However, understand that when Google spiders index (add your fresh content to their search database), they’re only interested in the meta tags (title tag and meta description).More importantly, they want to know the keywords that you’re targeting. This helps Google determine the industry your content will benefit, e.g., health, business, small business, internet marketing, etc.For best results, you should optimize for search robots like this:Add the primary keyword in your title tag and meta description, once.Add alternative keywords in your introduction and make sure that it flows well. If the keyword doesn’t flow well, ignore it and just write naturally.Keywords like “best seo web design NY” won’t work in the title tag, description and content. The best approach is to use the keyword naturally, like this:How To Find The Best SEO Firm and Web Design In NYOn-page optimization: On-page SEO doesn’t have to be tedious or complicated. A lot of posts have been written to address this topic.Elements that add value to your site, such as internal links, are very important.You control 98% of what happens within your site.That’s why Google pays attention to your web pages and measures the engagement, bounce rate, retention rate and social shares.The foundation of an effective SEO campaign is what happens in-house (on your site). In other words, pay attention to how you target your keywords, which anchor is used to link internal pages, meta tags, etc.This on-page optimization infographic from Backlinko will show you what matters, when it comes to creating SEO-friendly content pages.Click here to view the full size.Off-page optimization: In today’s digital marketing, the public determines how relevant and useful your content is. And, Google uses the off-page factors to gauge the authority and value of your content pages.Generally, you can’t control what happens outside your site. For example, you don’t control who links to you and you don’t control the quality of sites that choose to reference your work.But, if you’re smart, you can use off-page SEO techniques to build a solid brand online and increase organic traffic.According to Chris Ainsworth, the 5 proven off-page SEO strategies that work well are:Build and engage a raving community through social mediaExpose your business and take advantage of localInstill brand confidence through business reviewsPromote local citation and Name/Address/Phone (NAP) consistencyLink building through: blogging, guest posting, competitor link analysis, blog outreach & networking and dofollow blog commenting.Step #4: Copywriting - Getting People to ActThe final piece of the puzzle in this in-depth article is “persuasion” -- the ability of your copy to drive people to action. This isn't difficult, because there are many high-quality resources and tools that you can use.Copy is written to sell a product, service or an idea. But, it all begins with selling yourself, because you’ve only got a maximum of 30 seconds to sell yourself and leave people wanting more.Use bullet points: One of the ways to push people into action is to highlight the key points of your content or topic using bullet points. Before you write blog posts or articles, Vivian Giang recommends you list 3 or 4 strong benefits that you will cover. This is very important, as it also helps you create powerful headlines and paragraphs.Derek Halpern, founder of Social Triggers, a giant SEO firm, combines the power of psychology and copywriting to produce compelling content. He also employs the same strategy on his landing page.Create irresistible and valuable headlines: Columbia University recognized headlines as the most important element of copy. They advise that you think like a reader and write the headline first. The headline should target a keyword and also look attractive.Let’s craft more clickable headlines, using some of the results in Google. When I search for “diet plans,” here are the results I get:The screenshot above shows the headlines showing up at #1 and #2 in Google for the keyword “diet plans.”Original headline:Weight Loss & Diet Plans - Find Healthy Diet Plans And…Here’s a much better headline:The Best Diet Plans To Help You Stay Fit7-Day Weight Loss Diet Plans For WomenOriginal headline:28-Day Fat-Burning Diet and Meal Plan | Muscle & FitnessLet’s make the headline more compelling and useful:28-Day Diet Plans That Will Help You Burn FatBodyBuilding.com has compelling, catchy headlines that are the right length (50 - 60 characters) and target a particular keyword.Have clarity of purpose: Getting clear with your copy, blog post and message is very important. Wider Funnel increased their conversion rate from 10% to 277%, just by implementing clearer call-to-action buttons and reducing the number of form fields.When you write content for your blog, focus on one idea and write your post to address a challenge, solve a problem or explain a complicated issue.According to Success Consciousness, here are some of the ways that you can achieve clarity of purpose as you write your content:Know exactly what you want, before you write it -- e.g., How to Save $100 in the Grocery Store.Use the word “you,” when writing for B2C customers and “we,” when your recipients are mostly business organizations.Research accurate data that are relevant to your topic. This study by Conversion XL shows that using a data-driven approach and creating infographics that have accurate data points will improve social shares.Target 2 - 5 keywords in a blog post and ensure they read naturally. See an example below. If you read it aloud, you will notice how the keywords flow smoothly with the rest of the content.ConclusionI’ve used these SEO strategies to increase my blog’s traffic by 203%. Even if you don't achieve the same growth rate, you will absolutely generate more traffic, improve your brand and fall in love with content marketing.If you’re not leveraging “persuasion” and “psychology” to improve organic rankings and captivate your audience, I highly recommend that now is the best time to start.What’s your take on SEO copywriting? Do you think it’s a major factor for online content marketing success?

List of unsolved problems in mathematicsSince the Renaissance, every century has seen the solution of more mathematical problems than the century before, and yet many mathematical problems, both major and minor, still remain unsolved.Unsolved problems remain in multiple domains, including physics, computer science, algebra, additive and algebraic number theories, analysis, combinatorics, algebraic, discrete and Euclidean geometries, graph, group, model, number, set and Ramsey theories, dynamical systems, partial differential equations, and miscellaneous unsolved problems. Prizes are often awarded for the solution to a long-standing problem, and lists of unsolved problems (such as the list of Millennium Prize Problems) receive considerable attention.Lists of unsolved problems in mathematicsOver the course of time, several lists of unsolved mathematical problems have appeared.ListNumber of problemsProposed byProposed inHilbert's problems23David Hilbert1900Landau's problems4Edmund Landau1912Taniyama's problems[4]36Yutaka Taniyama1955Thurston's 24 questions[5][6]24William Thurston1982Smale's problems18Stephen Smale1998Millennium Prize problems7Clay Mathematics Institute2000Simon problems15Barry Simon2000Unsolved Problems on Mathematics for the 21st Century22Jair Minoro Abe, Shotaro Tanaka2001DARPA's math challenges[8][9]23DARPA2007Millennium Prize ProblemsOf the original seven Millennium Prize Problems set by the Clay Mathematics Institute in 2000, six have yet to be solved, as of 2018:P versus NPHodge conjectureRiemann hypothesisYang–Mills existence and mass gapNavier–Stokes existence and smoothnessBirch and Swinnerton-Dyer conjectureThe seventh problem, the Poincaré conjecture, has been solved.The smooth four-dimensional Poincaré conjecture—that is, whether a four-dimensional topological sphere can have two or more inequivalent smooth structures—is still unsolved.Unsolved problemsAlgebraHomological conjectures in commutative algebraHilbert's sixteenth problemHilbert's fifteenth problemHadamard conjectureJacobson's conjectureExistence of perfect cuboids and associated cuboid conjecturesZauner's conjecture: existence of SIC-POVMs in all dimensionsWild Problem: Classification of pairs of n×n matrices under simultaneous conjugation and problems containing it such as a lot of classification problemsKöthe conjectureBirch–Tate conjectureSerre's conjecture IIBombieri–Lang conjectureFarrell–Jones conjectureBost conjectureUniformity conjectureKaplansky's conjectureKummer–Vandiver conjectureSerre's multiplicity conjecturesPierce–Birkhoff conjectureEilenberg–Ganea conjectureGreen's conjectureGrothendieck–Katz p-curvature conjectureSendov's conjectureAlgebraic geometryAbundance conjectureBass conjectureDeligne conjectureFröberg conjectureFujita conjectureHartshorne conjecturesThe Jacobian conjectureManin conjectureNakai conjectureResolution of singularities in characteristic pStandard conjectures on algebraic cyclesSection conjectureTate conjectureTermination of flipsVirasoro conjectureZariski multiplicity conjectureAnalysisSchanuel's conjecture and four exponentials conjectureLehmer's conjecturePompeiu problemAre [math] γ {\displaystyle \gamma } [/math] (the Euler–Mascheroni constant), π + e, π − e, πe, π/e, πe, π√2, ππ, eπ2, ln π, 2e, ee, Catalan's constant, or Khinchin's constant rational, algebraic irrational, or transcendental? What is the irrationality measure of each of these numbers?[13][14][15]Khabibullin's conjecture on integral inequalitiesHilbert's thirteenth problemVitushkin's conjectureCombinatoricsFrankl's union-closed sets conjecture: for any family of sets closed under sums there exists an element (of the underlying space) belonging to half or more of the sets[16]The lonely runner conjecture: if [math] k + 1 {\displaystyle k+1} [/math] runners with pairwise distinct speeds run round a track of unit length, will every runner be "lonely" (that is, be at least a distance [math] 1 / ( k + 1 ) {\displaystyle 1/(k+1)} [/math] from each other runner) at some time?[17]Singmaster's conjecture: is there a finite upper bound on the multiplicities of the entries greater than 1 in Pascal's triangle?[18]Finding a function to model n-step self-avoiding walks.[19]The 1/3–2/3 conjecture: does every finite partially ordered set that is not totally ordered contain two elements x and y such that the probability that x appears before y in a random linear extension is between 1/3 and 2/3?[20]The uniqueness conjecture for Markov numbers[21]Give a combinatorial interpretation of the Kronecker coefficients.[22]Differential geometryFilling area conjectureHopf conjectureYau's conjectureDiscrete geometrySolving the happy ending problem for arbitrary [math] n {\displaystyle n} [/math][23]Finding matching upper and lower bounds for k-sets and halving lines[24]The Hadwiger conjecture on covering n-dimensional convex bodies with at most 2n smaller copies[25]The Kobon triangle problem on triangles in line arrangements[26]The McMullen problem on projectively transforming sets of points into convex position[27]Ulam's packing conjecture about the identity of the worst-packing convex solid[28]Kissing number problem for dimensions other than 1, 2, 3, 4, 8 and 24[29]How many unit distances can be determined by a set of n points in the Euclidean plane?[30]Euclidean geometryThe einstein problem – does there exist a two-dimensional shape that forms the prototile for an aperiodic tiling, but not for any periodic tiling?[31]Falconer's conjecture that sets of Hausdorff dimension greater than [math] [/math]must have a distance set of nonzero Lebesgue measure[32]Inscribed square problem – does every Jordan curve have an inscribed square?[33]The Kakeya conjecture – double dimensional sets that contain a unit line segment in every dimension necessarily have Hausdorff dimension and Minkowski dimension equal toMoser's worm problem – what is the smallest area of a shape that can cover every unit-length curve in the plane?[35]The moving sofa problem – what is the largest area of a shape that can be maneuvered through a unit-width L-shaped corridor?[36]Shephard's problem (a.k.a. Dürer's conjecture) – does every convex polyhedron have a net?[37]The Thomson problem – what is the minimum energy configuration of N particles bound to the surface of a unit sphere that repel each other with a 1/r potential (or any potential in general)?g-conjectureCircle packing in an equilateral triangleCircle packing in an isosceles right triangleIs the Weaire–Phelan structure an optimal solution to the Kelvin problem?Lebesgue's universal covering problem – what is the convex shape in the plane of least area which provides an isometric cover for any shape of diameter one?Bellman's lost in a forest problem – for a given shape of forest find the shortest escape path which will intersect the edge of the forest at some point for any given starting point and direction inside the forest.Find the complete set of uniform 5-polytopes[38]Covering problem of RadoThe strong bellows conjecture – must the Dehn invariant of a self-intersection free flexible polyhedron stay constant as it flexes?Dissection into orthoschemes – is it possible for simplices of every dimension?[39]Dynamical systemsCollatz conjecture (3n + 1 conjecture)Lyapunov's second method for stability – For what classes of ODEs, describing dynamical systems, does the Lyapunov’s second method formulated in the classical and canonically generalized forms define the necessary and sufficient conditions for the (asymptotical) stability of motion?Furstenberg conjecture – Is every invariant and ergodic measure for the action on the circle either Lebesgue or atomic?Margulis conjecture – Measure classification for diagonalizable actions in higher-rank groupsMLC conjecture – Is the Mandelbrot set locally connected?Weinstein conjecture – Does a regular compact contact type level set of a Hamiltonian on a symplectic manifold carry at least one periodic orbit of the Hamiltonian flow?Arnold–Givental conjecture and Arnold conjecture – relating symplectic geometry to Morse theoryEremenko's conjecture that every component of the escaping set of an entire transcendental function is unboundedIs every reversible cellular automaton in three or more dimensions locally reversible?[40]Many problems concerning an outer billiard, for example show that outer billiards relative to almost every convex polygon has unbounded orbits.Games and puzzlesSudoku: What is the maximum number of givens for a minimal puzzle?[41] How many puzzles have exactly one solution?[41] How many minimal puzzles have exactly one solution?[41]Tic-tac-toe variants: Given a width of tic-tac-toe board, what is the smallest dimension such that X is guaranteed a winning strategy?[42]Graph theoryPaths and cycles in graphsBarnette's conjecture that every cubic bipartite three-connected planar graph has a Hamiltonian cycle[43]Chvátal's toughness conjecture, that there is a number t such that every t-tough graph is Hamiltonian[44]The cycle double cover conjecture that every bridgeless graph has a family of cycles that includes each edge twice[45]The Erdős–Gyárfás conjecture on cycles with power-of-two lengths in cubic graphs[46]The linear arboricity conjecture on decomposing graphs into disjoint unions of paths according to their maximum degree[47]The Lovász conjecture on Hamiltonian paths in symmetric graphs[48]The Oberwolfach problem on which 2-regular graphs have the property that a complete graph on the same number of vertices can be decomposed into edge-disjoint copies of the given graph.[49]Graph coloring and labelingThe Erdős–Faber–Lovász conjecture on coloring unions of cliques[50]The Gyárfás–Sumner conjecture on χ-boundedness of graphs with a forbidden induced tree[51]The Hadwiger conjecture relating coloring to clique minors[52]The Hadwiger–Nelson problem on the chromatic number of unit distance graphs[53]Hedetniemi's conjecture on the chromatic number of tensor products of graphs[54]Jaeger's Petersen-coloring conjecture that every bridgeless cubic graph has a cycle-continuous mapping to the Petersen graph[55]The list coloring conjecture that, for every graph, the list chromatic index equals the chromatic index[56]The Ringel–Kotzig conjecture on graceful labeling of trees[57]The total coloring conjecture of Behzad and Vizing that the total chromatic number is at most two plus the maximum degree[58]Graph drawingThe Albertson conjecture that the crossing number can be lower-bounded by the crossing number of a complete graph with the same chromatic number[59]The Blankenship–Oporowski conjecture on the book thickness of subdivisions[60]Conway's thrackle conjecture[61]Harborth's conjecture that every planar graph can be drawn with integer edge lengths[62]Negami's conjecture on projective-plane embeddings of graphs with planar covers[63]The strong Papadimitriou–Ratajczak conjecture that every polyhedral graph has a convex greedy embedding[64]Turán's brick factory problem – Is there a drawing of any complete bipartite graph with fewer crossings than the number given by Zarankiewicz?[65]Universal point sets of subquadratic size for planar graphs[66]Miscellaneous graph theoryThe Erdős–Hajnal conjecture on large cliques or independent sets in graphs with a forbidden induced subgraph[67]The implicit graph conjecture on the existence of implicit representations for slowly-growing hereditary families of graphs[68]Jørgensen's conjecture that every 6-vertex-connected K6-minor-free graph is an apex graph[69]Does a Moore graph with girth 5 and degree 57 exist?What is the largest possible pathwidth of an n-vertex cubic graph?The reconstruction conjecture and new digraph reconstruction conjecture on whether a graph is uniquely determined by its vertex-deleted subgraphs.Tutte's conjectures that every bridgeless graph has a nowhere-zero 5-flow and every Petersen-minor-free bridgeless graph has a nowhere-zero 4-flowVizing's conjecture on the domination number of cartesian products of graphs[72]Group theoryIs every finitely presented periodic group finite?The inverse Galois problem: is every finite group the Galois group of a Galois extension of the rationals?For which positive integers m, n is the free Burnside group B(m,n) finite? In particular, is B(2, 5) finite?Is every group surjunctive?Andrews–Curtis conjectureHerzog–Schönheim conjectureDoes generalized moonshine exist?Are there an infinite number of Leinster Groups?Number theoryGeneralGrand Riemann hypothesis Generalized Riemann hypothesis Riemann hypothesisn conjecture abc conjecture (Proof claimed in 2012, currently under review.)Hilbert's ninth problemHilbert's eleventh problemHilbert's twelfth problemCarmichael's totient function conjectureErdős–Straus conjecturePillai's conjectureHall's conjectureLindelöf hypothesisMontgomery's pair correlation conjectureHilbert–Pólya conjectureGrimm's conjectureLeopoldt's conjectureDo any odd perfect numbers exist?Are there infinitely many perfect numbers?Do quasiperfect numbers exist?Do any odd weird numbers exist?Do any Lychrel numbers exist?Is 10 a solitary number?Catalan–Dickson conjecture on aliquot sequencesDo any Taxicab(5, 2, n) exist for n > 1?Brocard's problem: existence of integers, (n,m), such that n! + 1 = m2 other than n = 4, 5, 7Beilinson conjectureLittlewood conjectureSzpiro's conjectureVojta's conjectureGoormaghtigh conjectureCongruent number problem (a corollary to Birch and Swinnerton-Dyer conjecture, per Tunnell's theorem)Lehmer's totient problem: if φ(n) divides n − 1, must n be prime?Are there infinitely many amicable numbers?Are there any pairs of amicable numbers which have opposite parity?Are there any pairs of relatively prime amicable numbers?Are there infinitely many betrothed numbers?Are there any pairs of betrothed numbers which have same parity?The Gauss circle problem – how far can the number of integer points in a circle centered at the origin be from the area of the circle?Piltz divisor problem, especially Dirichlet's divisor problemExponent pair conjectureIs π a normal number (its digits are "random")?[86]Casas-Alvero conjectureSato–Tate conjectureFind value of De Bruijn–Newman constantWhich integers can be written as the sum of three perfect cubes?[87]Erdős–Moser problem: is 11 + 21 = 31 the only solution to the Erdős–Moser equation?Is there a covering system with odd distinct moduli?[88]Additive number theorySee also: Problems involving arithmetic progressionsBeal's conjectureFermat–Catalan conjectureGoldbach's conjectureThe values of g(k) and G(k) in Waring's problemLander, Parkin, and Selfridge conjectureGilbreath's conjectureErdős conjecture on arithmetic progressionsErdős–Turán conjecture on additive basesPollock octahedral numbers conjectureSkolem problemDetermine growth rate of rk(N) (see Szemerédi's theorem)Minimum overlap problemDo the Ulam numbers have a positive density?Algebraic number theoryAre there infinitely many real quadratic number fields with unique factorization (Class number problem)?Characterize all algebraic number fields that have some power basis.Stark conjectures (including Brumer–Stark conjecture)Kummer–Vandiver conjectureCombinatorial number theorySingmaster's conjecture: Is there a finite upper bound on the number of times that a number other than 1 can appear in Pascal's triangle?Computational number theoryInteger factorization: Can integer factorization be done in polynomial time?Prime numbersvtePrime number conjecturesBrocard's ConjectureCatalan's Mersenne conjectureAgoh–Giuga conjectureThe Gaussian moat problem: is it possible to find an infinite sequence of distinct Gaussian prime numbers such that the difference between consecutive numbers in the sequence is bounded?New Mersenne conjectureErdős–Mollin–Walsh conjectureAre there infinitely many prime quadruplets?Are there infinitely many cousin primes?Are there infinitely many sexy primes?Are there infinitely many Mersenne primes (Lenstra–Pomerance–Wagstaff conjecture); equivalently, infinitely many even perfect numbers?Are there infinitely many Wagstaff primes?Are there infinitely many Sophie Germain primes?Are there infinitely many Pierpont primes?Are there infinitely many regular primes, and if so is their relative densityFor any given integer b which is not a perfect power and not of the form −4k4 for integer k, are there infinitely many repunit primes to base b?Are there infinitely many Cullen primes?Are there infinitely many Woodall primes?Are there infinitely many Carol primes?Are there infinitely many Kynea primes?Are there infinitely many palindromic primes to every base?Are there infinitely many Fibonacci primes?Are there infinitely many Lucas primes?Are there infinitely many Pell primes?Are there infinitely many Newman–Shanks–Williams primes?Are all Mersenne numbers of prime index square-free?Are there infinitely many Wieferich primes?Are there any Wieferich primes in base 47?Are there any composite c satisfying 2c − 1 ≡ 1 (mod c2)?For any given integer a > 0, are there infinitely many primes p such that ap − 1 ≡ 1 (mod p2)?[89]Can a prime p satisfy 2p − 1 ≡ 1 (mod p2) and 3p − 1 ≡ 1 (mod p2) simultaneously?[90]Are there infinitely many Wilson primes?Are there infinitely many Wolstenholme primes?Are there any Wall–Sun–Sun primes?For any given integer a > 0, are there infinitely many Lucas–Wieferich primes associated with the pair (a, −1)? (Specially, when a = 1, this is the Fibonacci-Wieferich primes, and when a = 2, this is the Pell-Wieferich primes)Is every Fermat number 22n + 1 composite for [math] n > 4 {\displaystyle n>4} [/math]?Are all Fermat numbers square-free?For any given integer a which is not a square and does not equal to −1, are there infinitely many primes with a as a primitive root?Artin's conjecture on primitive rootsIs 78,557 the lowest Sierpiński number (so-called Selfridge's conjecture)?Is 509,203 the lowest Riesel number?Fortune's conjecture (that no Fortunate number is composite)Landau's problemsFeit–Thompson conjectureDoes every prime number appear in the Euclid–Mullin sequence?Does the converse of Wolstenholme's theorem hold for all natural numbers?Elliott–Halberstam conjectureProblems associated to Linnik's theoremFind the smallest Skewes' numberPartial differential equationsRegularity of solutions of Vlasov–Maxwell equationsRegularity of solutions of Euler equationsRamsey theoryThe values of the Ramsey numbers, particularly [math] R ( 5 , 5 ) {\displaystyle R(5,5)} [/math]The values of the Van der Waerden numbersSet theoryThe problem of finding the ultimate core model, one that contains all large cardinals.If ℵω is a strong limit cardinal, then 2ℵω < ℵω1 (see Singular cardinals hypothesis). The best bound, ℵω4, was obtained by Shelah using his pcf theory.Woodin's Ω-hypothesis.Does the consistency of the existence of a strongly compact cardinal imply the consistent existence of a supercompact cardinal?(Woodin) Does the Generalized Continuum Hypothesis below a strongly compact cardinal imply the Generalized Continuum Hypothesis everywhere?Does there exist a Jónsson algebra on ℵω?Without assuming the axiom of choice, can a nontrivial elementary embedding V→V exist?TopologyBorel conjectureHilbert–Smith conjectureNovikov conjectureUnknotting problemWhitehead conjectureZeeman conjectureOtherSee also: List of conjecturesList of unsolved problems in statisticsList of unsolved problems in computer scienceList of unsolved problems in physicsProblems in loop theory and quasigroup theoryProblems in Latin squaresInvariant subspace problemKaplansky's conjectures on group ringsPainlevé conjectureDixmier conjectureBaum–Connes conjectureProve Turing completeness for all unique elementary cellular automataGeneralized star height problemAssorted sphere packing problems, e.g. the densest irregular hypersphere packingsClosed curve problem: Find (explicit) necessary and sufficient conditions that determine when, given two periodic functions with the same period, the integral curve is closed.[91]Keating–Snaith conjectureKung–Traub conjectureAtiyah conjecture on configurationsToeplitz' conjecture (open since 1911)Carathéodory conjectureWeight-monodromy conjectureBerry–Tabor conjectureBirkhoff conjectureGuralnick–Thompson conjectureMNOP conjectureMazur's conjecturesRendezvous problemScholz conjectureNirenberg–Treves conjectureQuantum unique ergodicity conjectureDensity hypothesisZhou conjectureErdős–Ulam problemProblems solved since 1995Pentagonal tiling (Michaël Rao, 2017)[92]Erdős–Burr conjecture (Choongbum Lee, 2017)[93]Boolean Pythagorean triples problem (Marijn Heule, Oliver Kullmann, Victor Marek, 2016)[94]Babai's problem (Problem 3.3 in "Spectra of Cayley graphs") (A. Abdollahi, M. Zallaghi, 2015)[95]Main conjecture in Vinogradov's mean-value theorem (Jean Bourgain, Ciprian Demeter, Larry Guth, 2015)[96]Erdős discrepancy problem (Terence Tao, 2015)[97]Umbral moonshine conjecture (John F. R. Duncan, Michael J. Griffin, Ken Ono, 2015)[98]Anderson conjecture (Cheeger, Naber, 2014)[99]Gaussian correlation inequality (Thomas Royen, 2014)[100]Goldbach's weak conjecture (Harald Helfgott, 2013)[101][102][103]Kadison–Singer problem (Adam Marcus, Daniel Spielman and Nikhil Srivastava, 2013)[104][105] (and the Feichtinger's conjecture,Virtual Haken conjecture (Agol, Groves, Manning, 2012)[106] (and by work of Wise also virtually fibered conjecture)Hsiang–Lawson's conjecture (Brendle, 2012)[107]Willmore conjecture (Fernando Codá Marques and André Neves, 2012)[108]Ehrenpreis conjecture (Kahn, Markovic, 2011)[109]Hanna Neumann conjecture (Mineyev, 2011)[110]Bloch–Kato conjecture (Voevodsky, 2011)[111] (and Quillen–Lichtenbaum conjecture and by work of Geisser and Levine (2001) also Beilinson–Lichtenbaum conjecture[112][113][114])Erdős distinct distances problem (Larry Guth, Netz Hawk Katz, 2011)[115]Density theorem (Namazi, Souto, 2010)[116]Hirsch conjecture (Francisco Santos Leal, 2010)[117][118]Sidon set problem (J. Cilleruelo, I. Ruzsa and C. Vinuesa, 2010)[119]Atiyah conjecture (Austin, 2009)[120]Kauffman–Harary conjecture (Matmann, Solis, 2009)[121]Surface subgroup conjecture (Kahn, Markovic, 2009)[122]Scheinerman's conjecture (Jeremie Chalopin and Daniel Gonçalves, 2009)[123]Cobordism hypothesis (Jacob Lurie, 2008)[124]Full classification of finite simple groups (Harada, Solomon, 2008)Geometrization conjecture (proof was completed by Morgan and Tian in 2008[125] and it is based mostly on work of Grigori Perelman, 2002)[126]Serre's modularity conjecture (Chandrashekhar Khare and Jean-Pierre Wintenberger, 2008)[127][128][129]Heterogeneous tiling conjecture (squaring the plane) (Frederick V. Henle and James M. Henle, 2008)[130]Erdős–Menger conjecture (Aharoni, Berger 2007)[131]Road coloring conjecture (Avraham Trahtman, 2007)[132]The angel problem (Various independent proofs, 2006)[133][134][135][136]Lax conjecture (Lewis, Parrilo, Ramana, 2005)[137]The Langlands–Shelstad fundamental lemma (Ngô Bảo Châu and Gérard Laumon, 2004)[138]Tameness conjecture and Ahlfors measure conjecture (Ian Agol, 2004)[139]Robertson–Seymour theorem (Robertson, Seymour, 2004)[140]Stanley–Wilf conjecture (Gábor Tardos and Adam Marcus, 2004)[141] (and also Alon–Friedgut conjecture)Green–Tao theorem (Ben J. Green and Terence Tao, 2004)[142]Ending lamination theorem (Jeffrey F. Brock, Richard D. Canary, Yair N. Minsky, 2004)[143]Carpenter's rule problem (Connelly, Demaine, Rote, 2003)[144]Cameron–Erdős conjecture (Ben J. Green, 2003, Alexander Sapozhenko, 2003)[145][146]Milnor conjecture (Vladimir Voevodsky, 2003)[147]Kemnitz's conjecture (Reiher, 2003, di Fiore, 2003)[148]Nagata's conjecture (Shestakov, Umirbaev, 2003)[149]Kirillov's conjecture (Baruch, 2003)[150]Poincaré conjecture (Grigori Perelman, 2002)[126]Strong perfect graph conjecture (Maria Chudnovsky, Neil Robertson, Paul Seymour and Robin Thomas, 2002)[151]Kouchnirenko’s conjecture (Haas, 2002)[152]Vaught conjecture (Knight, 2002)[153]Double bubble conjecture (Hutchings, Morgan, Ritoré, Ros, 2002)[154]Catalan's conjecture (Preda Mihăilescu, 2002)[155]n! conjecture (Haiman, 2001)[156] (and also Macdonald positivity conjecture)Kato's conjecture (Auscher, Hofmann, Lacey, McIntosh and Tchamitchian, 2001)[157]Deligne's conjecture on 1-motives (Luca Barbieri-Viale, Andreas Rosenschon, Morihiko Saito, 2001)[158]Modularity theorem (Breuil, Conrad, Diamond and Taylor, 2001)[159]Erdős–Stewart conjecture (Florian Luca, 2001)[160]Berry–Robbins problem (Atiyah, 2000)[161]Erdős–Graham problem (Croot, 2000)[162]Honeycomb conjecture (Thomas Hales, 1999)[163]Gradient conjecture (Krzysztof Kurdyka, Tadeusz Mostowski, Adam Parusinski, 1999)[164]Bogomolov conjecture (Emmanuel Ullmo, 1998, Shou-Wu Zhang, 1998)[165][166]Lafforgue's theorem (Laurent Lafforgue, 1998)[167]Kepler conjecture (Ferguson, Hales, 1998)[168]Dodecahedral conjecture (Hales, McLaughlin, 1998)[169]Ganea conjecture (Iwase, 1997)[170]Torsion conjecture (Merel, 1996)[171]Harary's conjecture (Chen, 1996)[172]Fermat's Last Theorem (Andrew Wiles and Richard Taylor, 1995)[173][174]