Zero-Knowledge Proofs for Beginners

Published here originally.

Introduction

I Spy—did you play as a kid? One person chose a room object, and the other had to guess it by answering yes or no questions. I Spy was entertaining, but did you know it could teach you cryptography?

Zero Knowledge Proofs let you show your pal you know what they picked without exposing how. Math replaces electronics in this secret spy mission. Zero-knowledge proofs (ZKPs) are sophisticated cryptographic tools that allow one party to prove they have particular knowledge without revealing it. This proves identification and ownership, secures financial transactions, and more. This article explains zero-knowledge proofs and provides examples to help you comprehend this powerful technology.

What is a Proof of Zero Knowledge?

Zero-knowledge proofs prove a proposition is true without revealing any other information. This lets the prover show the verifier that they know a fact without revealing it. So, a zero-knowledge proof is like a magician's trick: the prover proves they know something without revealing how or what. Complex mathematical procedures create a proof the verifier can verify.

Want to find an easy way to test it out? Try out with tis awesome example! ZK Crush

Describe it as if I'm 5

Alex and Jack found a cave with a center entrance that only opens when someone knows the secret. Alex knows how to open the cave door and wants to show Jack without telling him.

Alex and Jack name both pathways (let’s call them paths A and B).

1. In the first phase, Alex is already inside the cave and is free to select either path, in this case A or B.

2. As Alex made his decision, Jack entered the cave and asked him to exit from the B path.

3. Jack can confirm that Alex really does know the key to open the door because he came out for the B path and used it.

To conclude, Alex and Jack repeat:

1. Alex walks into the cave.

2. Alex follows a random route.

3. Jack walks into the cave.

4. Alex is asked to follow a random route by Jack.

5. Alex follows Jack's advice and heads back that way.

What is a Zero Knowledge Proof?

At a high level, the aim is to construct a secure and confidential conversation between the prover and the verifier, where the prover convinces the verifier that they have the requisite information without disclosing it. The prover and verifier exchange messages and calculate in each round of the dialogue.

The prover uses their knowledge to prove they have the information the verifier wants during these rounds. The verifier can verify the prover's truthfulness without learning more by checking the proof's mathematical statement or computation.

Zero knowledge proofs use advanced mathematical procedures and cryptography methods to secure communication. These methods ensure the evidence is authentic while preventing the prover from creating a phony proof or the verifier from extracting unnecessary information.

ZK proofs require examples to grasp. Before the examples, there are some preconditions.

Criteria for Proofs of Zero Knowledge

1. Completeness: If the proposition being proved is true, then an honest prover will persuade an honest verifier that it is true.

2. Soundness: If the proposition being proved is untrue, no dishonest prover can persuade a sincere verifier that it is true.

3. Zero-knowledge: The verifier only realizes that the proposition being proved is true. In other words, the proof only establishes the veracity of the proposition being supported and nothing more.

The zero-knowledge condition is crucial. Zero-knowledge proofs show only the secret's veracity. The verifier shouldn't know the secret's value or other details.

Example after example after example

To illustrate, take a zero-knowledge proof with several examples:

Initial Password Verification Example

You want to confirm you know a password or secret phrase without revealing it.

Use a zero-knowledge proof:

1. You and the verifier settle on a mathematical conundrum or issue, such as figuring out a big number's components.

2. The puzzle or problem is then solved using the hidden knowledge that you have learned. You may, for instance, utilize your understanding of the password to determine the components of a particular number.

3. You provide your answer to the verifier, who can assess its accuracy without knowing anything about your private data.

4. You go through this process several times with various riddles or issues to persuade the verifier that you actually are aware of the secret knowledge.

You solved the mathematical puzzles or problems, proving to the verifier that you know the hidden information. The proof is zero-knowledge since the verifier only sees puzzle solutions, not the secret information.

In this scenario, the mathematical challenge or problem represents the secret, and solving it proves you know it. The evidence does not expose the secret, and the verifier just learns that you know it.

My simple example meets the zero-knowledge proof conditions:

1. Completeness: If you actually know the hidden information, you will be able to solve the mathematical puzzles or problems, hence the proof is conclusive.

2. Soundness: The proof is sound because the verifier can use a publicly known algorithm to confirm that your answer to the mathematical conundrum or difficulty is accurate.

3. Zero-knowledge: The proof is zero-knowledge because all the verifier learns is that you are aware of the confidential information. Beyond the fact that you are aware of it, the verifier does not learn anything about the secret information itself, such as the password or the factors of the number. As a result, the proof does not provide any new insights into the secret.

Explanation #2: Toss a coin.

One coin is biased to come up heads more often than tails, while the other is fair (i.e., comes up heads and tails with equal probability). You know which coin is which, but you want to show a friend you can tell them apart without telling them.

Use a zero-knowledge proof:

1. One of the two coins is chosen at random, and you secretly flip it more than once.

2. You show your pal the following series of coin flips without revealing which coin you actually flipped.

3. Next, as one of the two coins is flipped in front of you, your friend asks you to tell which one it is.

4. Then, without revealing which coin is which, you can use your understanding of the secret order of coin flips to determine which coin your friend flipped.

5. To persuade your friend that you can actually differentiate between the coins, you repeat this process multiple times using various secret coin-flipping sequences.

In this example, the series of coin flips represents the knowledge of biased and fair coins. You can prove you know which coin is which without revealing which is biased or fair by employing a different secret sequence of coin flips for each round.

The evidence is zero-knowledge since your friend does not learn anything about which coin is biased and which is fair other than that you can tell them differently. The proof does not indicate which coin you flipped or how many times you flipped it.

The coin-flipping example meets zero-knowledge proof requirements:

1. Completeness: If you actually know which coin is biased and which is fair, you should be able to distinguish between them based on the order of coin flips, and your friend should be persuaded that you can.

2. Soundness: Your friend may confirm that you are correctly recognizing the coins by flipping one of them in front of you and validating your answer, thus the proof is sound in that regard. Because of this, your acquaintance can be sure that you are not just speculating or picking a coin at random.

3. Zero-knowledge: The argument is that your friend has no idea which coin is biased and which is fair beyond your ability to distinguish between them. Your friend is not made aware of the coin you used to make your decision or the order in which you flipped the coins. Consequently, except from letting you know which coin is biased and which is fair, the proof does not give any additional information about the coins themselves.

Figure out the prime number in Example #3.

You want to prove to a friend that you know their product n=pq without revealing p and q. Zero-knowledge proof?

Use a variant of the RSA algorithm. Method:

1. You determine a new number s = r2 mod n by computing a random number r.

2. You email your friend s and a declaration that you are aware of the values of p and q necessary for n to equal pq.

3. A random number (either 0 or 1) is selected by your friend and sent to you.

4. You send your friend r as evidence that you are aware of the values of p and q if e=0. You calculate and communicate your friend's s/r if e=1.

5. Without knowing the values of p and q, your friend can confirm that you know p and q (in the case where e=0) or that s/r is a legitimate square root of s mod n (in the situation where e=1).

This is a zero-knowledge proof since your friend learns nothing about p and q other than their product is n and your ability to verify it without exposing any other information. You can prove that you know p and q by sending r or by computing s/r and sending that instead (if e=1), and your friend can verify that you know p and q or that s/r is a valid square root of s mod n without learning anything else about their values. This meets the conditions of completeness, soundness, and zero-knowledge.

Zero-knowledge proofs satisfy the following:

1. Completeness: The prover can demonstrate this to the verifier by computing q = n/p and sending both p and q to the verifier. The prover also knows a prime number p and a factorization of n as p*q.

2. Soundness: Since it is impossible to identify any pair of numbers that correctly factorize n without being aware of its prime factors, the prover is unable to demonstrate knowledge of any p and q that do not do so.

3. Zero knowledge: The prover only admits that they are aware of a prime number p and its associated factor q, which is already known to the verifier. This is the extent of their knowledge of the prime factors of n. As a result, the prover does not provide any new details regarding n's prime factors.

Types of Proofs of Zero Knowledge

Each zero-knowledge proof has pros and cons. Most zero-knowledge proofs are:

1. Interactive Zero Knowledge Proofs: The prover and the verifier work together to establish the proof in this sort of zero-knowledge proof. The verifier disputes the prover's assertions after receiving a sequence of messages from the prover. When the evidence has been established, the prover will employ these new problems to generate additional responses.

2. Non-Interactive Zero Knowledge Proofs: For this kind of zero-knowledge proof, the prover and verifier just need to exchange a single message. Without further interaction between the two parties, the proof is established.

3. A statistical zero-knowledge proof is one in which the conclusion is reached with a high degree of probability but not with certainty. This indicates that there is a remote possibility that the proof is false, but that this possibility is so remote as to be unimportant.

4. Succinct Non-Interactive Argument of Knowledge (SNARKs): SNARKs are an extremely effective and scalable form of zero-knowledge proof. They are utilized in many different applications, such as machine learning, blockchain technology, and more. Similar to other zero-knowledge proof techniques, SNARKs enable one party—the prover—to demonstrate to another—the verifier—that they are aware of a specific piece of information without disclosing any more information about that information.

5. The main characteristic of SNARKs is their succinctness, which refers to the fact that the size of the proof is substantially smaller than the amount of the original data being proved. Because to its high efficiency and scalability, SNARKs can be used in a wide range of applications, such as machine learning, blockchain technology, and more.

Uses for Zero Knowledge Proofs

ZKP applications include:

1. Verifying Identity ZKPs can be used to verify your identity without disclosing any personal information. This has uses in access control, digital signatures, and online authentication.

2. Proof of Ownership ZKPs can be used to demonstrate ownership of a certain asset without divulging any details about the asset itself. This has uses for protecting intellectual property, managing supply chains, and owning digital assets.

3. Financial Exchanges Without disclosing any details about the transaction itself, ZKPs can be used to validate financial transactions. Cryptocurrency, internet payments, and other digital financial transactions can all use this.

4. By enabling parties to make calculations on the data without disclosing the data itself, Data Privacy ZKPs can be used to preserve the privacy of sensitive data. Applications for this can be found in the financial, healthcare, and other sectors that handle sensitive data.

5. By enabling voters to confirm that their vote was counted without disclosing how they voted, elections ZKPs can be used to ensure the integrity of elections. This is applicable to electronic voting, including internet voting.

6. Cryptography Modern cryptography's ZKPs are a potent instrument that enable secure communication and authentication. This can be used for encrypted messaging and other purposes in the business sector as well as for military and intelligence operations.

Proofs of Zero Knowledge and Compliance

Kubernetes and regulatory compliance use ZKPs in many ways. Examples:

1. Security for Kubernetes ZKPs offer a mechanism to authenticate nodes without disclosing any sensitive information, enhancing the security of Kubernetes clusters. ZKPs, for instance, can be used to verify, without disclosing the specifics of the program, that the nodes in a Kubernetes cluster are running permitted software.

2. Compliance Inspection Without disclosing any sensitive information, ZKPs can be used to demonstrate compliance with rules like the GDPR, HIPAA, and PCI DSS. ZKPs, for instance, can be used to demonstrate that data has been encrypted and stored securely without divulging the specifics of the mechanism employed for either encryption or storage.

3. Access Management Without disclosing any private data, ZKPs can be used to offer safe access control to Kubernetes resources. ZKPs can be used, for instance, to demonstrate that a user has the necessary permissions to access a particular Kubernetes resource without disclosing the details of those permissions.

4. Safe Data Exchange Without disclosing any sensitive information, ZKPs can be used to securely transmit data between Kubernetes clusters or between several businesses. ZKPs, for instance, can be used to demonstrate the sharing of a specific piece of data between two parties without disclosing the details of the data itself.

5. Kubernetes deployments audited Without disclosing the specifics of the deployment or the data being processed, ZKPs can be used to demonstrate that Kubernetes deployments are working as planned. This can be helpful for auditing purposes and for ensuring that Kubernetes deployments are operating as planned.

ZKPs preserve data and maintain regulatory compliance by letting parties prove things without revealing sensitive information. ZKPs will be used more in Kubernetes as it grows.

The easiest online explanation.

Web3 is growing. Crypto companies are growing.

Instagram, Adidas, and Stripe adopted cryptocurrency.

Bitcoin and other cryptocurrencies made web3 famous.

Most don't know where to start. Cryptocurrency, DeFi, etc. are investments.

Since we don't understand web3, I'll help you today.

Let’s go.

1. Web3

It is the third generation of the web, and it is built on the decentralization idea which means no one can control it.

There are static webpages that we can only read on the first generation of the web (i.e. Web 1.0).

Web 2.0 websites are interactive. Twitter, Medium, and YouTube.

Each generation controlled the website owner. Simply put, the owner can block us. However, data breaches and selling user data to other companies are issues.

They can influence the audience's mind since they have control.

Assume Twitter's CEO endorses Donald Trump. Result? Twitter would have promoted Donald Trump with tweets and graphics, enhancing his chances of winning.

We need a decentralized, uncontrollable system.

And then there’s Web3.0 to consider. As Bitcoin and Ethereum values climb, so has its popularity. Web3.0 is uncontrolled web evolution. It's good and bad.

Dapps, DeFi, and DAOs are here. It'll all be explained afterwards.

2. Cryptocurrencies:

No need to elaborate.

Bitcoin, Ethereum, Cardano, and Dogecoin are cryptocurrencies. It's digital money used for payments and other uses.

Programs must interact with cryptocurrencies.

3. Blockchain:

Blockchain facilitates bitcoin transactions, investments, and earnings.

This technology governs Web3. It underpins the web3 environment.

Let us delve much deeper.

Blockchain is simple. However, the name expresses the meaning.

Blockchain is a chain of blocks.

Let's use an image if you don't understand.

The graphic above explains blockchain. Think Blockchain. The block stores related data.

Here's more.

4. Smart contracts

Programmers and developers must write programs. Smart contracts are these blockchain apps.

That’s reasonable.

Decentralized web3.0 requires immutable smart contracts or programs.

5. NFTs

Blockchain art is NFT. Non-Fungible Tokens.

Explaining Non-Fungible Token may help.

Two sorts of tokens:

1. These tokens are fungible, meaning they can be changed. Think of Bitcoin or cash. The token won't change if you sell one Bitcoin and acquire another.

2. Non-Fungible Token: Since these tokens cannot be exchanged, they are exclusive. For instance, music, painting, and so forth.

Right now, Companies and even individuals are currently developing worthless NFTs.

The concept of NFTs is much improved when properly handled.

6. Dapp

Decentralized apps are Dapps. Instagram, Twitter, and Medium apps in the same way that there is a lot of decentralized blockchain app.

Curve, Yearn Finance, OpenSea, Axie Infinity, etc. are dapps.

7. DAOs

DAOs are member-owned and governed.

Consider it a company with a core group of contributors.

8. DeFi

We all utilize centrally regulated financial services. We fund these banks.

If you have $10,000 in your bank account, the bank can invest it and retain the majority of the profits.

We only get a penny back. Some banks offer poor returns. To secure a loan, we must trust the bank, divulge our information, and fill out lots of paperwork.

DeFi was built for such issues.

Decentralized banks are uncontrolled. Staking, liquidity, yield farming, and more can earn you money.

Web3 beginners should start with these resources.

If you think NFTs are awful, check out the art market.

The fervor around NFTs has subsided in recent months due to the crypto market crash and the media's short attention span. They were all anyone could talk about earlier this spring. Last semester, when passions were high and field luminaries were discussing "slurp juices," I asked my students and students from over 20 other universities what they thought of NFTs.

According to many, NFTs were either tasteless pyramid schemes or a new way for artists to make money. NFTs contributed to the climate crisis and harmed the environment, but so did air travel, fast fashion, and smartphones. Some students complained that NFTs were cheap, tasteless, algorithmically generated schlock, but others asked how this was different from other art.

I'm not sure what I expected, but the intensity of students' reactions surprised me. They had strong, emotional opinions about a technology I'd always considered administrative. NFTs address ownership and accounting, like most crypto/blockchain projects.

Art markets can be irrational, arbitrary, and subject to the same scams and schemes as any market. And maybe a few shenanigans that are unique to the art world.

The Fairness Question

Fairness, a deflating moral currency, was the general sentiment (the less of it in circulation, the more ardently we clamor for it.) These students, almost all of whom are artists, complained to the mismatch between the quality of the work in some notable NFT collections and the excessive amounts these items were fetching on the market. They can sketch a Bored Ape or Lazy Lion in their sleep. Why should they buy ramen with school loans while certain swindlers get rich?

I understand students. Art markets are unjust. They can be irrational, arbitrary, and governed by chance and circumstance, like any market. And art-world shenanigans.

Almost every mainstream critique leveled against NFTs applies just as easily to art markets

Over 50% of artworks in circulation are fake, say experts. Sincere art collectors and institutions are upset by the prevalence of fake goods on the market. Not everyone. Wealthy people and companies use art as investments. They can use cultural institutions like museums and galleries to increase the value of inherited art collections. People sometimes buy artworks and use family ties or connections to museums or other cultural taste-makers to hype the work in their collection, driving up the price and allowing them to sell for a profit. Money launderers can disguise capital flows by using market whims, hype, and fluctuating asset prices.

Almost every mainstream critique leveled against NFTs applies just as easily to art markets.

Art has always been this way. Edward Kienholz's 1989 print series satirized art markets. He stamped 395 identical pieces of paper from $1 to $395. Each piece was initially priced as indicated. Kienholz was joking about a strange feature of art markets: once the last print in a series sells for $395, all previous works are worth at least that much. The entire series is valued at its highest auction price. I don't know what a Kienholz print sells for today (inquire with the gallery), but it's more than $395.

I love Lee Lozano's 1969 "Real Money Piece." Lozano put cash in various denominations in a jar in her apartment and gave it to visitors. She wrote, "Offer guests coffee, diet pepsi, bourbon, half-and-half, ice water, grass, and money." "Offer real money as candy."

Lee Lozano kept track of who she gave money to, how much they took, if any, and how they reacted to the offer of free money without explanation. Diverse reactions. Some found it funny, others found it strange, and others didn't care. Lozano rarely says:

Apr 17 Keith Sonnier refused, later screws lid very tightly back on. Apr 27 Kaltenbach takes all the money out of the jar when I offer it, examines all the money & puts it all back in jar. Says he doesn’t need money now. Apr 28 David Parson refused, laughing. May 1 Warren C. Ingersoll refused. He got very upset about my “attitude towards money.” May 4 Keith Sonnier refused, but said he would take money if he needed it which he might in the near future. May 7 Dick Anderson barely glances at the money when I stick it under his nose and says “Oh no thanks, I intend to earn it on my own.” May 8 Billy Bryant Copley didn’t take any but then it was sort of spoiled because I had told him about this piece on the phone & he had time to think about it he said.

Smart Contracts (smart as in fair, not smart as in Blockchain)

Cornell University's Cheryl Finley has done a lot of research on secondary art markets. I first learned about her research when I met her at the University of Florida's Harn Museum, where she spoke about smart contracts (smart as in fair, not smart as in Blockchain) and new protocols that could help artists who are often left out of the economic benefits of their own work, including women and women of color.

Her talk included findings from her ArtNet op-ed with Lauren van Haaften-Schick, Christian Reeder, and Amy Whitaker.

NFTs allow us to think about and hack on formal contractual relationships outside a system of laws that is currently not set up to service our community.

The ArtNet article The Recent Sale of Amy Sherald's ‘Welfare Queen' Symbolizes the Urgent Need for Resale Royalties and Economic Equity for Artists discussed Sherald's 2012 portrait of a regal woman in a purple dress wearing a sparkling crown and elegant set of pearls against a vibrant red background.

Amy Sherald sold "Welfare Queen" to Princeton professor Imani Perry. Sherald agreed to a payment plan to accommodate Perry's budget.

Amy Sherald rose to fame for her 2016 portrait of Michelle Obama and her full-length portrait of Breonna Taylor, one of the most famous works of the past decade.

As is common, Sherald's rising star drove up the price of her earlier works. Perry's "Welfare Queen" sold for $3.9 million in 2021.

Imani Perry's early investment paid off big-time. Amy Sherald, whose work directly increased the painting's value and who was on an artist's shoestring budget when she agreed to sell "Welfare Queen" in 2012, did not see any of the 2021 auction money. Perry and the auction house got that money.

Sherald sold her Breonna Taylor portrait to the Smithsonian and Louisville's Speed Art Museum to fund a $1 million scholarship. This is a great example of what an artist can do for the community if they can amass wealth through their work.

NFTs haven't solved all of the art market's problems — fakes, money laundering, market manipulation — but they didn't create them. Blockchain and NFTs are credited with making these issues more transparent. More ideas emerge daily about what a smart contract should do for artists.

NFTs are a copyright solution. They allow us to hack formal contractual relationships outside a law system that doesn't serve our community.

Amy Sherald shows the good smart contracts can do (as in, well-considered, self-determined contracts, not necessarily blockchain contracts.) Giving back to our community, deciding where and how our work can be sold or displayed, and ensuring artists share in the equity of our work and the economy our labor creates.

As a marketer, I joined Twitter on August 31, 2022 to use it.

Growth has been volatile, causing up-and-down engagements. 500 followers in 11 days.

I met amazing content creators, marketers, and people.

Those who use Twitter may know that one-liners win the algorithm, especially if they're funny or humorous, but as a marketer I can't risk posting content that my audience won't like.

I researched, learned some strategies, and A/B tested; some worked, some didn't.

In this article, I share what worked for me so you can do the same.

Thanks for reading!

Let's check my Twitter stats.

• Tweets: how many tweets I sent in the first 28 days.

• A user may be presented with a Tweet in their timeline or in search results.

• In-person visits how many times my Twitter profile was viewed in the first 28 days.

• Mentions: the number of times a tweet has mentioned my name.

• Number of followers: People who were following me

Getting 500 Twitter followers isn't difficult.

Not easy, but doable.

Follow these steps to begin:

Determine your content pillars in step 1.

My formula is Growth = Content + Marketing + Community.

I discuss growth strategies.

My concept for growth is : 1. Content = creating / writing + sharing content in my niche. 2. Marketing = Marketing everything in business + I share my everyday learnings in business, marketing & entrepreneurship. 3. Community = Building community of like minded individuals (Also,I share how to’s) + supporting marketers to build & grow through community building.

Identify content pillars to create content for your audience.

2. Make your profile better

Create a profile picture. Your recognition factor is this.

Professional headshots are worthwhile.

This tool can help you create a free, eye-catching profile pic.

Use a niche-appropriate avatar if you don't want to show your face.

2. Create a bio that converts well mainly because first impressions count.

what you're sharing + why + +social proof what are you making

Be brief and precise. (155 characters)

3. Configure your banner

Banners complement profile pictures.

Use this space to explain what you do and how Twitter followers can benefit.

Canva's Twitter header maker is free.

Birdy can test multiple photo, bio, and banner combinations to optimize your profile.

• Versions A and B of your profile should be completed.

• Find the version that converts the best.

• Use the profile that converts the best.

4. Special handle

If your username/handle is related to your niche, it will help you build authority and presence among your audience. Mine on Twitter is @marketershruti.

5. Participate expertly

Proficiently engage while you'll have no audience at first. Borrow your dream audience for free.

Steps:

• Find a creator who has the audience you want.

• Activate their post notifications and follow them.

• Add a valuable comment first.

6. Create fantastic content

Use:

• Medium (Read articles about your topic.)

• Podcasts (Listen to experts on your topics)

• YouTube (Follow channels in your niche)

Tweet what?

• Listicle ( Hacks, Books, Tools, Podcasts)

• Lessons (Teach your audience how to do 1 thing)

• Inspirational (Inspire people to take action)

Consistent writing?

• You MUST plan ahead and schedule your Tweets.

• Use a scheduling tool that is effective for you; hypefury is mine.

Lastly, consistency is everything that attracts growth. After optimizing your profile, stay active to gain followers, engagements, and clients.

If you found this helpful, please like and comment below.

For some people, the glass is half empty. For others, it’s half full. And for some, the question is, How do I get this glass totally full again?

Problem-solvers are the last group. They're neutral. Pragmatists.

Problems surround them. They fix things instead of judging them. Problem-solvers improve the world wherever they go.

Some fail. Sometimes their good intentions have terrible results. Like when they try to help a grandma cross the road because she can't do it alone but discover she never wanted to.

Most programmers, software engineers, and data scientists solve problems. They use computer code to fix problems they see.

Coding is best done by understanding and solving the problem.

Despite your best intentions, building the wrong solution may have negative consequences. Helping an unwilling grandma cross the road.

How can you improve problem-solving?

1. Examine your presumptions.

Don’t think There’s a grandma, and she’s unable to cross the road. Therefore I must help her over the road. Instead think This grandma looks unable to cross the road. Let’s ask her whether she needs my help to cross it.

Maybe the grandma can’t cross the road alone, but maybe she can. You can’t tell for sure just by looking at her. It’s better to ask.

Maybe the grandma wants to cross the road. But maybe she doesn’t. It’s better to ask!

Building software is similar. Do only I find this website ugly? Who can I consult?

We all have biases, mental shortcuts, and worldviews. They simplify life.

Problem-solving requires questioning all assumptions. They might be wrong!

Think less. Ask more.

Secondly, fully comprehend the issue.

Grandma wants to cross the road? Does she want flowers from the shop across the street?

Understanding the problem advances us two steps. Instead of just watching people and their challenges, try to read their intentions.

Don't ask, How can I help grandma cross the road? Why would this grandma cross the road? What's her goal?

Understand what people want before proposing solutions.

3. Request more information. This is not a scam!

People think great problem solvers solve problems immediately. False!

Problem-solvers study problems. Understanding the problem makes solving it easy.

When you see a grandma struggling to cross the road, you want to grab her elbow and pull her over. However, a good problem solver would ask grandma what she wants. So:

Problem solver: Excuse me, ma’am? Do you wish to get over the road? Grandma: Yes indeed, young man! Thanks for asking. Problem solver: What do you want to do on the other side? Grandma: I want to buy a bouquet of flowers for my dear husband. He loves flowers! I wish the shop wasn’t across this busy road… Problem solver: Which flowers does your husband like best? Grandma: He loves red dahlia. I usually buy about 20 of them. They look so pretty in his vase at the window! Problem solver: I can get those dahlia for you quickly. Go sit on the bench over here while you’re waiting; I’ll be back in five minutes. Grandma: You would do that for me? What a generous young man you are!

A mediocre problem solver would have helped the grandma cross the road, but he might have forgotten that she needs to cross again. She must watch out for cars and protect her flowers on the way back.

A good problem solver realizes that grandma's husband wants 20 red dahlias and completes the task.

4- Rapid and intense brainstorming

Understanding a problem makes solutions easy. However, you may not have all the information needed to solve the problem.

Additionally, retrieving crucial information can be difficult.

You could start a blog. You don't know your readers' interests. You can't ask readers because you don't know who they are.

Brainstorming works here. Set a stopwatch (most smartphones have one) to ring after five minutes. In the remaining time, write down as many topics as possible.

No answer is wrong. Note everything.

Sort these topics later. Programming or data science? What might readers scroll past—are these your socks this morning?

Rank your ideas intuitively and logically. Write Medium stories using the top 35 ideas.

5 - Google it.

Doctor Google may answer this seemingly insignificant question. If you understand your problem, try googling or binging.

Someone has probably had your problem before. The problem-solver may have posted their solution online.

Use others' experiences. If you're social, ask a friend or coworker for help.

6 - Consider it later

Rest your brain.

Reread. Your brain needs rest to function.

Hustle culture encourages working 24/7. It doesn't take a neuroscientist to see that this is mental torture.

Leave an unsolvable problem. Visit friends, take a hot shower, or do whatever you enjoy outside of problem-solving.

Nap.

I get my best ideas in the morning after working on a problem. I couldn't have had these ideas last night.

Sleeping subconsciously. Leave it alone and you may be surprised by the genius it produces.

7 - Learn to live with frustration

There are problems that you’ll never solve.

Mathematicians are world-class problem-solvers. The brightest minds in history have failed to solve many mathematical problems.

A Gordian knot problem can frustrate you. You're smart!

Frustration-haters don't solve problems well. They choose simple problems to avoid frustration.

No. Great problem solvers want to solve a problem but know when to give up.

Frustration initially hurts. You adapt.

Famous last words

If you read this article, you probably solve problems. We've covered many ways to improve, so here's a summary:

1. Test your presumptions. Is the issue the same for everyone else when you see one? Or are your prejudices and self-judgments misguiding you?

2. Recognize the issue completely. On the surface, a problem may seem straightforward, but what's really going on? Try to see what the current situation might be building up to by thinking two steps ahead of the current situation.

3. Request more information. You are no longer a high school student. A two-sentence problem statement is not sufficient to provide a solution. Ask away if you need more details!

4. Think quickly and thoroughly. In a constrained amount of time, try to write down all your thoughts. All concepts are worthwhile! Later, you can order them.

5. Google it. There is a purpose for the internet. Use it.

6. Consider it later at night. A rested mind is more creative. It might seem counterintuitive to leave a problem unresolved. But while you're sleeping, your subconscious will handle the laborious tasks.

7. Accept annoyance as a normal part of life. Don't give up if you're feeling frustrated. It's a step in the procedure. It's also perfectly acceptable to give up on a problem because there are other, more pressing issues that need to be addressed.

You might feel stupid sometimes, but that just shows that you’re human. You care about the world and you want to make it better.

At the end of the day, that’s all there is to problem solving — making the world a little bit better.