MediMath Science

I have watched a few recent UFC fights, and the bout between Ilia Topuria and Justin Gaethje in mid-June 2026 was particularly memorable. Most people predicted a victory for Ilia, but the outcome was different from expectations. Both fighters displayed exceptional stamina and endurance, suggesting that they had invested a tremendous amount of time in training. However, some analysts believe that although Ilia preferred high-intensity training camps, he may have absorbed fewer realistic punches in sparring because his training partners were reluctant to engage him at full intensity due to the risk of being knocked out by his formidable punching power. Many critics dismiss mixed martial arts as little more than a modern version of Roman gladiatorial combat.  (The comparison, however, is imperfect. Gladiators were often forced into combat, whereas UFC fighters voluntarily dedicate years of their lives to earning a place among the sport's elite. Countless athletes train relentlessly fo...

This blog discusses the AI-related stock market, which has delivered remarkable performance over the past several years and whose long-term outlook still appears favorable. Recent volatility in AI-related stocks is driven by extremely high market expectations colliding with uncertainty over the profitability of AI, while high valuations, interest-rate sensitivity, geopolitical risks, and export controls further amplify short-term price swings. The purpose of this blog is to better understand the outlook of the AI-related stock market.  Before beginning, I would like to clarify that I am not a financial expert and have only been actively trading stocks for about one year. However, I do have expertise in mathematics, AI, engineering, medical imaging, and related fields. This background, combined with feedback from many friends and the assistance of ChatGPT, has helped me organize and articulate my thoughts more clearly. The AI market is actually a vast industrial ecosystem composed o...

Before beginning this blog, I should acknowledge that I do not have the ability to speak with complete confidence about the current confrontation between the U.S. and Iran (March 2026). Those who are not direct participants in the conflict cannot fully understand the deeper motives, internal calculations, and hidden tensions between the parties. For that reason, as an outside observer, I am not in a position to make definitive judgments, since much of the true structure of the conflict is neither visible nor easily knowable. Most media reports portray the current confrontation between the U.S. and Iran as a struggle between good and evil, or as the product of the greed of a few actors. While this framing attracts attention, it is analytically weak. Consequently, individual investors influenced by such narratives may misinterpret the prospects for war and make costly financial decisions. A recurring reality is that individual investors who simply follow sensational news headlines of...

The performance of supervised learning in digital medical imaging modalities such as ultrasound and low-dose CBCT depends critically on the availability of paired datasets. These datasets must capture variability across patients, anatomical structures, and disease presentations, while providing accurate and consistent labels aligned with the measured images. Diagnostic tasks—including segmentation and detection—are particularly dependent on such paired data, requiring reliable annotations such as lesion localization, bounding regions, and clinically meaningful diagnostic labels. Consequently, robust model training requires large-scale datasets with high-quality annotations spanning diverse patient populations. However, in real clinical settings, such high-quality paired datasets are often unavailable due to the limited representation of abnormal cases, the absence of ground truth, inter-observer variability in annotations, patient-specific image heterogeneity, and the inherent variabil...

This blog examines a recurring pattern that has persisted in mathematics since the mid-20th century. A substantial fraction of highly capable researchers devote their efforts to extending or resolving longstanding theoretical problems inherited from earlier generations. This, in itself, is not surprising—mathematics is inherently cumulative, and deep problems often require decades of sustained attention. What is striking, however, is the scale of this concentration. Today, the global population of mathematicians exceeds, by a wide margin, the total number that existed prior to the mid-20th century. At the same time, the set of mathematically grounded problems emerging from modern society—ranging from medical imaging and data-driven modeling to complex systems and engineering constraints—has expanded dramatically. Yet a significant portion of mathematical effort remains focused on classical, internally defined questions rather than on these rapidly growing external demands. At first gla...

 In recent years, many discussions of innovation policy have emphasized the need to “tolerate failure.” While I strongly agree with this principle, I worry that the slogan risks diverting attention from a more fundamental issue: the structure of research evaluation and the design of public R&D investment. Encouraging risk-taking alone does not explain why the descendants of successful entrepreneurs in countries such as Japan and Korea often become effective long-term managers and R&D investors, nor why governments that rely heavily on expert committees frequently struggle to achieve comparable innovation outcomes. The repeated call to “accept failure” can therefore oversimplify the problem. Many researchers are not avoiding risk because they fear failure. Rather, the structure of academic incentives often encourages work that is theoretically elegant and readily publishable rather than work that addresses long-term, system-oriented technological challenges. As a result, res...