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Jenn Leach

Jenn Leach

3 years ago

I created a faceless TikTok account. Six months later.

More on Entrepreneurship/Creators

Startup Journal

Startup Journal

3 years ago

The Top 14 Software Business Ideas That Are Sure To Succeed in 2023

Software can change any company.

Photo by Marvin Meyer on Unsplash

Software is becoming essential. Everyone should consider how software affects their lives and others'.

Software on your phone, tablet, or computer offers many new options. We're experts in enough ways now.

Software Business Ideas will be popular by 2023.

ERP Programs

ERP software meets rising demand.

ERP solutions automate and monitor tasks that large organizations, businesses, and even schools would struggle to do manually.

ERP software could reach $49 billion by 2024.

CRM Program

CRM software is a must-have for any customer-focused business.

Having an open mind about your business services and products allows you to change platforms.

Another company may only want your CRM service.

Medical software

Healthcare facilities need reliable, easy-to-use software.

EHRs, MDDBs, E-Prescribing, and more are software options.

The global medical software market could reach $11 billion by 2025, and mobile medical apps may follow.

Presentation Software in the Cloud

SaaS presentation tools are great.

They're easy to use, comprehensive, and full of traditional Software features.

In today's cloud-based world, these solutions make life easier for people. We don't know about you, but we like it.

Software for Project Management

People began working remotely without signs or warnings before the 2020 COVID-19 pandemic.

Many organizations found it difficult to track projects and set deadlines.

With PMP software tools, teams can manage remote units and collaborate effectively.

App for Blockchain-Based Invoicing

This advanced billing and invoicing solution is for businesses and freelancers.

These blockchain-based apps can calculate taxes, manage debts, and manage transactions.

Intelligent contracts help blockchain track transactions more efficiently. It speeds up and improves invoice generation.

Software for Business Communications

Internal business messaging is tricky.

Top business software tools for communication can share files, collaborate on documents, host video conferences, and more.

Payroll Automation System

Software development also includes developing an automated payroll system.

These software systems reduce manual tasks for timely employee payments.

These tools help enterprise clients calculate total wages quickly, simplify tax calculations, improve record-keeping, and support better financial planning.

System for Detecting Data Leaks

Both businesses and individuals value data highly. Yahoo's data breach is dangerous because of this.

This area of software development can help people protect their data.

You can design an advanced data loss prevention system.

AI-based Retail System

AI-powered shopping systems are popular. The systems analyze customers' search and purchase patterns and store history and are equipped with a keyword database.

These systems offer many customers pre-loaded products.

AI-based shopping algorithms also help users make purchases.

Software for Detecting Plagiarism

Software can help ensure your projects are original and not plagiarized.

These tools detect plagiarized content that Google, media, and educational institutions don't like.

Software for Converting Audio to Text

Machine Learning converts speech to text automatically.

These programs can quickly transcribe cloud-based files.

Software for daily horoscopes

Daily and monthly horoscopes will continue to be popular.

Software platforms that can predict forecasts, calculate birth charts, and other astrology resources are good business ideas.

E-learning Programs

Traditional study methods are losing popularity as virtual schools proliferate and physical space shrinks.

Khan Academy online courses are the best way to keep learning.

Online education portals can boost your learning. If you want to start a tech startup, consider creating an e-learning program.

Conclusion

Software is booming. There's never been a better time to start a software development business, with so many people using computers and smartphones. This article lists eight business ideas for 2023. Consider these ideas if you're just starting out or looking to expand.

SAHIL SAPRU

SAHIL SAPRU

3 years ago

Growth tactics that grew businesses from 1 to 100

Source: Freshworks

Everyone wants a scalable startup.

Innovation helps launch a startup. The secret to a scalable business is growth trials (from 1 to 100).

Growth marketing combines marketing and product development for long-term growth.

Today, I'll explain growth hacking strategies popular startups used to scale.

1/ A Facebook user's social value is proportional to their friends.

Facebook built its user base using content marketing and paid ads. Mark and his investors feared in 2007 when Facebook's growth stalled at 90 million users.

Chamath Palihapitiya was brought in by Mark.

The team tested SEO keywords and MAU chasing. The growth team introduced “people you may know

This feature reunited long-lost friends and family. Casual users became power users as the retention curve flattened.

Growth Hack Insights: With social network effect the value of your product or platform increases exponentially if you have users you know or can relate with.

2/ Airbnb - Focus on your value propositions

Airbnb nearly failed in 2009. The company's weekly revenue was $200 and they had less than 2 months of runway.

Enter Paul Graham. The team noticed a pattern in 40 listings. Their website's property photos sucked.

Why?

Because these photos were taken with regular smartphones. Users didn't like the first impression.

Graham suggested traveling to New York to rent a camera, meet with property owners, and replace amateur photos with high-resolution ones.

A week later, the team's weekly revenue doubled to $400, indicating they were on track.

Growth Hack Insights: When selling an “online experience” ensure that your value proposition is aesthetic enough for users to enjoy being associated with them.

3/ Zomato - A company's smartphone push ensured growth.

Zomato delivers food. User retention was a challenge for the founders. Indian food customers are notorious for switching brands at the drop of a hat.

Zomato wanted users to order food online and repeat orders throughout the week.

Zomato created an attractive website with “near me” keywords for SEO indexing.

Zomato gambled to increase repeat orders. They only allowed mobile app food orders.

Zomato thought mobile apps were stickier. Product innovations in search/discovery/ordering or marketing campaigns like discounts/in-app notifications/nudges can improve user experience.

Zomato went public in 2021 after users kept ordering food online.

Growth Hack Insights: To improve user retention try to build platforms that build user stickiness. Your product and marketing team will do the rest for them.

4/ Hotmail - Signaling helps build premium users.

Ever sent or received an email or tweet with a sign — sent from iPhone?

Hotmail did it first! One investor suggested Hotmail add a signature to every email.

Overnight, thousands joined the company. Six months later, the company had 1 million users.

When serving an existing customer, improve their social standing. Signaling keeps the top 1%.

5/ Dropbox - Respect loyal customers

Dropbox is a company that puts people over profits. The company prioritized existing users.

Dropbox rewarded loyal users by offering 250 MB of free storage to anyone who referred a friend. The referral hack helped Dropbox get millions of downloads in its first few months.

Growth Hack Insights: Think of ways to improve the social positioning of your end-user when you are serving an existing customer. Signaling goes a long way in attracting the top 1% to stay.

These experiments weren’t hacks. Hundreds of failed experiments and user research drove these experiments. Scaling up experiments is difficult.

Contact me if you want to grow your startup's user base.

Sanjay Priyadarshi

Sanjay Priyadarshi

3 years ago

A 19-year-old dropped out of college to build a $2,300,000,000 company in 2 years.

His success was unforeseeable.

2014 saw Facebook's $2.3 billion purchase of Oculus VR.

19-year-old Palmer Luckey founded Oculus. He quit journalism school. His parents worried about his college dropout.

Facebook bought Oculus VR in less than 2 years.

Palmer Luckey started Anduril Industries. Palmer has raised $385 million with Anduril.

The Oculus journey began in a trailer

Palmer Luckey, 19, owned the trailer.

Luckey had his trailer customized. The trailer had all six of Luckey's screens. In the trailer's remaining area, Luckey conducted hardware tests.

At 16, he became obsessed with virtual reality. Virtual reality was rare at the time.

Luckey didn't know about VR when he started.

Previously, he liked "portabilizing" mods. Hacking ancient game consoles into handhelds.

In his city, fewer portabilizers actively traded.

Luckey started "ModRetro" for other portabilizers. Luckey was exposed to VR headsets online.

Luckey:

“Man, ModRetro days were the best.”

Palmer Luckey used VR headsets for three years. His design had 50 prototypes.

Luckey used to work at the Long Beach Sailing Center for minimum salary, servicing diesel engines and cleaning boats.

Luckey worked in a USC Institute for Creative Technologies mixed reality lab in July 2011. (ICT).

Luckey cleaned the lab, did reports, and helped other students with VR projects.

Luckey's lab job was dull.

Luckey chose to work in the lab because he wanted to engage with like-minded folks.

By 2012, Luckey had a prototype he hoped to share globally. He made cheaper headsets than others.

Luckey wanted to sell an easy-to-assemble virtual reality kit on Kickstarter.

He realized he needed a corporation to do these sales legally. He started looking for names. "Virtuality," "virtual," and "VR" are all taken.

Hence, Oculus.

If Luckey sold a hundred prototypes, he would be thrilled since it would boost his future possibilities.

John Carmack, legendary game designer

Carmack has liked sci-fi and fantasy since infancy.

Carmack loved imagining intricate gaming worlds.

His interest in programming and computer science grew with age.

He liked graphics. He liked how mismatching 0 and 1 might create new colors and visuals.

Carmack played computer games as a teen. He created Shadowforge in high school.

He founded Id software in 1991. When Carmack created id software, console games were the best-sellers.

Old computer games have weak graphics. John Carmack and id software developed "adaptive tile refresh."

This technique smoothed PC game scrolling. id software launched 3-D, Quake, and Doom using "adaptive tile refresh."

These games made John Carmack a gaming star. Later, he sold Id software to ZeniMax Media.

How Palmer Luckey met Carmack

In 2011, Carmack was thinking a lot about 3-D space and virtual reality.

He was underwhelmed by the greatest HMD on the market. Because of their flimsiness and latency.

His disappointment was partly due to the view (FOV). Best HMD had 40-degree field of view.

Poor. The best VR headset is useless with a 40-degree FOV.

Carmack intended to show the press Doom 3 in VR. He explored VR headsets and internet groups for this reason.

Carmack identified a VR enthusiast in the comments section of "LEEP on the Cheap." "PalmerTech" was the name.

Carmack approached PalmerTech about his prototype. He told Luckey about his VR demos, so he wanted to see his prototype.

Carmack got a Rift prototype. Here's his May 17 tweet.

John Carmack tweeted an evaluation of the Luckey prototype.

Dan Newell, a Valve engineer, and Mick Hocking, a Sony senior director, pre-ordered Oculus Rift prototypes with Carmack's help.

Everyone praised Luckey after Carmack demoed Rift.

Palmer Luckey received a job offer from Sony.

  • It was a full-time position at Sony Computer Europe.

  • He would run Sony’s R&D lab.

  • The salary would be $70k.

Who is Brendan Iribe?

Brendan Iribe started early with Startups. In 2004, he and Mike Antonov founded Scaleform.

Scaleform created high-performance middleware. This package allows 3D Flash games.

In 2011, Iribe sold Scaleform to Autodesk for $36 million.

How Brendan Iribe discovered Palmer Luckey.

Brendan Iribe's friend Laurent Scallie.

Laurent told Iribe about a potential opportunity.

Laurent promised Iribe VR will work this time. Laurent introduced Iribe to Luckey.

Iribe was doubtful after hearing Laurent's statements. He doubted Laurent's VR claims.

But since Laurent took the name John Carmack, Iribe thought he should look at Luckey Innovation. Iribe was hooked on virtual reality after reading Palmer Luckey stories.

He asked Scallie about Palmer Luckey.

Iribe convinced Luckey to start Oculus with him

First meeting between Palmer Luckey and Iribe.

The Iribe team wanted Luckey to feel comfortable.

Iribe sought to convince Luckey that launching a company was easy. Iribe told Luckey anyone could start a business.

Luckey told Iribe's staff he was homeschooled from childhood. Luckey took self-study courses.

Luckey had planned to launch a Kickstarter campaign and sell kits for his prototype. Many companies offered him jobs, nevertheless.

He's considering Sony's offer.

Iribe advised Luckey to stay independent and not join a firm. Iribe asked Luckey how he could raise his child better. No one sees your baby like you do?

Iribe's team pushed Luckey to stay independent and establish a software ecosystem around his device.

After conversing with Iribe, Luckey rejected every job offer and merger option.

Iribe convinced Luckey to provide an SDK for Oculus developers.

After a few months. Brendan Iribe co-founded Oculus with Palmer Luckey. Luckey trusted Iribe and his crew, so he started a corporation with him.

Crowdfunding

Brendan Iribe and Palmer Luckey launched a Kickstarter.

Gabe Newell endorsed Palmer's Kickstarter video.

Gabe Newell wants folks to trust Palmer Luckey since he's doing something fascinating and answering tough questions.

Mark Bolas and David Helgason backed Palmer Luckey's VR Kickstarter video.

Luckey introduced Oculus Rift during the Kickstarter campaign. He introduced virtual reality during press conferences.

Oculus' Kickstarter effort was a success. Palmer Luckey felt he could raise $250,000.

Oculus raised $2.4 million through Kickstarter. Palmer Luckey's virtual reality vision was well-received.

Mark Zuckerberg's Oculus discovery

Brendan Iribe and Palmer Luckey hired the right personnel after a successful Kickstarter campaign.

Oculus needs a lot of money for engineers and hardware. They needed investors' money.

Series A raised $16M.

Next, Andreessen Horowitz partner Brain Cho approached Iribe.

Cho told Iribe that Andreessen Horowitz could invest in Oculus Series B if the company solved motion sickness.

Mark Andreessen was Iribe's dream client.

Marc Andreessen and his partners gave Oculus $75 million.

Andreessen introduced Iribe to Zukerberg. Iribe and Zukerberg discussed the future of games and virtual reality by phone.

Facebook's Oculus demo

Iribe showed Zuckerberg Oculus.

Mark was hooked after using Oculus. The headset impressed him.

The whole Facebook crew who saw the demo said only one thing.

“Holy Crap!”

This surprised them all.

Mark Zuckerberg was impressed by the team's response. Mark Zuckerberg met the Oculus team five days after the demo.

First meeting Palmer Luckey.

Palmer Luckey is one of Mark's biggest supporters and loves Facebook.

Oculus Acquisition

Zuckerberg wanted Oculus.

Brendan Iribe had requested for $4 billion, but Mark wasn't interested.

Facebook bought Oculus for $2.3 billion after months of drama.

After selling his company, how does Palmer view money?

Palmer loves the freedom money gives him. Money frees him from small worries.

Money has allowed him to pursue things he wouldn't have otherwise.

“If I didn’t have money I wouldn’t have a collection of vintage military vehicles…You can have nice hobbies that keep you relaxed when you have money.”

He didn't start Oculus to generate money. His virtual reality passion spanned years.

He didn't have to lie about how virtual reality will transform everything until he needed funding.

The company's success was an unexpected bonus. He was merely passionate about a good cause.

After Oculus' $2.3 billion exit, what changed?

Palmer didn't mind being rich. He did similar things.

After Facebook bought Oculus, he moved to Silicon Valley and lived in a 12-person shared house due to high rents.

Palmer might have afforded a big mansion, but he prefers stability and doing things because he wants to, not because he has to.

“Taco Bell is never tasted so good as when you know you could afford to never eat taco bell again.”

Palmer's leadership shifted.

Palmer changed his leadership after selling Oculus.

When he launched his second company, he couldn't work on his passions.

“When you start a tech company you do it because you want to work on a technology, that is why you are interested in that space in the first place. As the company has grown, he has realized that if he is still doing optical design in the company it’s because he is being negligent about the hiring process.”

Once his startup grows, the founder's responsibilities shift. He must recruit better firm managers.

Recruiting talented people becomes the top priority. The founder must convince others of their influence.

A book that helped me write this:

The History of the Future: Oculus, Facebook, and the Revolution That Swept Virtual Reality — Blake Harris


*This post is a summary. Read the full article here.

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Will Lockett

Will Lockett

3 years ago

The World Will Change With MIT's New Battery

MIT’s new battery is made from only aluminium (left), sulphur (middle) and salt (left) — MIT

It's cheaper, faster charging, longer lasting, safer, and better for the environment.

Batteries are the future. Next-gen and planet-saving technology, including solar power and EVs, require batteries. As these smart technologies become more popular, we find that our batteries can't keep up. Lithium-ion batteries are expensive, slow to charge, big, fast to decay, flammable, and not environmentally friendly. MIT just created a new battery that eliminates all of these problems.  So, is this the battery of the future? Or is there a catch?

When I say entirely new, I mean it. This battery employs no currently available materials. Its electrodes are constructed of aluminium and pure sulfur instead of lithium-complicated ion's metals and graphite. Its electrolyte is formed of molten chloro-aluminate salts, not an organic solution with lithium salts like lithium-ion batteries.

How does this change in materials help?

Aluminum, sulfur, and chloro-aluminate salts are abundant, easy to acquire, and cheap. This battery might be six times cheaper than a lithium-ion battery and use less hazardous mining. The world and our wallets will benefit.

But don’t go thinking this means it lacks performance.

This battery charged in under a minute in tests. At 25 degrees Celsius, the battery will charge 25 times slower than at 110 degrees Celsius. This is because the salt, which has a very low melting point, is in an ideal state at 110 degrees and can carry a charge incredibly quickly. Unlike lithium-ion, this battery self-heats when charging and discharging, therefore no external heating is needed.

Anyone who's seen a lithium-ion battery burst might be surprised. Unlike lithium-ion batteries, none of the components in this new battery can catch fire. Thus, high-temperature charging and discharging speeds pose no concern.

These batteries are long-lasting. Lithium-ion batteries don't last long, as any iPhone owner can attest. During charging, metal forms a dendrite on the electrode. This metal spike will keep growing until it reaches the other end of the battery, short-circuiting it. This is why phone batteries only last a few years and why electric car range decreases over time. This new battery's molten salt slows deposition, extending its life. This helps the environment and our wallets.

These batteries are also energy dense. Some lithium-ion batteries have 270 Wh/kg energy density (volume and mass). Aluminum-sulfur batteries could have 1392 Wh/kg, according to calculations. They'd be 5x more energy dense. Tesla's Model 3 battery would weigh 96 kg instead of 480 kg if this battery were used. This would improve the car's efficiency and handling.

These calculations were for batteries without molten salt electrolyte. Because they don't reflect the exact battery chemistry, they aren't a surefire prediction.

This battery seems great. It will take years, maybe decades, before it reaches the market and makes a difference. Right?

Nope. The project's scientists founded Avanti to develop and market this technology.

So we'll soon be driving cheap, durable, eco-friendly, lightweight, and ultra-safe EVs? Nope.

This battery must be kept hot to keep the salt molten; otherwise, it won't work and will expand and contract, causing damage. This issue could be solved by packs that can rapidly pre-heat, but that project is far off.

Rapid and constant charge-discharge cycles make these batteries ideal for solar farms, homes, and EV charging stations. The battery is constantly being charged or discharged, allowing it to self-heat and maintain an ideal temperature.

These batteries aren't as sexy as those making EVs faster, more efficient, and cheaper. Grid batteries are crucial to our net-zero transition because they allow us to use more low-carbon energy. As we move away from fossil fuels, we'll need millions of these batteries, so the fact that they're cheap, safe, long-lasting, and environmentally friendly will be huge. Who knows, maybe EVs will use this technology one day. MIT has created another world-changing technology.

Frederick M. Hess

Frederick M. Hess

2 years ago

The Lessons of the Last Two Decades for Education Reform

My colleague Ilana Ovental and I examined pandemic media coverage of education at the end of last year. That analysis examined coverage changes. We tracked K-12 topic attention over the previous two decades using Lexis Nexis. See the results here.

I was struck by how cleanly the past two decades can be divided up into three (or three and a half) eras of school reform—a framing that can help us comprehend where we are and how we got here. In a time when epidemic, political unrest, frenetic news cycles, and culture war can make six months seem like a lifetime, it's worth pausing for context.

If you look at the peaks in the above graph, the 21st century looks to be divided into periods. The decade-long rise and fall of No Child Left Behind began during the Bush administration. In a few years, NCLB became the dominant K-12 framework. Advocates and financiers discussed achievement gaps and measured success with AYP.

NCLB collapsed under the weight of rigorous testing, high-stakes accountability, and a race to the bottom by the Obama years. Obama's Race to the Top garnered attention, but its most controversial component, the Common Core State Standards, rose quickly.

Academic standards replaced assessment and accountability. New math, fiction, and standards were hotly debated. Reformers and funders chanted worldwide benchmarking and systems interoperability.

We went from federally driven testing and accountability to government encouraged/subsidized/mandated (pick your verb) reading and math standardization. Last year, Checker Finn and I wrote The End of School Reform? The 2010s populist wave thwarted these objectives. The Tea Party, Occupy Wall Street, Black Lives Matter, and Trump/MAGA all attacked established institutions.

Consequently, once the Common Core fell, no alternative program emerged. Instead, school choice—the policy most aligned with populist suspicion of institutional power—reached a half-peak. This was less a case of choice erupting to prominence than of continuous growth in a vacuum. Even with Betsy DeVos' determined, controversial efforts, school choice received only half the media attention that NCLB and Common Core did at their heights.

Recently, culture clash-fueled attention to race-based curriculum and pedagogy has exploded (all playing out under the banner of critical race theory). This third, culture war-driven wave may not last as long as the other waves.

Even though I don't understand it, the move from slow-building policy debate to fast cultural confrontation over two decades is notable. I don't know if it's cyclical or permanent, or if it's about schooling, media, public discourse, or all three.

One final thought: After doing this work for decades, I've noticed how smoothly advocacy groups, associations, and other activists adapt to the zeitgeist. In 2007, mission statements focused on accomplishment disparities. Five years later, they promoted standardization. Language has changed again.

Part of this is unavoidable and healthy. Chasing currents can also make companies look unprincipled, promote scepticism, and keep them spinning the wheel. Bearing in mind that these tides ebb and flow may give educators, leaders, and activists more confidence to hold onto their values and pause when they feel compelled to follow the crowd.

Vitalik

Vitalik

4 years ago

An approximate introduction to how zk-SNARKs are possible (part 2)

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.

see part 3