🇧🇬 Nikola Veselinov

Most science-fair projects build something: a filter, a robot, an app. Nikola Veselinov's project built nothing you can touch. The seventeen-year-old from Sofia, Bulgaria, arrived at the 2026 Regeneron International Science and Engineering Fair with a proof — a new theorem about when equations cannot be solved — and left Phoenix with the $75,000 Regeneron Young Scientist Award, one of the three biggest prizes at the largest pre-college science competition on earth.

The problem he attacked is among the oldest in mathematics. For centuries, mathematicians have asked which equations can be solved 'in elementary functions' — using the familiar toolkit of arithmetic, roots, exponentials, logarithms and trigonometry. Some equations of the form f(x) = a always yield; a stubborn few provably cannot. What was missing was a unified account of why.

Veselinov analyzed those isolated cases of unsolvability and found their common thread. Combining ideas from topology, symmetry and Galois theory — the branch of algebra born when the French teenager Évariste Galois described why fifth-degree equations resist general solution — he described the precise conditions under which f(x) = a cannot be solved with basic functions.

A new theorem, judged correct by professional mathematicians, is the rarest currency a young researcher can present. ISEF's Mathematics category is where the world's most abstract teenagers meet, and Veselinov won it outright — the category prize, sponsored by the Akamai Foundation, on top of his Young Scientist Award.

The scale of the competition frames the achievement. ISEF 2026 gathered more than 1,700 finalists from 64 countries, regions and territories, competing for over $7 million in awards. Above Veselinov's prize stood only the $100,000 top award, won by Japan's Hikaru Kuribayashi; alongside him, the American chemist Lakshmi Agrawal took the other $75,000 award. The podium photograph from Phoenix — Veselinov, Kuribayashi, Agrawal — is the class picture of his scientific generation.

The judges' citation noted the theorem's reach: the equations it classifies appear in physics and in the mathematics describing how objects move through space. Pure results about solvability have a long habit of becoming practical — Galois theory itself, pure beyond imagining in 1830, now underwrites error-correcting codes and cryptography.

Veselinov's selection for the Research Science Institute — the elite summer research program hosted at MIT, which admits a sliver of applicants worldwide — followed as a kind of confirmation: he will attend as an international student selected from Bulgaria, joining the program that has incubated a disproportionate share of the world's mathematical careers.

Bulgaria's role in this story is no accident. The country runs one of the world's most respected mathematical traditions relative to its size — a legacy of the Eastern European olympiad school, with Sofia's specialized mathematics gymnasium at its core, and a national olympiad program that regularly outperforms countries thirty times larger.

The mathematics itself belongs to a specific and beautiful lineage. Galois wrote his theory as a twenty-year-old on the eve of a fatal duel; Abel proved the quintic unsolvable at twenty-two while poor and tubercular. Solvability theory is, historically, young people's mathematics — and a seventeen-year-old extending it in 2026 is writing another line in that particular family register.

What distinguishes Veselinov's result from typical elite student work is its shape: not the application of known tools to a new dataset, but a synthesis across three fields — topology, symmetry, algebra — aimed at a structural question. That instinct for synthesis, more than computational firepower, is what research mathematics selects for, and what the judges in Phoenix paid $75,000 to encourage.

The trajectory from here is well-marked and demanding: RSI, then the world's mathematics departments, where prize-winning teenagers are converted — sometimes — into theorem-proving adults. The attrition is real; so is the pipeline's record. ISEF's alumni rolls carry Nobel laureates and Fields-adjacent names in numbers no other youth competition matches.

The prize money attached to his theorem — $75,000, on top of the category award — is designed to do one specific thing: keep a mathematical talent in mathematics. The field's brightest teenagers are relentlessly recruited by finance and technology; ISEF's largest awards function as counter-offers on behalf of pure research, and the judges spent theirs on Veselinov deliberately.

Bulgaria's press treated the Phoenix result as a national event, and the framing was apt. For a country whose greatest exports include mathematicians and chess players, a Sofia teenager standing on the world's biggest young-science podium — for algebra, of all things — was confirmation of a national tradition still producing at the highest level.

For now, the fact stands on its own, and it is worth stating plainly: a seventeen-year-old looked at a question mathematicians have circled since the age of Galois, saw a pattern the literature had not articulated, and proved it. The equations he classified will stay unsolvable forever — but because of a Bulgarian teenager, it is finally clear why.