If tasked with the problem of coming up with a zk-SNARK protocol, many people would make their way to this point and then get stuck and give up. How can a verifier possibly check every single piece of the computation, without looking at each piece of the computation individually? But it turns out that there is a clever solution.

Polynomials

Polynomials are a special class of algebraic expressions of the form:

• x+5
• x^4
• x^3+3x^2+3x+1
• 628x^{271}+318x^{270}+530x^{269}+…+69x+381

i.e. they are a sum of any (finite!) number of terms of the form cx^k

There are many things that are fascinating about polynomials. But here we are going to zoom in on a particular one: polynomials are a single mathematical object that can contain an unbounded amount of information (think of them as a list of integers and this is obvious). The fourth example above contained 816 digits of tau, and one can easily imagine a polynomial that contains far more.

Furthermore, a single equation between polynomials can represent an unbounded number of equations between numbers. For example, consider the equation A(x)+ B(x) = C(x). If this equation is true, then it's also true that:

• A(0)+B(0)=C(0)
• A(1)+B(1)=C(1)
• A(2)+B(2)=C(2)
• A(3)+B(3)=C(3)

And so on for every possible coordinate. You can even construct polynomials to deliberately represent sets of numbers so you can check many equations all at once. For example, suppose that you wanted to check:

• 12+1=13
• 10+8=18
• 15+8=23
• 15+13=28

You can use a procedure called Lagrange interpolation to construct polynomials A(x) that give (12,10,15,15) as outputs at some specific set of coordinates (eg. (0,1,2,3)), B(x) the outputs (1,8,8,13) on thos same coordinates, and so forth. In fact, here are the polynomials:

• A(x)=-2x^3+\frac{19}{2}x^2-\frac{19}{2}x+12
• B(x)=2x^3-\frac{19}{2}x^2+\frac{29}{2}x+1
• C(x)=5x+13

Checking the equation A(x)+B(x)=C(x) with these polynomials checks all four above equations at the same time.

Comparing a polynomial to itself

You can even check relationships between a large number of adjacent evaluations of the same polynomial using a simple polynomial equation. This is slightly more advanced. Suppose that you want to check that, for a given polynomial F, F(x+2)=F(x)+F(x+1) with the integer range {0,1…89} (so if you also check F(0)=F(1)=1, then F(100) would be the 100th Fibonacci number)

As polynomials, F(x+2)-F(x+1)-F(x) would not be exactly zero, as it could give arbitrary answers outside the range x={0,1…98}. But we can do something clever. In general, there is a rule that if a polynomial P is zero across some set S=\{x_1,x_2…x_n\} then it can be expressed as P(x)=Z(x)*H(x), where Z(x)=(x-x_1)*(x-x_2)*…*(x-x_n) and H(x) is also a polynomial. In other words, any polynomial that equals zero across some set is a (polynomial) multiple of the simplest (lowest-degree) polynomial that equals zero across that same set.

Why is this the case? It is a nice corollary of polynomial long division: the factor theorem. We know that, when dividing P(x) by Z(x), we will get a quotient Q(x) and a remainder R(x) is strictly less than that of Z(x). Since we know that P is zero on all of S, it means that R has to be zero on all of S as well. So we can simply compute R(x) via polynomial interpolation, since it's a polynomial of degree at most n-1 and we know n values (the zeros at S). Interpolating a polynomial with all zeroes gives the zero polynomial, thus R(x)=0 and H(x)=Q(x).

Going back to our example, if we have a polynomial F that encodes Fibonacci numbers (so F(x+2)=F(x)+F(x+1) across x=\{0,1…98\}), then I can convince you that F actually satisfies this condition by proving that the polynomial P(x)=F(x+2)-F(x+1)-F(x) is zero over that range, by giving you the quotient:
H(x)=\frac{F(x+2)-F(x+1)-F(x)}{Z(x)}
Where Z(x) = (x-0)*(x-1)*…*(x-98).
You can calculate Z(x) yourself (ideally you would have it precomputed), check the equation, and if the check passes then F(x) satisfies the condition!

Now, step back and notice what we did here. We converted a 100-step-long computation into a single equation with polynomials. Of course, proving the N'th Fibonacci number is not an especially useful task, especially since Fibonacci numbers have a closed form. But you can use exactly the same basic technique, just with some extra polynomials and some more complicated equations, to encode arbitrary computations with an arbitrarily large number of steps.

With cryptocurrencies like Bitcoin, Ether, and Dogecoin gyrating in value over the past few months, many people are looking at so-called stablecoins like Terra to invest in because of their more predictable prices.

Terraform Labs, which oversees the Terra cryptocurrency project, has benefited from its rising popularity. The company said recently that investors like Arrington Capital, Lightspeed Venture Partners, and Pantera Capital have pledged $150 million to help it incubate various crypto projects that are connected to Terra.

Terraform Labs and its partners have built apps that operate on the company’s blockchain technology that helps keep a permanent and shared record of the firm’s crypto-related financial transactions.

Here’s what you need to know about Terra and the company behind it.

What is Terra?

Terra is a blockchain project developed by Terraform Labs that powers the startup’s cryptocurrencies and financial apps. These cryptocurrencies include the Terra U.S. Dollar, or UST, that is pegged to the U.S. dollar through an algorithm.

Terra is a stablecoin that is intended to reduce the volatility endemic to cryptocurrencies like Bitcoin. Some stablecoins, like Tether, are pegged to more conventional currencies, like the U.S. dollar, through cash and cash equivalents as opposed to an algorithm and associated reserve token.

To mint new UST tokens, a percentage of another digital token and reserve asset, Luna, is “burned.” If the demand for UST rises with more people using the currency, more Luna will be automatically burned and diverted to a community pool. That balancing act is supposed to help stabilize the price, to a degree.

“Luna directly benefits from the economic growth of the Terra economy, and it suffers from contractions of the Terra coin,” Terraform Labs CEO Do Kwon said.

Each time someone buys something—like an ice cream—using UST, that transaction generates a fee, similar to a credit card transaction. That fee is then distributed to people who own Luna tokens, similar to a stock dividend.

Who leads Terra?

The South Korean firm Terraform Labs was founded in 2018 by Daniel Shin and Kwon, who is now the company’s CEO. Kwon is a 29-year-old former Microsoft employee; Shin now heads the Chai online payment service, a Terra partner. Kwon said many Koreans have used the Chai service to buy goods like movie tickets using Terra cryptocurrency.

Terraform Labs does not make money from transactions using its crypto and instead relies on outside funding to operate, Kwon said. It has raised $57 million in funding from investors like HashKey Digital Asset Group, Divergence Digital Currency Fund, and Huobi Capital, according to deal-tracking service PitchBook. The amount raised is in addition to the latest $150 million funding commitment announced on July 16.

What are Terra’s plans?

Terraform Labs plans to use Terra’s blockchain and its associated cryptocurrencies—including one pegged to the Korean won—to create a digital financial system independent of major banks and fintech-app makers. So far, its main source of growth has been in Korea, where people have bought goods at stores, like coffee, using the Chai payment app that’s built on Terra’s blockchain. Kwon said the company’s associated Mirror trading app is experiencing growth in China and Thailand.

Meanwhile, Kwon said Terraform Labs would use its latest $150 million in funding to invest in groups that build financial apps on Terra’s blockchain. He likened the scouting and investing in other groups as akin to a “Y Combinator demo day type of situation,” a reference to the popular startup pitch event organized by early-stage investor Y Combinator.

The combination of all these Terra-specific financial apps shows that Terraform Labs is “almost creating a kind of bank,” said Ryan Watkins, a senior research analyst at cryptocurrency consultancy Messari.

In addition to cryptocurrencies, Terraform Labs has a number of other projects including the Anchor app, a high-yield savings account for holders of the group’s digital coins. Meanwhile, people can use the firm’s associated Mirror app to create synthetic financial assets that mimic more conventional ones, like “tokenized” representations of corporate stocks. These synthetic assets are supposed to be helpful to people like “a small retail trader in Thailand” who can more easily buy shares and “get some exposure to the upside” of stocks that they otherwise wouldn’t have been able to obtain, Kwon said. But some critics have said the U.S. Securities and Exchange Commission may eventually crack down on synthetic stocks, which are currently unregulated.

What do critics say?

Terra still has a long way to go to catch up to bigger cryptocurrency projects like Ethereum.

Most financial transactions involving Terra-related cryptocurrencies have originated in Korea, where its founders are based. Although Terra is becoming more popular in Korea thanks to rising interest in its partner Chai, it’s too early to say whether Terra-related currencies will gain traction in other countries.

Terra’s blockchain runs on a “limited number of nodes,” said Messari’s Watkins, referring to the computers that help keep the system running. That helps reduce latency that may otherwise slow processing of financial transactions, he said.

But the tradeoff is that Terra is less “decentralized” than other blockchain platforms like Ethereum, which is powered by thousands of interconnected computing nodes worldwide. That could make Terra less appealing to some blockchain purists.

Creating 10,000 auto-generated artworks, deploying a smart contract to the Ethereum / Polygon blockchain, setting up some tools, etc.

There is so much to do from launching to running an NFT project. Creating parts for artworks, generating 10,000 unique artworks and metadata, creating a smart contract and deploying it to a blockchain network, creating a website, creating a Twitter account, setting up a Discord server, setting up an OpenSea collection. In addition, you need to have MetaMask installed in your browser and have some ETH / MATIC. Did you get tired of doing all this? Don’t worry, once you know what you need to do, all you have to do is do it one by one.

To be honest, it’s best to run an NFT project in a team of three or more, including artists, developers, and marketers. However, depending on your motivation, you can do it by yourself. Some people might come later to offer help with your project. The most important thing is to take a step as soon as possible.

Creating Parts for Artworks

There are lots of free/paid software for drawing, but after all, I think Adobe Illustrator or Photoshop is the best. The images of Skulls In Love are a composite of 48x48 pixel parts created using Photoshop.

How Many Parts Should You Create?

Are you wondering how many parts you should create to avoid duplication as much as possible when generating your artworks? My friend Stephane, a developer, has created a great tool to help with that.

Generating 10,000 Unique Artworks and Metadata

I highly recommend using the HashLips Art Engine to generate your artworks and metadata. Perhaps there is no better artworks generation tool at the moment.

GitHub: https://github.com/HashLips/hashlips_art_engine
YouTube:

Storing Artworks and Metadata

Ideally, the generated artworks and metadata should be stored on-chain, but if you want to store them off-chain, you should use IPFS. Do not store in centralized storage. This is because data will be lost if the server goes down or if the company goes down. On the other hand, IPFS is a more secure way to find data because it utilizes a distributed, decentralized system.

Storing to IPFS is easy with Pinata, NFT.Storage, and so on. The Skulls In Love uses Pinata. It’s very easy to use, just upload the folder containing your artworks.

Creating and Deploying a Smart Contract

You don’t have to create a smart contract from scratch. There are many great NFT projects, many of which publish their contract source code on Etherscan / PolygonScan. You can choose the contract you like and reuse it. Of course, that requires some knowledge of Solidity, but it depends on your efforts. If you don’t know which contract to choose, use the HashLips smart contract. It’s very simple, but it has almost all the functions you need.

GitHub: https://github.com/HashLips/hashlips_nft_contract

Creating a Website

The website here is not just a static site to showcase your project, it’s a so-called dApp that allows you to access your smart contract and mint NFTs. In fact, this level of dApp is not too difficult for anyone who has ever created a website. Because the ethers.js / web3.js libraries make it easy to interact with your smart contract. There’s also no problem connecting wallets, as MetaMask has great documentation.

The Skulls In Love uses a simple, fast, and modern dApp that I built from scratch using Next.js. It is published on GitHub, so feel free to use it.

Why do people mint NFTs on a website?

Ethereum’s gas fees are high, so if you mint all your NFTs, there will be a huge initial cost. So it makes sense to get the buyers to help with the gas fees for minting.
What about Polygon? Polygon’s gas fees are super cheap, so even if you mint 10,000 NFTs, it’s not a big deal. But we don’t do that. Since NFT projects are a kind of game, it involves the fun of not knowing what will come out after minting.

Creating a Twitter Account

I highly recommend creating a Twitter account. Twitter is an indispensable tool for announcing giveaways and reaching more people. It’s better to announce your project and your artworks little by little, 1–2 weeks before launching your project.

Creating and Setting Up a Discord Server

I highly recommend creating a Discord server as well as a Twitter account. The Discord server is a community and its home. Fans of your NFT project will want to join your community and interact with many other members. So, carefully create each channel on your Discord server to make it a cozy place for your community members.

If you are unfamiliar with Discord, you may be particularly confused by the following:
What bots should I use?
How should I set roles and permissions?
But don’t worry. There are lots of great YouTube videos and blog posts about these.
It’s also a good idea to join the Discord servers of some NFT projects and see how they’re made. Our Discord server is so simple that even beginners will find it easy to understand. Please join us and see it!

UPDATED: As your Discord server grows, you cannot manage it on your own. In this case, you will be hiring several moderators, but choose carefully before hiring. And don’t give them important role permissions right after hiring. Initially, the same permissions as other members are sufficient. After a while, you can add permissions as needed, such as kicking/banning, using the “@every” tag, and adding roles. Again, don’t immediately give significant permissions to your Mod role. Your server can be messed up by fake moderators.

Setting Up Your OpenSea Collection

Before you start selling your NFTs, you need to reserve some for airdrops, giveaways, staff, and more. It’s up to you whether it’s 100, 500, or how many.

After minting some of your NFTs, your account and collection should have been created in OpenSea. Go to OpenSea, connect to your wallet, and set up your collection. Just set your logo, banner image, description, links, royalties, and more. It’s not that difficult.

Promoting Your Project

After all, promotion is the most important thing. In fact, almost every successful NFT project spends a lot of time and effort on it.

In addition to Twitter and Discord, it’s even better to use Instagram, Reddit, and Medium. Also, register your project in NFTCalendar and DISBOARD

About Promoters

You’ll probably get lots of contacts from promoters on your Discord, Twitter, Instagram, and more. But most of them are scams, so don’t pay right away. If you have a promoter that looks attractive to you, be sure to check the promoter’s social media accounts or website to see who he/she is. They basically charge in dollars. The amount they charge isn’t cheap, but promoters with lots of followers may have some temporary effect on your project. Some promoters accept 50% prepaid and 50% postpaid. If you can afford it, it might be worth a try. I never ask them, though.

When Should the Promotion Activities Start?

You may be worried that if you promote your project before it starts, someone will copy your project (artworks). It is true that some projects have actually suffered such damage. I don’t have a clear answer to this question right now, but:

• Do not publish all the information about your project too early
• The information should be released little by little
• Creating artworks that no one can easily copy
  I think these are important.
  If anyone has a good idea, please share it!

About Giveaways

When hosting giveaways, you’ll probably use multiple social media platforms. You may want to grow your Discord server faster. But if joining the Discord server is included in the giveaway requirements, some people hate it. I recommend holding giveaways for each platform. On Twitter and Reddit, you should just add the words “Discord members-only giveaway is being held now! Please join us if you like!”.

If you want to easily pick a giveaway winner in your browser, I recommend Twitter Picker.

Precautions for Distributing Free NFTs

If you want to increase your Twitter followers and Discord members, you can actually get a lot of people by holding events such as giveaways and invite contests. However, distributing many free NFTs at once can be dangerous. Some people who want free NFTs, as soon as they get a free one, sell it at a very low price on marketplaces such as OpenSea. They don’t care about your project and are only thinking about replacing their own “free” NFTs with Ethereum. The lower the floor price of your NFTs, the lower the value of your NFTs (project). Try to think of ways to get people to “buy” your NFTs as much as possible.

Ethereum vs. Polygon

Even though Ethereum has high gas fees, NFT projects on the Ethereum network are still mainstream and popular. On the other hand, Polygon has very low gas fees and fast transaction processing, but NFT projects on the Polygon network are not very popular.

Why? There are several reasons, but the biggest one is that it’s a lot of work to get MATIC (on Polygon blockchain, use MATIC instead of ETH) ready to use. Simply put, you need to bridge your tokens to the Polygon chain. So people need to do this first before minting your NFTs on your website. It may not be a big deal for those who are familiar with crypto and blockchain, but it may be complicated for those who are not. I hope that the tedious work will be simplified in the near future.

If you are confident that your NFTs will be purchased even if they are expensive, or if the total supply of your NFTs is low, you may choose Ethereum. If you just want to save money, you should choose Polygon. Keep in mind that gas fees are incurred not only when minting, but also when performing some of your smart contract functions and when transferring your NFTs.
If I were to launch a new NFT project, I would probably choose Ethereum or Solana.

Conclusion

Some people may want to start an NFT project to make money, but don’t forget to enjoy your own project. Several months ago, I was playing with creating generative art by imitating the CryptoPunks. I found out that auto-generated artworks would be more interesting than I had imagined, and since then I’ve been completely absorbed in generative art.

This is one of the Skulls In Love artworks:

This character wears a cowboy hat, black slim sunglasses, and a kimono. If anyone looks like this, I can’t help laughing!

The Skulls In Love NFTs can be minted for a small amount of MATIC on the official website. Please give it a try to see what kind of unique characters will appear 💀💖

Thank you for reading to the end. I hope this article will be helpful to those who want to launch an NFT project in the future ✨

Six Thinking Hats was written by Dr. Edward de Bono. "Six Thinking Hats" and parallel thinking allow groups to plan thinking processes in a detailed and cohesive way, improving collaboration.

Fundamental ideas

In order to develop strategies for thinking about specific issues, the method assumes that the human brain thinks in a variety of ways that can be intentionally challenged. De Bono identifies six brain-challenging directions. In each direction, the brain brings certain issues into conscious thought (e.g. gut instinct, pessimistic judgement, neutral facts). Some may find wearing hats unnatural, uncomfortable, or counterproductive.

The example of "mismatch" sensitivity is compelling. In the natural world, something out of the ordinary may be dangerous. This mode causes negative judgment and critical thinking.

Colored hats represent each direction. Putting on a colored hat symbolizes changing direction, either literally or metaphorically. De Bono first used this metaphor in his 1971 book "Lateral Thinking for Management" to describe a brainstorming framework. These metaphors allow more complete and elaborate thought separation. Six thinking hats indicate ideas' problems and solutions.

Similarly, his CoRT Thinking Programme introduced "The Five Stages of Thinking" method in 1973.

HAT	OVERVIEW	TECHNIQUE
BLUE	"The Big Picture" & Managing	CAF (Consider All Factors); FIP (First Important Priorities)
WHITE	"Facts & Information"	Information
RED	"Feelings & Emotions"	Emotions and Ego
BLACK	"Negative"	PMI (Plus, Minus, Interesting); Evaluation
YELLOW	"Positive"	PMI
GREEN	"New Ideas"	Concept Challenge; Yes, No, Po

Strategies and programs

After identifying the six thinking modes, programs can be created. These are groups of hats that encompass and structure the thinking process. Several of these are included in the materials for franchised six hats training, but they must often be adapted. Programs are often "emergent," meaning the group plans the first few hats and the facilitator decides what to do next.

The group agrees on how to think, then thinks, then evaluates the results and decides what to do next. Individuals or groups can use sequences (and indeed hats). Each hat is typically used for 2 minutes at a time, although an extended white hat session is common at the start of a process to get everyone on the same page. The red hat is recommended to be used for a very short period to get a visceral gut reaction – about 30 seconds, and in practice often takes the form of dot-voting.

ACTIVITY	HAT SEQUENCE
Initial Ideas	Blue, White, Green, Blue
Choosing between alternatives	Blue, White, (Green), Yellow, Black, Red, Blue
Identifying Solutions	Blue, White, Black, Green, Blue
Quick Feedback	Blue, Black, Green, Blue
Strategic Planning	Blue, Yellow, Black, White, Blue, Green, Blue
Process Improvement	Blue, White, White (Other People's Views), Yellow, Black, Green, Red, Blue
Solving Problems	Blue, White, Green, Red, Yellow, Black, Green, Blue
Performance Review	Blue, Red, White, Yellow, Black, Green, Blue

Use

Speedo's swimsuit designers reportedly used the six thinking hats. "They used the "Six Thinking Hats" method to brainstorm, with a green hat for creative ideas and a black one for feasibility.

Typically, a project begins with extensive white hat research. Each hat is used for a few minutes at a time, except the red hat, which is limited to 30 seconds to ensure an instinctive gut reaction, not judgement. According to Malcolm Gladwell's "blink" theory, this pace improves thinking.

De Bono believed that the key to a successful Six Thinking Hats session was focusing the discussion on a particular approach. A meeting may be called to review and solve a problem. The Six Thinking Hats method can be used in sequence to explore the problem, develop a set of solutions, and choose a solution through critical examination.

Everyone may don the Blue hat to discuss the meeting's goals and objectives. The discussion may then shift to Red hat thinking to gather opinions and reactions. This phase may also be used to determine who will be affected by the problem and/or solutions. The discussion may then shift to the (Yellow then) Green hat to generate solutions and ideas. The discussion may move from White hat thinking to Black hat thinking to develop solution set criticisms.

Because everyone is focused on one approach at a time, the group is more collaborative than if one person is reacting emotionally (Red hat), another is trying to be objective (White hat), and another is critical of the points which emerge from the discussion (Black hat). The hats help people approach problems from different angles and highlight problem-solving flaws.

The magnitude 5 earthquake was responsible for the discharge of energy that was 10 times greater than the previous record holder.

Any Martians who happen to be reading this should quickly learn how to duck and cover.

NASA's Jet Propulsion Laboratory in Pasadena, California, reported that on May 4, the planet Mars was shaken by an earthquake of around magnitude 5, making it the greatest Marsquake ever detected to this point. The shaking persisted for more than six hours and unleashed more than ten times as much energy as the earthquake that had previously held the record for strongest.

The event was captured on record by the InSight lander, which is operated by the United States Space Agency and has been researching the innards of Mars ever since it touched down on the planet in 2018 (SN: 11/26/18). The epicenter of the earthquake was probably located in the vicinity of Cerberus Fossae, which is located more than 1,000 kilometers away from the lander.

The surface of Cerberus Fossae is notorious for being broken up and experiencing periodic rockfalls. According to geophysicist Philippe Lognonné, who is the lead investigator of the Seismic Experiment for Interior Structure, the seismometer that is onboard the InSight lander, it is reasonable to assume that the ground is moving in that area. "This is an old crater from a volcanic eruption."

Marsquakes, which are similar to earthquakes in that they give information about the interior structure of our planet, can be utilized to investigate what lies beneath the surface of Mars (SN: 7/22/21). And according to Lognonné, who works at the Institut de Physique du Globe in Paris, there is a great deal that can be gleaned from analyzing this massive earthquake. Because the quality of the signal is so high, we will be able to focus on the specifics.

Madoff who?

Bernie Madoff ran the largest Ponzi scheme in history, defrauding thousands of investors over at least 17 years, and possibly longer. He pioneered electronic trading and chaired Nasdaq in the 1990s. On April 14, 2021, he died while serving a 150-year sentence for money laundering, securities fraud, and other crimes.

Understanding Madoff

Madoff claimed to generate large, steady returns through a trading strategy called split-strike conversion, but he simply deposited client funds into a single bank account and paid out existing clients. He funded redemptions by attracting new investors and their capital, but the market crashed in late 2008. He confessed to his sons, who worked at his firm, on Dec. 10, 2008. Next day, they turned him in. The fund reported $64.8 billion in client assets.

Madoff pleaded guilty to 11 federal felony counts, including securities fraud, wire fraud, mail fraud, perjury, and money laundering. Ponzi scheme became a symbol of Wall Street's greed and dishonesty before the financial crisis. Madoff was sentenced to 150 years in prison and ordered to forfeit $170 billion, but no other Wall Street figures faced legal ramifications.

Bernie Madoff's Brief Biography

Bernie Madoff was born in Queens, New York, on April 29, 1938. He began dating Ruth (née Alpern) when they were teenagers. Madoff told a journalist by phone from prison that his father's sporting goods store went bankrupt during the Korean War: "You watch your father, who you idolize, build a big business and then lose everything." Madoff was determined to achieve "lasting success" like his father "whatever it took," but his career had ups and downs.

Early Madoff investments

At 22, he started Bernard L. Madoff Investment Securities LLC. First, he traded penny stocks with $5,000 he earned installing sprinklers and as a lifeguard. Family and friends soon invested with him. Madoff's bets soured after the "Kennedy Slide" in 1962, and his father-in-law had to bail him out.

Madoff felt he wasn't part of the Wall Street in-crowd. "We weren't NYSE members," he told Fishman. "It's obvious." According to Madoff, he was a scrappy market maker. "I was happy to take the crumbs," he told Fishman, citing a client who wanted to sell eight bonds; a bigger firm would turn it down.

Recognition

Success came when he and his brother Peter built electronic trading capabilities, or "artificial intelligence," that attracted massive order flow and provided market insights. "I had all these major banks coming down, entertaining me," Madoff told Fishman. "It was mind-bending."

By the late 1980s, he and four other Wall Street mainstays processed half of the NYSE's order flow. Controversially, he paid for much of it, and by the late 1980s, Madoff was making in the vicinity of $100 million a year.  He was Nasdaq chairman from 1990 to 1993.

Madoff's Ponzi scheme

It is not certain exactly when Madoff's Ponzi scheme began. He testified in court that it began in 1991, but his account manager, Frank DiPascali, had been at the firm since 1975.

Why Madoff did the scheme is unclear. "I had enough money to support my family's lifestyle. "I don't know why," he told Fishman." Madoff could have won Wall Street's respect as a market maker and electronic trading pioneer.

Madoff told Fishman he wasn't solely responsible for the fraud. "I let myself be talked into something, and that's my fault," he said, without saying who convinced him. "I thought I could escape eventually. I thought it'd be quick, but I couldn't."

Carl Shapiro, Jeffry Picower, Stanley Chais, and Norm Levy have been linked to Bernard L. Madoff Investment Securities LLC for years. Madoff's scheme made these men hundreds of millions of dollars in the 1960s and 1970s.

Madoff told Fishman, "Everyone was greedy, everyone wanted to go on." He says the Big Four and others who pumped client funds to him, outsourcing their asset management, must have suspected his returns or should have. "How can you make 15%-18% when everyone else is making less?" said Madoff.

How Madoff Got Away with It for So Long

Madoff's high returns made clients look the other way. He deposited their money in a Chase Manhattan Bank account, which merged to become JPMorgan Chase & Co. in 2000. The bank may have made $483 million from those deposits, so it didn't investigate.

When clients redeemed their investments, Madoff funded the payouts with new capital he attracted by promising unbelievable returns and earning his victims' trust. Madoff created an image of exclusivity by turning away clients. This model let half of Madoff's investors profit. These investors must pay into a victims' fund for defrauded investors.

Madoff wooed investors with his philanthropy. He defrauded nonprofits, including the Elie Wiesel Foundation for Peace and Hadassah. He approached congregants through his friendship with J. Ezra Merkin, a synagogue officer. Madoff allegedly stole $1 billion to $2 billion from his investors.

Investors believed Madoff for several reasons:

• His public portfolio seemed to be blue-chip stocks.
• His returns were high (10-20%) but consistent and not outlandish. In a 1992 interview with Madoff, the Wall Street Journal reported: "[Madoff] insists the returns were nothing special, given that the S&P 500-stock index returned 16.3% annually from 1982 to 1992. 'I'd be surprised if anyone thought matching the S&P over 10 years was remarkable,' he says.
• "He said he was using a split-strike collar strategy. A collar protects underlying shares by purchasing an out-of-the-money put option.

SEC inquiry

The Securities and Exchange Commission had been investigating Madoff and his securities firm since 1999, which frustrated many after he was prosecuted because they felt the biggest damage could have been prevented if the initial investigations had been rigorous enough.

Harry Markopolos was a whistleblower. In 1999, he figured Madoff must be lying in an afternoon. The SEC ignored his first Madoff complaint in 2000.

Markopolos wrote to the SEC in 2005: "The largest Ponzi scheme is Madoff Securities. This case has no SEC reward, so I'm turning it in because it's the right thing to do."

Markopolos found irregularities using a "Mosaic Method." Madoff's firm claimed to be profitable even when the S&P fell, which made no mathematical sense given what he was investing in. Markopolos said Madoff Securities' "undisclosed commissions" were the biggest red flag (1 percent of the total plus 20 percent of the profits).

Markopolos concluded that "investors don't know Bernie Madoff manages their money." Markopolos learned Madoff was applying for large loans from European banks (seemingly unnecessary if Madoff's returns were high).

The regulator asked Madoff for trading account documentation in 2005, after he nearly went bankrupt due to redemptions. The SEC drafted letters to two of the firms on his six-page list but didn't send them. Diana Henriques, author of "The Wizard of Lies: Bernie Madoff and the Death of Trust," documents the episode.

In 2008, the SEC was criticized for its slow response to Madoff's fraud.

Confession, sentencing of Bernie Madoff

Bernard L. Madoff Investment Securities LLC reported 5.6% year-to-date returns in November 2008; the S&P 500 fell 39%. As the selling continued, Madoff couldn't keep up with redemption requests, and on Dec. 10, he confessed to his sons Mark and Andy, who worked at his firm. "After I told them, they left, went to a lawyer, who told them to turn in their father, and I never saw them again. 2008-12-11: Bernie Madoff arrested.

Madoff insists he acted alone, but several of his colleagues were jailed. Mark Madoff died two years after his father's fraud was exposed. Madoff's investors committed suicide. Andy Madoff died of cancer in 2014.

2009 saw Madoff's 150-year prison sentence and $170 billion forfeiture. Marshals sold his three homes and yacht. Prisoner 61727-054 at Butner Federal Correctional Institution in North Carolina.

Madoff's lawyers requested early release on February 5, 2020, claiming he has a terminal kidney disease that may kill him in 18 months. Ten years have passed since Madoff's sentencing.

Bernie Madoff's Ponzi scheme aftermath

The paper trail of victims' claims shows Madoff's complexity and size. Documents show Madoff's scam began in the 1960s. His final account statements show $47 billion in "profit" from fake trades and shady accounting.

Thousands of investors lost their life savings, and multiple stories detail their harrowing loss.

Irving Picard, a New York lawyer overseeing Madoff's bankruptcy, has helped investors. By December 2018, Picard had recovered $13.3 billion from Ponzi scheme profiteers.

A Madoff Victim Fund (MVF) was created in 2013 to help compensate Madoff's victims, but the DOJ didn't start paying out the $4 billion until late 2017. Richard Breeden, a former SEC chair who oversees the fund, said thousands of claims were from "indirect investors"

Breeden and his team had to reject many claims because they weren't direct victims. Breeden said he based most of his decisions on one simple rule: Did the person invest more than they withdrew? Breeden estimated 11,000 "feeder" investors.

Breeden wrote in a November 2018 update for the Madoff Victim Fund, "We've paid over 27,300 victims 56.65% of their losses, with thousands more to come." In December 2018, 37,011 Madoff victims in the U.S. and around the world received over $2.7 billion. Breeden said the fund expected to make "at least one more significant distribution in 2019"

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