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If you want the full answer, it’s long.The financial problem people were trying to solve from 2002 - 2006 was a huge supply of funds seeking low-risk, liquid investments, mainly from oil producing countries, China and Japan. Something similar happened in the late 70s and early 80s when banks “recycled petrodollars” into risky loans to developing countries which nearly destroyed the banking system from the mid-80s to the mid-90s. It was called “recycling” because the US, Europe and Japan sent lots of dollars to oil producers, who sent it back for investment. In that case, banks took the credit risk on the loans, so they were not willing to do the same thing again in the 21st century.The main solution this time was various forms of asset-backed securities. Banks and dealers took pools of risky assets, found a hedge fund to take the first losses, and got high credit ratings on the remainder. For example, you could take a pool of subprime mortgages on which you expected 5% to default, get a hedge fund to agree to accept the first 20% in losses, and the remaining 80% were considered very safe, since even if you got four times the expected defaults, the holder of the 80% piece would get paid in full. This was very successful, which led to lots of demand for the kind of risky assets that could be packaged this way, and we know the rest.One particular type of asset-backed security, collateralized debt obligations, typically had dozens or at most hundreds of components, as opposed to mortgage and other securities that could have many thousands. With the latter securities, people treated the pool as made up of an essentially infinite number of components, which led to one problem, a failure to consider seriously enough the credit quality of individual loans. People looked at overall pool statistics, which as it turned out, hid a lot of the risk.With collateralized debt obligations, you knew a lot about the default probability and recovery distribution of individual bonds in the pool. You had some very smart hedge funds who would figure out prices for the riskiest pieces. But the people buying the safer pieces didn’t want to do complicated valuation work. The hedge fund might be putting up $10 million figuring on losing in one time in five and making $5 million the other four times in five. That kind of bet is worth a lot of high-priced analysis. But the people buying the safer pieces might be getting 0.50% per year more than they could earn in US treasuries over a five year period, and they didn’t want any significant chance of a loss at all. If they had to think about it too hard, they’d find some other way to get the 0.50%.So the mathematical problem was how to take what you knew about individual bond defaults, plus what you knew from the pricing of the early loss pieces, to price the rest of the pieces in a systematic way that less sophisticated investors would accept as fair. Copula methods were the solution.Although people talk about copulas as if they were one model, they are really a general tool for estimating multivariate probabilities. People applied them in at least three major different ways: to the time to default, to a structural default index and to a default probability. You need to transform a 0/1 default indicator variable into a continuous variable that ends up at 0 if the bond defaults immediately with zero recovery and 1 if the bond makes every scheduled payment over the life of the obligation.Once you have that variable, the next step is to estimate its univariate distribution for each bond in the pool. This people knew how to do, there’s lot of data and theory about it. You calculate the function that transforms the losses on each bond to a standard normal distribution. For example, if there was a 10% chance of a loss of more than 3% on bond A, a 3% loss was transformed to -1.28, because there’s a 10% chance that a standard normal variable will be less than -1.28. People did not only use normal distributions, student-t and other fat-tailed distributions were common as well. However there’s no reason that the distribution you transform to has to match the shape of the actual loss distribution, and using a fat-tailed transformation distribution does not necessarily raise the estimated probability of tail events.The copula is a way of taking all of these transformed distributions on individual bond outcomes into a multivariate distribution on the joint probability of any set of bond defaults. You could calibrate the process by the prices on the high loss pieces you sold to the smart investors, then use the parameters to put prices on the rest of the pieces.So what went wrong? Take your pick.Copulas have never been shown to work in any real application. The theory is nice, but the trouble is the probabilities of reasonably likely events, such as 1, 2 or 3 out of 100 investment grade bonds defaulting, tells you nothing about the probabilities of extreme events, like 30 bonds defaulting. This is true for most things that are not exchangeable, which means most things people want to know about (things academics study are usually exchangeable, which is why copulas are better loved in universities than on trading floors). However, as it happened, this wasn’t the problem.The actual market prices of the safer pieces never matched the theoretical computations. Even though the entire exercise had been about getting systematic prices for sales and accounting purposes, not trading prices, a lot of shops ate their own cooking. Some dealers ended up selling only the pieces that could be sold for their theoretical prices or more, and kept the rest. Thus they ended up with the petrodollar mistake of keeping a lot of the credit risk. The models justified high accounting profits, when the firms were actually losing money on the business and taking on a lot of additional risk. This led to big losses for most firms in the business, but not the level of losses that threatened the financial system.Smarter firms found some not-smart investors to take the pieces that medium-smart investors refused. This led to a lot of disguised risk stuffed into inappropriate places. This led to a lot of pain and confusion, but again, not enough to threaten the financial system.When things started getting bad the prices on the early loss pieces, which were held by smart people who knew their values, crashed. This was not a problem in itself, the total losses were small, and were borne by investors who knew how to survive losses. But when these prices were fed into the models, it caused the price of the safer pieces to fall to unreasonably low levels. For example, a hedge fund might have held a first loss piece that it figured had a 50% chance of being worth $10 million and a 50% chance of being worth zero, so the fund paid $3 million for it. When the fund decided it was near worthless and sold it for $10,000, that caused a super-senior AAA piece that was supposed to have less than a 0.01% chance of defaulting to look as if it had a 10% chance of defaulting. In other words, the models that had been too optimistic until 2007 suddenly got absurdly pessimistic. This turned out to be copulas biggest contribution to the crisis.So 1 was a problem in theory, but not much in practice. 2 and 3 led to severe losses that made the panic worse, but didn’t trigger anything and were survivable on their own. 4 was only one of the reasons that things got so bad, but it contributed to the heart of the crisis.See, credit never got anywhere near as bad as late-2008 prices suggested. In fact, it was probably economically impossible for credit get anywhere near that bad, even in a double-Great-Depression disaster scenario. But the prices led to demand for huge mark-to-market collateral calls, which required huge amounts of cash, which no one had or was willing to provide. The key to the crisis was that no one had the cash to pay for everyone’s worst fears. It was fear, not losses, that caused the crisis.The copula model can be blamed for (1) enabling a business that grew far to rapidly and recklessly, (2) seducing dealers into taking disguised credit risk, (3) encouraging stuffing of risk in inappropriate places and (4) enabling panic both by appearing to give mathematical support to fantastic disaster scenarios and by appearing to break down when they were needed.But to be fair, people didn’t rely entirely on copulas. Rating agencies used mainly historical statistics, which turned out to be pretty solid when applied to CDOs, but failed disastrously for CDO^2s. Sophisticated credit investors had more complicated models that worked pretty well. Most investors were never sophisticated enough to rely on copula in the first place. So copulas were a piece of the puzzle, but they didn’t cause the crisis. It takes a village to make a financial crisis.

While "successful" is completely dependent upon how you measure success, there are a few lists out there that give (some) potential signal on what other people have thought were interesting companies.For example, the companies on the Forbes 50 FinTech List for 2015 were[1] :Acorns: App links to debit and credit cards, rounds up each purchase to nearest dollar, investing extra pennies in a portfolio of ETFs.; Irvine CaliforniaAddepar, LLC: Develops software for the wealth management industryAdyen: Payment platform system for e-commerce; AmsterdamAffirm: Finances purchases with instant loans at interest rates of 0% to 30%.; San FranciscoAlgomi: Honeycomb bond-trading information system; LondonAlphasense: Smart search engine for investment pros spares them irrelevant Google search results; San FranciscoAvant: Makes instant online loans of $1,000 to $35,000 to average Joes, at 10% to 36% interest for two to five years; ChicagoBraintree: Online payments processor for comsumer apps including AirBnB and Uber; San FranciscoC2FO: Uses bid system and algorithms to match retailers sitting on extra cash with suppliers ready to accept discounts for payment within 48 hours.; Fairway, KansasChain: Builds tools to exploit “blockchain” technology underlying Bitcoin; San FranciscoCircleUp: Crowdfunding site for new consumer products; San FranciscoCredit Karma: Founded in 2008, provides truly free credit scores and credit monitoring to consumers; San FranciscoDigit: Monitors cash flow in your checking account, diverting small amounts into savings; San FranciscoEarnest: Refinance student debt for young borrowers with scanty credit records; San FranciscoEquityZen: Connects employees at pre-IPO companies looking to sell stock with prospective buyers; New York CityEstimize: Crowdsourcing corporate-earnings estimates from general public; New York CityFundbox: Crowdsourcing corporate-earnings estimates from general public; San FranciscoFundera: Small-business loan marketplace allows borrowers to compare terms from 28 lenders; New York CityFundrise: Real estate crowdfunding site ; Washington DCHelloWallet: Sold as employee benefit, links all a worker’s bank, credit,savings and investing accounts; Washington DCIEX: Stock exchange designed to blunt predatory high-frequency traders’ edge; New York CityKensho: Combines latest big data and 
machine-learningtechniques to analyze 
how real-world events affect markets; Cambridge, MassachusettsLearnVest: Connects average folks with financial plans and planners on the Web and in the workplace.; New York CityLevel Money: Mobile budgeting app; San FranciscoMoney.net: Provides real-time financial market data, news, messaging and analytics for $95 a month per user; New York CityMotif: Enables investors to design, share and buy themed ETF-likeportfolios (Motifs) of up to 30 stocks for $9.95 a transaction; San Mateo CaliforniaNav: Gives small-business owners access to their business and personal credit scores, help comparing rates from 36 lenders; San Mateo CaliforniaPersonal Capital: Offers free dashboard to track and analyze all your finances; Redwood City CaliforniaPlaid: Provides tools for other fintech startups to link bank and credit accounts and process transactions; San FranciscoPremise Data: Real-time economic data tracking platformProsper: Peer-to-peer lending site; San FranciscoQuantopia: Crowdsources hedge fund by offering quants free platform for back-testing their algorithms; BostonR3CEV: Has signed up 30 banks to jointly develop projects using technology that underlies Bitcoin; New York CityRipple: Allows banks to transfer funds in any currency in real time; San FranciscoRiskalyze: Software helps financial advisors quantify clients’ risk tolerance and build suitable portfolios; Auburn CaliforniaRobinhood: Commission-free stock trading app; Palo Alto, CaliforniaSimple: Online bank offering no-fee checking and personal finance tools, such as automatic daily saving; Portland OregonSoFi: Offers student loan refinancing, personal loans and mortgages to young borrowers with high-end jobs and degrees; San FranciscoStripe: Online and in-app payment platform with easy-to-use customer interface; San FranciscoThe Betterment Fund: Robo-advisor with more than 118,000 individual customers, now branching into 401(k) management; New York CityTransferWise: Chops the high fees individuals and small businesses pay for international money transfers by (invisibly to customers) matching buyers and sellers of each currency; LondonTrueAccord: Brings debt collection into the 21st century by using machine learning programs to analyze individual debtor’s responses and customize contacts; San FranciscoTrueEx: Electronic interest rate swaps exchange allows big players to make trades anonymously; New York CityVouch: New social network variant on the old concept of loan cosigners; San FranciscoWealthfront: Robo-advisor with nearly $3 billion under management; Palo Alto, CaliforniaWorldRemit: Phone app for money transfers to Third World; LondonXapo: Stores Bitcoin for wealthy investors on encrypted servers scattered across the globe; Palo Alto, CaliforniaXignite: Supplies financial market data to more than 1,000 financial companies for their apps and websites; San Mateo CaliforniaZenefits: Free cloud-based software to help small businesses automate payroll and benefits; San FranciscoZestFinance: Uses unconventional metrics to underwrite loans to those with low credit scores or thin credit histories; Los AngelesKPMG also released a list of 100 "Fintech Innovators"[2] I won't list them all here, so feel free to check it out yourself!Footnotes[1] Fintech 50: The Future Of Your Money[2] Fintech 100

I think American High School curriculum could use a 21st century update, but the basic format of attending classes is still valid.I would also suggest that current high school curriculum is a bit unnecessary in a world where an interested student can study some materials on their own.So what we have now is a school system that teaches students;History, but not how to vote, how to choose reliable media sources, how to understand the meaning of laws and the constitution.Math, but not how to work out interest charges on a credit card or how to compare home mortgage deals.Science, but not how to understand its daily principles and applications.Biology, but no understanding of what to look for in a life-partner husband / wife / etc.English. But not the kind you speak, and not the kind that involved emojis and text messages.Spanish or some other foreign language, but not the way people native to those places speak or text message.You get the idea.We teach our kids various levels of not-very-applicable stuff for 18 years and wonder why they don’t understand.Fortunately, they are pretty good at figuring stuff out on their own….