On the other side, there is literature—fiction and nonfiction, especially philosophical works written1 by some of the greatest minds who walk the Earth. I’d say there’s a lot of room for interpretation, isn’t there? I know I could start a discussion about the “probability of interpretation” in both mathematics and philosophy.

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I believe philosophy connects more closely to a reader’s mind, emotions, and life experiences, which is why it invites interpretation. You might be wondering, how can numbers and narratives possibly intertwine? Well, let me share with you how these worlds collided for me.

A compelling love story unfolds through classic storytelling arcs—introducing conflict, building tension, and culminating in a climactic resolution. Similarly, mathematicians begin with foundational premises (axioms), heighten intrigue through logical steps (lemmas and theorems), and ultimately deliver closure in the form of a proof.

The parallels between these two worlds are striking. We might even coin the term “classic proof arcs” to describe this structure. In this light, mathematics, much like philosophy, reveals itself as a form of storytelling—only its language is composed of symbols instead of words.

I initially suggested that philosophy resonates with the reader’s mind, emotions, and life experience, but, to be honest, that description lacked precision. Behind books, stories, and mathematical theories stand real people—philosophers and mathematicians—shaped by their own minds, emotions, and life experiences. Their personal perspectives and intellectual journeys find expression in the ideas they create and the narratives they build. Who would we be if we were incapable of feeling, unable to process emotions or give them voice?

In the end, whether we seek answers through the rigor of mathematics2 or the introspection of philosophy, both queens of science show us the importance of precision and emotion in their storytelling.

I remember my first attempts at proving theorems from Mathematical Analysis or Probability Theory, which were always accompanied by excitement and curiosity, as well as the time I read the entire “The Roads to Freedom” by Jean-Paul Sartre in a single weekend.

Perhaps the book I’d take to that deserted island wouldn’t be about choosing between numbers and narratives. The most profound stories—whether told through equations or words—challenge us to think, feel, and wonder.

And isn’t that what makes any story worth reading?

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Nikola Tesla was one of the greatest innovators to have ever lived, yet many of his inventions were far ahead of their time. Reading his biography reveals Tesla’s remarkable persistence, creativity, and willingness to take risks. Without exaggeration, it is fair to say that he faced—or came close to—bankruptcy on multiple occasions, he demonstrated unwavering determination to pursue his dreams. It raises an intriguing question: does venturing into uncharted territory—where others fear to tread—make one a visionary or simply reckless?

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The Fine Line

Would pursuing my dreams make me merely reckless, or could it be the mark of true vision? Of course not. I don't think it's that simplistic. There is a clear distinction between those who take calculated risks and those who act recklessly. Calculated risk-takers weigh the potential outcomes, plan carefully, and proceed with purpose. In contrast, reckless individuals tend to leap without looking, and charge forward without consideration for consequences.

“There's a fine line between genius and insanity. I have erased this line.” — Oscar Levant

The venture capital market is a prime example of a high-stakes environment where investors constantly navigate the fine line between calculated risk and recklessness. Investing in startups, in particular, reflects the dynamics of the power law, where a small number of investments yield phenomenal returns, while many others fail. Can you imagine that even 9 out of 10 startups fail?

Vision Role

In such a high-risk environment, I am really curious about what separates the founders who succeed from the many who don’t. The answer often lies in vision. Vision is about the future; I believe deeply that it is the ability to see possibilities where others see limitations.

People like Elon Musk, who envision a future of sustainable energy and space exploration, crave risks like nobody else. The stories behind Tesla and SpaceX show us how much he can risk to achieve his goals. In 2009, Musk himself admitted that he survived this period solely thanks to loans. How does his vision drive him to make such risky decisions? Maybe it is about the pressure to reach peak performance.

Embrace Failure

However, having a vision is only part of the journey. The path toward realizing that vision is rarely smooth. Obstacles arise, plans falter, and failures happen. The obstacle is the way. This is where resilience becomes indispensable. Resilience embodies elements of both courage and confronting failure. It embodies the strength of persistence despite setbacks, making it a fitting link between these two ideas.

Life can be tough; however, resilience empowers us. I have suffered many failures in my life, which is like boxing – you lose focus for a moment, and you are on the ropes. Rising from that position is a long process that can take even a few years. While we can learn from the past, we shouldn't let it limit our aspirations.

Developing resilience is not an easy task, but it can be achieved by embracing challenges, maintaining optimism, and seeking support. For me, resilience is the capacity to recover quickly from difficulties. It's the foundation that allows us to transform challenges into opportunities. By upholding resilience, we don’t merely endure—we stand prepared to act boldly and welcome every new opportunity.

Carpe diem

Imagine a Formula 1 driver at the starting line, engines roaring, ready to take on the sharp turns at breakneck speed. In more minutes, the drivers will need to make life's high-stakes decisions. They'll be making split-second decisions that could mean the difference between victory and disaster. Am I like a Formula 1 driver, pushing the limits at every sharp turn, overtaking the stragglers? Perhaps I am. I choose to push the limits with intention and precision.

It's impossible to ignore the crucial role that data analysis, team strategy, and meticulous preparation play in racing. I am truly impressed by how quickly drivers make calculated-risk decisions under intense pressure. I am still pondering risks and wondering where the line truly lies. Both of us take risks, after all.

Today, fortified by resilience and driven by vision, I have nothing to lose, and everything to gain. So, let’s crank up the pace, take risks, and drive like there’s no tomorrow—because who knows? Maybe tomorrow won’t come, every tomorrow is the result of today's decisions.

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I can’t imagine my mornings without energetic music and a mug of coffee, or a Friday evening with a glass of wine and the romantic sounds of rhythm and blues or jazz. Music amplifies my emotions, helping me process and release them quickly. Music and memories are deeply connected, aren’t they?

Imagine a world without loud, unpleasant, or even frightening sounds. Join me on a journey through dreams, values, and the things that disturb us. Noise, to me, is a metaphor for anything that distracts us from our routines. A critical reader may notice that I often write about dreams. I believe that, along with values, they are powerful forces driving us toward a better future.

Think about a fast car and a driver striving to stay on track — that’s exactly how I feel right now. It’s one of the most challenging things in my life.

I want to share with you a few things about routine, something simple, about daily routine which I believe is crucial to be successful in life. Is it a simple path to follow?

I don’t think so. I fail often (a curious reader should check out my blog post, The Art of Failing), but each failure teaches me more about myself and how to adapt to a changing environment.

My goal is straightforward: to execute my daily routine every day. Consistently.

One of my biggest mistakes was micromanaging my calendar — trying to fill every day, hour, and minute with activities. I know it sounds extreme, but I was so driven to succeed. I read countless self-development books, convinced they would bring me closer to my dreams. But honestly? Today, I can hardly look at those books. Now, I believe it’s better to read selectively, focusing on topics that truly interest us. I’m much more discerning about what I choose to read.

I used to have rigid time blocks in my calendar — for instance, from 9 a.m. to 11 a.m., I’d work on math problems, and between math and work, I’d squeeze in a bike ride or a run. The first 15 minutes are always the hardest, but each step after that brings us closer to our dreams. I’m much more flexible.

Another mistake was keeping my to-do list far too long. Sure, it’s useful to outline tasks for the day, week, or month, but I used to try to check off as many as possible every day — which was unrealistic. Now, I choose about five of the most important tasks to focus on each day, and it works well.

Still, I’ve noticed that even one unpredictable event can disrupt my routine. But I don’t give up easily; I’m stubborn. How about you?

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When was the last time you gave up? I know that feeling because I have failed many times (of course). Edison’s example represents a healthy ratio between failure and success.

This article describes my approach to building an innovation mindset in a leader who fails then quickly jumps back to the top of the leadership board. Let’s start with some thoughts about innovation.

The Little Black Book of Innovation by Scott D. Anthony is an endless inspiration for me. This book contains a lot of food for thought (for example, the 28-day program for building an innovative venture). I would recommend the book to anyone interested in leveraging their experience to build something incredible. Anthony shares four points to develop an innovation mindset:

1)    Be externally focused.

2)    Recognise that your first idea is wrong.

3)    Release your inner Edison, and start sweating.

4)    Break the sucking sound of the core.

My thoughts?

Being externally focused is an important reminder to not forget the economic environment of a venture. Understanding market trends, customer needs, and competitor landscapes are factors in success.

What about recognizing that my first idea was wrong? This means being open to continuous improvements and being sure that an initial idea is not the final form. The concept of a lean startup shows the loop of improvements to an idea.

Edison’s persistence is an inspiration to not give up easily and to try new ways of solving customer problems. Edison mentioned that people don’t even imagine how close get to actually solving their problems. I would be angry if I knew that I was only one step away from solving a difficult problem or creating a great product for a wide audience.

Finally, innovation often involves thoroughly examining the core of a problem or situation to discover new solutions or insights. The phrase “the sucking sound of the core” implies that deep concentration and effort are required to delve into the heart of an issue and propel innovation forward or extract the fundamental elements of ideas from a complex situation. This kind of innovation mindset involves a shift in thinking about delivering results.

But what if we fail or fall?

There is no situation without a solution. We can always jump back on top of the leadership board again. We can cope with obstacles and adversities by implementing strategies to mitigate risks. A never-give-up attitude can steer you toward unwavering determination and give you an advantage over competitors.

It is important to discover what limits us. For example, I had a problem with negative thoughts, so the solution was simple. I joined the psychotherapeutic sessions based on CBT. It was a pleasure to imagine my negative thoughts enclosed in a train leaving the platform.

The entrepreneurial journey is about relationships; on the other side, there is always a human being. There is no shame in asking for help or getting a psychotherapist to join your journey and help you with your struggles.

Edison’s approach, based on seeing failed attempts as steps toward success, emphasizes the role of perspective in leadership. Having an “elastic” perspective means being able to reinterpret negative results as more positive (for example, seeing them as opportunities for reflection and experience).

I needed a lot of time to understand Edison’s perspective. However, this way of thinking makes me calmer about the future.

Of course, everything depends on you. Awaken the giant inside you. Strategies to keep yourself motivated depend only on you.

I hope this has given you some inspiration and food for thought about the innovation mindset and the never-give-up attitude.

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I have, and I often think about the biographies of people who inspire me and give me a strong stimulus to achieve more and to be brave. What does courage mean in the context of entrepreneurship? Courage means the virtue of being brave when you face obstacles, dangerous situations, or even when you are seriously ill.

If you ask me what that virtue means for the entrepreneurial journey, I would say that it is how we face fears, take calculated risks, and persist despite failures. Of course, perseverance helps a lot.

As an experienced entrepreneur or a complete novice, who among us has never faced challenges? I think none of us.

All of us have some experience with more difficult events or even borderline experiences in our lives where we lost our footing. Leaving a comfort zone is essential for making tough decisions, venturing into the unknown, and overcoming the fear of failure. Also, courage plays a primary role in innovation and breaking new ground.

Vincent van Gogh said that emotions are at the heart of people's lives. I strongly agree with his words.

Common fears such as fear of failure, imposter syndrome, fear of the unknown, and financial fear are very common. How do you cope with them?

When I feel emotions that block me, I breathe deeply and gather strength to take strong actions against my fears. I remember Ryan Holiday's words — discipline now, freedom later. It helps, as does doing sports, to reduce mental tension and manage difficult emotions. It can be difficult, but what about embracing failure as a learning opportunity?

What would be my tips for building a courageous mindset? Firstly, I always have small and achievable goals in mind, or even better written down on paper; it is my braga document, which allows me to track my achievements and progress.

Secondly, mentorship can help to increase our skills and knowledge sharing. It is a good idea to exchange knowledge and expertise with more mature entrepreneurs or some experts with specialties in a crucial field for us. Even coaching with therapeutic elements can be a game-changer for us and give us an unfair advantage over our competitors. It can be a great starting point for challenging ourselves and learning from our failures. Please don’t give up easily.

Lastly, self-reflection allows us to cultivate a growth mindset. As a homegrown philosopher, I had the chance to read wise people; it taught me introspection and the skills of analysis of complex ideas.

In conclusion, courage is not a one-time act but a continuous journey of growth, learning, and resilience. I want to inspire you to embrace your entrepreneurial journey with courage, regardless of where you are starting from. Please don’t forget about dreaming like da Vinci; maybe one day your dreams will come true.

What I want to convey is that our experiences, coupled with knowledge, change over time. As we grow older, we become more mature. My view of education has evolved over the years, but I would never underestimate its importance.

Education is a crucial part of our lives, as are role models. Please don't forget that education is a potent weapon against societal inequalities. It serves as a powerful tool for addressing these inequalities by providing opportunities for advancement, regardless of one's background. This is one of the reasons why education matters. 

It is becoming increasingly evident that education is not solely about acquiring knowledge from books or classrooms. It is a lifelong process that shapes our values, character, and the way we perceive the world. That's why education extends beyond formal learning; it encompasses self-directed, continuous learning and takes a holistic approach to personal growth.

When I was a high school student, I fell in love with philosophy. Philosophical books provided me with food for thought and encompassed social and emotional intelligence, critical thinking, problem-solving, and adaptability. 

Role models are essential in education. They inspire, guide, and show what’s possible through learning. These mentors might be teachers, family, leaders, or historical figures we admire. They remind us that with hard work and a love for learning, we can achieve great things and make a difference.

In short, education is a powerful, ever-changing force in our lives. It grows with us, shaped by our experiences and view of the world. Beyond providing knowledge, it builds character and helps us tackle social challenges. By valuing education and learning from role models, we can grow with purpose and help create a better future for ourselves and others.

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Today, I am a software engineer, and I take great satisfaction in collaborating with skilled and dedicated individuals on fascinating projects.

One of the paramount attributes for any entrepreneur is the essence of leadership. In my view, being an entrepreneur equals being a leader. Both roles carry immense significance, as being a leader is pivotal in shaping a company's culture. As I continue on my journey, I wish to share my contemplation on the subject of leadership and my plans. 

Why is leadership a challenging journey? 

One key definition of leadership is a process that involves exerting influence over others to drive transformative changes for the common good. How do you inspire people to follow you? Lead by example and communicate your vision. When embarking on a new venture, it's crucial to possess a clear vision. I found statistics showing that leaders spend about 10% to 20% of their time looking ahead. Enhance your sense of purpose, curiosity, and foresight. Don’t let history hold you back. Vision is about the future.  

Of course, there is accountability. Leaders take responsibility for the results of their choices. I noticed that when I am taking on more responsibility in my life, I am a stronger doer, more confident, and not afraid to make risky decisions. Affirmation helps. Develop the values that drive you. Ask good questions to clarify, align, and build on ideas. 

In thinking about becoming an effective leader, I prepared a kind of map with milestones. I realized that one of my weaknesses — which I am working on — is about trying implement all my ideas at once. Therefore, I decided to take it step by step, not all at once.  

Don’t assume the experts are right; however, know that role models are important. I don’t have just one role model, but a few for different areas of life. I know that people have disadvantages — some of which raise controversies — but I admire them. I love people; I love humanity. People are beautiful because we are different — all of us. Although people often disappoint us, I seek examples of excellence and morality in their acts. 

I read stories of founders who suffer from anxiety and stress, they have got problems with mental tension. As an entrepreneur, you need to consider accountability, problems with interpersonal relationships, and the complexity of the venture.  

Leaders need to possess a combination of strategic thinking, emotional intelligence, communication skills, and resilience to navigate these challenges successfully.

I really like the half-joking, half-serious definition of futurology, written by Leszek Kołakowski, who noted that futurology is a scientific science about something that actually does not exist: the future. I want to ask a question what a being is, and whether we can predict the future. I believe that our actions can have a positive impact on events that happen later in our life. People laughed at Leonardo da Vinci when he was dreaming about aircrafts, drawing incredible machines, and observing birds during flight. A few centuries later, the Wright brothers flew for the first time with their plane. It took a few centuries for Leonardo’s dream to come true. Today, Apollo missions are exploring space, which is changing our imagination and knowledge about the universe. Curiosity fulfills human minds more than ever before.

In 2022, Elon Musk tweeted, “a new philosophy of the future is needed. I believe it should be curiosity about the Universe – expand humanity to become a multiplanet, then interstellar, species to see what’s out there.”

I am thinking about a new philosophy for the future that will be an interdisciplinary science—an intersection of modern philosophy, economy, psychology, and linguistics. In a strict sense, this science should prepare the world we know for a new economic and cognitive reality in which people living on Earth will be able to conduct research on the Moon, for example. Humans should be able to learn and understand “foreign language” quickly. In a larger sense, a science allowing people to manifest their experience into accessible science. If there will be interaction between science and our insights, what it would look like? Maybe authors of science fiction books know how to answer that question? Science fiction writers show us the fantasy and imagination of different worlds and how they perceive the future.

Curiosity lends itself to question whether we are ready to settle other planets. One factor necessary for success is being able to cooperate with people here on Earth. Scientists and astronauts will probably soon create a permanent base on the Moon, which will likely be a first step toward landing people on Mars. When might it happen? I don’t know; however, in dreaming like da Vinci, maybe one day your dreams will come true.

My curiosity led me to a new journey, and I joined an MBA program in the field of entrepreneurship for those interested in startup development. Is it an easy path? I don’t think so. It requires skills to think outside the box. I must read challenging books, analyze information, and monitor market trends, but I love it. Lecturers, too, give me food for thought. Being open-minded helps. In addition, I think that if you don’t know where to start, a business degree is a good option. There are, of course, founders without business education, but studying in a business school can help a future entrepreneur to avoid common pitfalls made among startup teams. Most startups never obtain unicorn status because everything has cause and effect; there are actions and results. I never thought that I would be interested in business because I have a strong motivation to be a researcher and an academic teacher.

What is challenging me now? The idea of developing a product or service, providing a valuable commodity that people enjoy using. Creating something that does not yet exist and with the potential to dominate a market and compete with innovative business models. Looking at startups’ histories, we notice that creating requires time. The process—from ideation to execution—can take years. It can be a long, uncertain venture. But I am ready.

Can entrepreneurship be learned by everyone? Yes, and everything depends on you—just awaken the giant within. I am at the beginning of the path which I undertook a few months ago. I have a plan with a list of books to read and reflect on. Now, it is time to execute my plan.

You likely achieve a lot in your field, moving quickly up the career ladder—but after working in perhaps a toxic environment, you suffer from burnout. It is a negative situation but a realistic scenario. Believe me, though: it is not hopeless. A few months ago, I started looking for new knowledge, skills, and expertise. Imagine you’re standing at a crossroads, and there is a choice of which path to take. Asking questions is my method to achieve milestones. I invite you to go on a journey with me through several questions.

“I would rather have questions that can't be answered than answers that can't be questioned.” ― Richard Feynman

If I were to write my own biography, it would be about, among other things, asking questions that lead us to better solutions. After having worked many years as a software engineer specializing in back-end development with the Ruby on Rails framework and developing other people’s startups, I feel that I must change something in my professional life.

Am I doing what I want with my life?

Life is like a business, and you need a plan with a strategy. “Strategy” is knowledge of an entire situation that helps you make the best decisions going forward. The purpose of my plan—my strategy—was to start living authentically; it is also worth knowing where you want to be two and five years from now, for example.

Am I really living the way I want to live? Am I living my values?

What does it mean to live an authentic life? It is about living according to values. A good start might be the Personal Values Card Sort prepared by W.R. Miller, J. C’de Baca, D.B. Matthews, and P.L. Wilbourne, which allows you to find core values for yourself. Why is this important? Because these values form principles—a kind of morality—and wisdom to determine a mission in life. I have started defining my principles for life, which takes the form of quick sentences, or aphorisms, to influence my life.

What has changed at work? In life?

I felt that I was stuck in place. I had stopped thinking about my goals, dreams, and ambitions. I’d forgotten about dreaming, which had in the past persuaded me to take the next steps. Some people dream about owning a new car or home, taking holidays in exotic places, changing the world for the better, achieving world peace, or simply living a peaceful life. What was my dream?

Well, in dreaming, I discovered my life plan. I knew that I didn’t want a “peaceful” life because I tend to think better under stress—working under pressure is good for my performance. However, stress with proper time for rest allows me to grow. I have started planning some days off, city breaks, longer holidays—without them, I am on a straight path to burnout.

How am I feeling? And am I having fun?

It is crucial to build emotional resistance, especially because working under pressure requires a special toolkit. I realized that mindfulness with breathing techniques allows me to be here and now, decreasing the feeling of being overwhelmed. My favorite activities are sports such as cycling and running; I would like to learn swimming.  Maybe one day I will participate in Ironman? I am still having fun with web development because I have found new meaning in familiar territory. I jumped into the JavaScript community, and I have progressed in web development with tools and frameworks such as React, Express, and Node with TypeScript flavors. Maybe my side project will change into a new venture?

Have my dreams changed? Do I still believe in my vision of my future?

I dream big, and I’d like to start a small company soon. My vision of my future has changed a little over the last few years. When I was 19 years old, I wanted to be a philosopher—I believe that there is a chance to change the world toward peace through educating people. I consider education as a tool that can transform the world. Therefore, my professional activities relate to education and software engineering in a wide sense: I am working on a project to make the Internet a safer place to be.

Going forward

I realized that it is good to have a roadmap with a detailed plan of where I want to be in a few years. It is worth knowing that questions allow us to get back on right path—especially because sometimes we can get lost. Building emotional resistance and forming new habits is difficult but crucial for peak performance. Also helpful is engaging in sports to decrease mental tension quickly.